Category Archives: Maths

Numerical Reasoning – from 11 plus through GCSE to careers

Numerical reasoning – what is it, what type of questions?

Working in the Maths tutoring arena, I’m hearing more about the topic of numerical reasoning and therefore so will pupils and parents. This blogpost helps you understand it and try lots of examples yourself. Numerical reasoning is more than addition, multiplication, and division. But equally it’s not about quadratic equations or calculus.

In general, its more about real-life problem-solving and in particular about interpretation of numerical charts, graphs, tables, data sets, trends and series. Leading to a conclusion often requiring choosing an answer to a multiple choice question, and the wording of the question often needs careful attention.

The specific underlying maths skills needed are quite limited in their topic-scope and are mostly KS3 level. Principally:

  • accurate, quick mental arithmetic backed up with calculator if allowed
  • BIDMAS order of operations and execution thereof
  • fractions decimals, percents including operations with percents
  • ratios
  • pie charts, bar charts, line graphs
  • two way tables of data
  • money calculations from simple pounds and pennies to basic sales units, value, costs and profit, and currency conversion
  • series, sequences and patterns
  • speed time and distance formula triangle
  • units of measure, conversions, multiples of 10

In fact, it’s the generic skill requirements which differentiate numerical reasoning questions. Interpreting data involves understanding the data, regardless of the various presentation formats, or sometimes column-headings not seen before. Then being able to manipulate the data, perhaps involving combinations of the maths techniques above, or realising a two-step process is needed to calculate missing information to finally answer the question.

Comprehension of the data, deciphering patterns, performing estimates and determining relevant information are other requirements – for instance quickly realising the question is pointing you to just one bar in a bar chart or just one row and column in a table.

Because the actual maths topics, like percentages, are fairly basic, then the surprising result is that you could find the same numerical reasoning question in almost any age-group test. In theory at least these questions should be accessible to anyone who’s been to school, not necessarily a high performing school or top maths set. So it is an “equalising” method. All you need is generic maths intuition, rather than specific difficult techniques, or so it is claimed! (I have my doubts – if you struggle with percents and ratios you will probably struggle with interpretational maths skills too).  Which leads us to the question, where could you come across these questions?

Which tests and exams feature particular types of numerical reasoning questions?

Let us start with 11-plus entrance exams.

Most selective independent or grammar schools will have some kind of Maths test as part of the admissions process. And most of these tests will contain at least a few numerical reasoning questions to back up the basic numbers-only questions.

An example would be this:

Q1. A purely numerical “fractions” question might be, what is ½ plus ¼?
(Ans. ¾ )

Q2. A version of this, shall we say on its way to numerical reasoning style, might be: if I have £10 to spend, and spend a quarter on sweets and a half on drinks, how much change do I get? (Ans. £2.50)

Selective schools typically use exam Boards such as ISEB, GL, CEM and Ukiset for admissions testing. All of these will contain numerical reasoning to a certain extent, but two stand out.

First CEM, which has a specific paper called “Numerical Reasoning”.  A typical question might be:

Rick is 1.8m tall and John is the same as Rick. Peter is taller than Rick. Carol is 57cm shorter than Peter. John is 45cm taller than Carol. What height is Peter?

Ans. Carol must be 1m 80cm less 45 cm = 1m 35 cm. So Peter must be 1m 35cm plus 57 cm = 1m 92 cm

Or a sequence question like:   

Q3. This picture represents a sequence of triangle numbers. How many blocks would be in the next pattern? Ans. 10

Second, Ukiset, the UK Independent Schools’ Entry Test, (particularly for international students) This is a test nearest to what the purists would regard as classic numerical reasoning. (Like many exam Boards, it also contains verbal and non-verbal reasoning, but we’ll not cover those here). A score is generated after the test which can be benchmarked to indicate potential.

Here are some examples of typical style of Ukiset questions

Q4. From the graph above, what is the percentage increase in Hare population between 1970 and 1980? Choose from A 10%   B 20%   C 25%   D 30%

Ans C 25%.  (10,000 – 8,000) / 8,000   x 100%

Q5. The total attendance for three South Coast football teams was 1,200,000 in 2018 and 1,000,000 in 2019. Using the Pie charts above how much greater was the attendance for Portsmouth in 2019 than 2018

Choose from A 25,000    B 50,000   C 75,000   D 100,000

Ans B 50,000
2018 = 60/360 x 1,200,000 = 1/6 x 1,200,000 = 200,000
2019 = ¼ x 1,000,000 = 250,000
Difference = 50,000

Q6a. From the table below, showing which sports 100 male and female pupils play at school. What is the ratio of male to female pupils at the school, expressed in its simplest form?
A 4:6   B 6:4   C 2:3   D 3:2

Ans. C 2:3. Male total = 40, female total = 60 so ratio = 40:60 = 2:3

Q6b. Amongst the males only, what percentage of them play soccer? 
A 25%    B 40%   C 50%   C 75%

Ans C 50%.  20/40 x 100% = 50% 


A business sells two products and the units sold in thousands are shown above by year. Some financial details for 1980 are shown below.

Profit is calculated as sales value (sales price per unit x number of units sold), less total costs.

How much more profit was made in $ in 1980 for product 1 than product 2?
A $ 20,000    B $40,000   C $60,000   D $80,000

Ans. C $60,000   

Product 1 Sales value  =  10,000 x £10 = £100,000 so profit after deducting £20,000 costs = £80,000.
Product 2 Sales value  = 1,000 x £50 = £50,000 so profit after deducting £10,000 costs = £40,000
Difference = £40,000 x 1.5 = $ 60.000

The UKMT U.K. Maths Challenge from Junior to Senior provides a good source of numerical reasoning practice. Here is an example:

Q8. To paint a room, half of a 3 litre can of paint was used for the first coat then 2/3 of the remainder was used for the 2nd coat. How much paint remained?

Ans 0.5 litre = 500 ml.  ½ of 3 = 1.5 and 2/3 of 1.5 – 1.0 so 0.5 left.

Let us move on to GCSE Maths exams.

In the O-Level years we had Pure Maths and Applied Maths, with numerical reasoning very much in the latter category. While it is clear that in recent years examiners have aspired to introduce more “real-world” and “wordy” Maths questions to GCSE 9-1 graded exams, we can be a bit nore specific and identify certain questions in the style of some of the above numerical reasoning questions. All of the below are based on actual recent questions. 

Q9. A firm has a total of 160 vehicles. They are cars and lorries.
The number of cars : the number of lorries = 3 : 7
Each car and each lorry uses electricity or diesel or petrol.
1/8 of the cars use electricity.
25% of the cars use diesel.
The rest of the cars use petrol.

How many cars use petrol? You must show all your working.

Ans 30. 160 vehicles = 10 shares so 1 share = 16
Cars = 3 x 16 = 48 so electricity = 1/8 x 48 = 6
Diesel = ¼ of 48 = 12 so petrol = 48 – 6 – 12 = 30

Q10. In Europe, Rick pays 27 euros for 18 litres of petrol. In the U.K., Malcolm pays £40 for 8 gallons of the same type of petrol.
1 euro = £0.85 and 4.5 litres = 1 gallon
Rick thinks that petrol is cheaper in Spain than in U.K. Is he correct?
You must show how you get your answer

Many ways to prove it for instance: in Europe 1.5 Euros = 1 litre =£1.275
In U.K. £5 = 1 gallon = 4.5 litres so 1 litre = £1.11 So cheaper in


Q11. Ellie makes cakes in a restaurant using potato, cheese and onion so that
weight of potato : weight of cheese : weight of onion = 9 : 2 : 1
Ellie needs to make 6000 g of cakes.
Cheese costs £2.25 for 175 g.

Work out the cost of the cheese needed to make 6000 g of cakes.

12 shares = 6000 so 1 share = 500 g so cheese = 2 x 500 = 1000g
So cheese = 1000 / 175  x 2.25 = £12.86

Q12. A sign on a motorway says the time to reach a junction 30 miles way is 26 minutes. The driver thinks they would have to drive faster than the speed limit of 70 miles per hour to do that. Are they right?

Ans. No . Speed = distance / time = 30 / (26/60) = 1800 /26 = 69.2 mph

Q13. In a survey of 10 people their fruit preferences are shown in the table below

In a second survey of more people the preferences are shown in the pie chart below. Explain how the second survey shows a lower preference for bananas.

Ans. First survey: 5/10 is a half. Second survey: yellow slice is less than 1/2


Many questions at Maths A-Level feature “real world” scenarios but do not qualify as classic numerical reasoning questions because they require high level mathematical techiques such as calculus and standard deviation, not accessible to most people. However, there is a set question each year which contains the spirit of numerical reasoning, namely the large data set.

Typically the data set and graph questions at GCSE and earlier contain rolled up summaries of accumulated data. But this annual A-Level question pre-releases a large data set of original detail in Microsoft Excel from which the student can make summaries themselves and draw conclusions. An example is shown.

Original data

Question Q14: does the data and graph prove that the amount of salt consumed reduced greatly in the period shown: Ans: not completely because “greatly” is ill- defined and purchasing does not necessarily correlate with consumption 

Numerical reasoning skills can help your career

In the new worlld of AI, programming, algorithms, information technology and even socila media, the use of Maths in general and numerical reasoning in particular is becoming a more important skill. Even the Prime Minister says so! And the use of graphs and statistics in the pandemic encourged non-mathemticians to evaluate data.

So it is not surprising that numerical reasoning is becoming part of the job application process – not just in the technical sector but also in a variety of other areas such as private companies like Amazon and many banks, consultancies and energy companies. Also the public sector such as Civil Service, Police and to focus upon one, the Military. Officer applications must undertake Aptitude tests including spatial awareness, verbal, non-verbal and numerical reasoning, for which some typical questions are shown below: 

Q15. A worker who has to work for 8 hours a day is entitled to three 20-min­ute breaks, and an hour for lunch during the working day. If they work for 5 days per week for 4 weeks, how many hours will they have actually worked?
Ans 120 hours. Working day = 8 – 1 – 1 = 6 hours x 5 x 4 = 120

Below is a table listing the percentage changes in profit from 2014 to 2016 for five different companies.

Using the above table, if company Q earned £412,500 in 2014, how much profit did they make in 2016?

Ans: £485,100    
412,500 x 1.12
= 462,000
x 1.05   = 485,100   


The table shows journeys from factory to depot and cost per hour to travel. If a driver from company R drives at 50 km/hr what is the cost?
Ans: £40     100 km at 50 km/hr = 2 hr x 20 = 40
Q16c. If a driver from company T leaves at 09.00 and arrives at 11.00 am what is their average speed in km/hr?
Ans: 60 km/hr    2 hours to drive 120 km = 60 km/hr


A service’s costs are shown in total for the hours a customer uses. How much would the customer pay for 8 hours?

Ans: £24 . Double £12 : or £12 = 4 hours so £3 = 1 hour so 8 hours = 8 x 3 = £24


In fact the customer uses 2 hour of the service. The bus stop to the service is exactly at their home but on reaching the terminus a half hour walk is needed to the service and then half hour back to the terminus. Using the timetables, what is the latest bus the customer can catch from home to be sure of getting home after the service for 3.45 pm?

Ans: 10 am bus . This would reach terminus at 11 am, arrive at service at 11.30, take 2 hour service to 1.30 pm, walk back to Terminus by 2pm, catch 2.30 pm bus back and arrive at home at 3.30 pm. This is 15 minutes in hand but later bus would be 45 minutes late. The 9am bus would be unnecessarily early.

Edexcel’s Pearson is in the Job applicant arena too.

Pupils will be familiar with the Pearson Edexcel GCSE papers. Well, Pearson have a job applicant’s test too called NDIT (numerical data intepretation test). They say that “NDIT measures candidate ability to manipulate and interpret numerical information from dashboards and reports. These skills are rated as “important” for nearly 300 jobs ranging from sales managers to executives”. 

The questions could range from the simple ones like this:
Q18. What number must replace N to make this correct?

+ N

A5 B6 C8 D9

Ans D9. There is an element of reasoning in this because if the question is algebraic then the answer might be N = 11 since 8 times N would be 88. However, that’s not an available answer so it must be a simple sum of
79 + 9 = 88 so N = 9.

And then typically business oriented questions like this:

Q19. A consultancy’s operating costs to turnover ratio is 3:20 each year. If the company’s turnover is £213,250 in Year 1, £268,460 in Year 2, and £328,915 in Year 3 what are the total operating costs for the three-year period?

Ans: £121,594  

There are many different Job Application reasoning tests. Another is “EPSO” for e.g. EU applicants and a typical question is this:

Q20 .In 2012, Belgium represented 2,5% of the total EU output value of the agricultural industry. In 2013, the total EU output value is expected to grow by 15%. Given France is expected to increase its total share by 5 percentage points, what is France’s expected output value in 2013?

Ans 117,300

Belgium is 2.5% so 2012 total EU is 40 x 8500 = 340.000
France share = 85,000/340,000 = 25% in 2012 so 30% in 2013

2013 total = 340,000 x 1.15 = 391,000
So France = 0.3 x 391,000 = 117,300

And finally, GMAT the Graduate Management Admission Test

Although the test contains many conventional numerical reasoning tests it does assume quite an advanced maths knowledge such as Surds. And some follow a very specific style as follows:

Question 21: Does 2x + 8 = 12?

Then comes the standard format:

You are given two statements:

In this case the statements are::

  1. 2x + 10 = 14
  2. 3x + 8 = 14

Then choose one answer from:  

  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  4. EACH statement ALONE is sufficient.
  5. Statements (1) and (2) TOGETHER are NOT sufficient.

The answer is option 4 since in both cases x = 2, which fits the original.


Here is some advice – my top ten tips – for approaching Numerical Reasoning tests in general: first before the Test:

  • Know which test you are taking. This sounds obvious but this can be vital in identifying the style and typical format of the questions. Then you can hopefully find some free practice pehaps on the internet, or at worst invest a small amount of money in a license, or a book, or a little tutoring.
  • Practice the key topic areas outlined at the beginning such as BIDMAS and ratios – not just within your specific test but in general e.g. from past GCSE papers. Of all the techniques, probably percentage is the most important to be tight on,  including for instance “10% of…” , or a “5% increase…”
  • Practice both mental arithmetic and calculator skills – assume you can use a calculator but if, as is likely the case you are told not to, then there are certain key operations to perfect which might be quicker in your head anyway, such as “1/2 of…” or “180 degrees of a pie chart circle….” or “50 % of…”.
  • Practice working at speed as this can be a key differentiator
  • Whether out and about or listening the news or reading newspapers, whenver a graph or data table appears then you or your children should take the opportunity to understand it

    Then during the test:
  • Understand the question but do not over complicate or be intimidated: for instance if a column heading in a data table contains a term you are unfamilar with – let us say job title “actuary” – then don’t worry simply use the number beneath it. Look out for key words or phrases like “more than” or “cumulative” or “value”
  • When looking at graphs ensure you look at the units of measure carefully on the axes such as “thousands of units”
  • In tables of data identify the correct row and column or intersection depending on the question. Note also that in some cases some data may be irrelevant. Hence a quick look at the question before you look at the table or graph may be useful.
  • In multiple choice questions it is sometimes possible to eliminate obviously wrong answers. Sometimes a quick estimate will point to perhaps only two possible answers.  
  • Work at a good pace and remember that a blank answer scores zero. Don’t get stuck on one question to the detriment of others.

And in conclusion

Numerical reasoning tests are a great leveller. In principle anyone from 9 (admitedly pretty good at maths) to 90 could take a test and get a similar score. Indeed, the same numerical reasoning question could appear in an 11 plus exam as a job application aptitude test.

The large majority of maths techniques needed to suceed are not of the “quadratic equation” type, rather the “basics” type.  
But you do need to be very comfortable with the basics, that is a prerequisite; however, that in itself is not enough because higher order skills are needed such as understanding the question, processing and analysing the data, determing your approach – and all very quickly.

The rise of such tests is welcome in terms of the numerical skills needeed for the future of work, – see the Barclays Life Skills video – not just in technical roles but in for example sports,  managerial and military, and (it would be nice!) among local and national politicians too.

In terms of inclusion of numerical reasoning questions beginning to appear in for example GCSE exams, this is good, but it would be naïve to believe pupils are desperate for real world, wordy, problems – most simply want the most straight forward in line with their standard revision. So examiners, be kind!


First a link to a quiz made myself

Links to free tests: most of these links take you directly to free sample numerical tests, or just need you to register. They may suggest furhter acess for more questions needs a payment – if so don’t pay if you don’t want to.

Assessment days test 1

Assessment day test 2

Practice Aptitude tests

Barclays Life Skills   

Test partnership

Ukiset Easy-Quizz

Business or Economics – which qualification?

The study of Business and Economics qualifications at school is growing – for instance both Economics and Business uptake at A-Level grew about 10% in a year from 2021-2022 and Business has grown 25% in four years.  Many parents and pupils ponder whether to enroll in these relatively unfamiliar topics and if they do confirm, then the decision is which to take – generally its difficult to take both, because of availability or time constraints.

I tutor both of these topics academically and have a strong background in industry so perhaps I can help.

How popular?

First, what’s available and what’s the uptake.

For GCSE Economics, of the two major Boards, AQA offer Economics but Pearson Edexcel don’t, unless you can do International GCSE. Other Boards like OCR and CIE also offer GCSE Economics.

For GCSE Business (used to be called Business Studies) both AQA and Pearson Edexcel offer Business as well as other Boards.

For A Level, both Edexcel and AQA offer both Economics and Business, as do other Boards.

So essentially both topics are available at both GCSE and A-Level – if, and it’s a big if – the school has teaching capability. With fairly small cohorts of pupils, some schools may opt not to teach it.

For GCSE, around 12% of all pupils took Business, and around 2% took Economics.

This large difference is not shown at A-Level, where about 12% of all pupils took Business, and about 11% took Economics.

How does that compare to other subjects? You may be surprised to learn that this puts Business or Economics at about the same level as Physics and above Geography for A Level.  

So in summary, both Business and Economics are growing in popularity; Business is taken by a reasonable proportion of the cohort at GCSE level, while at A-Level both are.

What do they cover?

First Business

Obviously A-Level is more developed than GCSE but both Business qualifications cover broadly the same themes and topics such as:

  • Understanding what a business is and how it operates, is organised  and meets customer needs, and what characteristics its start-up entrepreneurs and leaders display, such as attitude to risk.  
  • Both generic business aspects and also many individual businesses; for instance portfolio analysis of multinationals like Apple or Nissan, or strengths and weaknesses of smaller business.
  • Marketing definition, research, segmentation, planning, positioning, and strategies in a U.K, in a U.K. and global context for both niche and mainstream businesses.
  • Marketing mix across Product Price Place and Promotion
  • Sales concepts such as price elasticity of demand and sales forecasting and methods
  • Financial sources and planning ,managing finance, the financial ratios associated with the three key reports namely profit and loss, balance sheet and cashflow; project appraisal methods such as payback time; and external influences such as interest rate, Inflation and exchange rate.
  • Operational aspects such as factors and type of production, economies of scale, quality, and measures such as productivity and capacity utilisation
  • Business objectives and strategy – such as focus on cost or differentiation; business growth, and decision-making techniques; competitive advantage and overcoming barriers to entry
  • Human resources aspects such as organisation design, legal aspects and employee motivation

    Then  Economics, again for GCSE and A-Level
  • Nature of economics – the fundamental economic problem of allocating scarce resources to meet unlimited demand
  • Economics as a social science including both behavioural economics and balancing economic policy with moral and political concerns such as poverty and inequality
  • Markets – how markets are structured and governments work, why they can fail economically and what interventions can be made
  • The UK economy – its performance and macroeconomic aspects
  • Measures of economic performance like G.D.P. and economic objectives like 2% inflation
  • Definitions and calculations of aggregate supply and demand, and key diagrams like supply-demand graphs of price against output, and shifts,  and production frontiers.
  • Supply-demand case studies such as for Oil, Housing and Transport
  • Economic philosophies such as Keynesian, Classical and Laissez-Faire free market
  • Mixed economy concept such as private and public sector, public and private goods, merit and de-merit goods
  • Macroeconomic policies such as fiscal (taxation and Government spending); and monetary policies such as interest rate
  • Role of bank of England, Banks and financial markets
  • Supply-side and demand-side initiatives such as productivity and tax-cuts.
  • Microeconomic aspects such as business behaviour and the labour market; business growth, objectives and revenues, costs and profits
  • Price, Income and cross elasticity of demand and supply
  • Competitive aspects such as, perfect competition,  oligopolies and monopolies
  • Time based considerations such as short and long-run; and scale-based such as marginal versus average cost
  • Trade on a UK and International basis; trade bodies like E.U. and W.T.O; globalisation

What are the crossovers/similariries and what are the differences?

There are many cross-overs in topics, ranging from factors of production, employment legislation, through effect of interest rates, to membership of international trade bodies. Three of the main differences are:

– the level of detail in which a topic is approached: for instance the supply-demand equilibrium diagram is only a small part of the Business syllabus but forms a major element of Economics.

– the micro or macro perspective: the Business syllabus is much more focused upon individual company case-studies, ranging from household names down to the smallest start-up; whereas Economics is much more tuned to the aggregate of the whole economy (in our case U.K.) Another example would be the approach to a current hot-topic, electric vehicles: Economics might look at the benefits of Government subsidies to the whole industry, and whether consumers or companies as a whole would take the major share of the subsidy benefit; whereas Business would look at individual car companies like Ford or Nissan. and how EV’s fit in with their specific objectives and strategies, for instance of growth and diversification, and the implications for a new type of manufacturing.

– The type of calculation : Business requires students to perform a host of calculations for individual businesses such as profitability and liquidity ratios, project appraisals, break-even, gearing, capacity utilisation, critical path analyses, moving average sales forecast, and decision trees. Whereas with Economics, there are some calculations to do, but much more at the whole-country economy level such as the formulae for components of Aggregate Demand (the total U.K spending on goods and services); marginal propensities to consume or save; the multiplier effect; the GINI coefficient for inequality.   

The Maths skills are easier than you think.

You can see above that many calculations are required. Of course you need to know and understand the formulae – they will be taught. But the actual Maths techniques are often not much more than BIDMAS and % calculations of % change and % of one quantity to another. Calculators are always allowed. There would never be a quadratic equation, or geometric proof, for instance. At A-Level you would cover standard deviation in Maths, but not in Economics, where you would think it might fit, or Business.

You do need to understand graphs, typically bar charts or line charts. The two approaches for Business and Economics are fundamentally different through. In Business, a graph will usually have a numerical scale from which a specific number can be gleaned. Whereas in Economics the graphs and diagrams are generally without a scale, since you just need to explain the overall shape or trend or shift.  

How do the examiners mark exams?

There is a lot of similarity in the approaches for instance both have four “Assessment Objectives” : AO1, for Knowledge, AO2 for Application, AO3 for Analysis and AO4 for Evaluation. Both have short-sharp questions, and also longer essay questions where reasoned logic and justified conclusions are important. A slight difference is that Economics is more likely to have some multiple choice questions.

What are the alternatives and natural A-Level partners?

The beauty of both these topics is that being essentially social sciences, they could fit with Arts topics like languages; mid spectrum topics like Geography or Politics, Religious Studies or Sociology; or STEM topics like Maths or Physics. An alternative incidentally is the very new T-Level range of technical qualifications which includes Management and Administration, which is a single topic equivalent to three A-Levels as it involves a practical placement and workplace project as well as theory.  

Further Education and Career prospects

Both topics have very firm University and career paths, albeit slightly different. A Business degree could lead to a Masters qualification in the famous MBA (Master of Business Administration) and a career to a senior position within a Business or starting up your own. A typical Economics Degree is with Politics and Philosophy; a career might ensue in Government, in Accountancy (with an extra qualification) or in banking or the finance or planning department of a company..  


Both Business and Economics are growing in popularity. While not quite mainstream they are moving above niche, especially at A-Level. There are many cross-over similarities; the main differences are the types of calculations and approach to graphs, and that Economics tends towards the Macro aggregate of a country whereas Business is more Micro at the individual company level.

The topics may be the first time a student has come across them. It will help if they have a particular prior interest or future related goal but not essential. A student needs to be reasonable at both Maths and Essay writing, but not exceptional at either.

There is a very clear path to University degree choice and often rewarding career path beyond.  

International Baccalaureate – growing out of the shadows

What is the IB Diploma Programme?

The International Baccalaureate (IB as it is known) is emerging from the niche into the mainstream in the U.K. It is no longer education’s “best kept secret”.

I tutor IB Maths and so I have accumulated some research into this growing option.

The IBDP (Diploma Programme) is studied by the same age group as the A-Level cohort and is taken instead of (not as well as) UK A-Levels. Although still a minority option it is a growing choice. IBDP is over 50 years-old and by 2022 UK take-up had increased to over 5,000 students (from the 170,000 worldwide). This compared to 800,000 A-Level students – so clearly A-Level is and will remain the most popular and safest choice for post GCSE study – so what attracts parents and pupils to IB? Let’s try and find out why, by describing it.

The IBDP students take a module from within each of six compulsory subject groups, namely: studies in language and literature; language acquisition; individuals and societies; sciences; mathematics; and the arts. They choose three Higher Level (HL) and three Standard Level subjects. For Maths, for example, a student chooses Analysis and Approaches (AA), or Applications and Interpretations (AI) at the HL or SL levels. At Science IB subject group. the individual subjects are biology, computer science, chemistry, design technology, physics, and sports and health (the student can choose two).

Students also study three additional topics, to encourage a more “rounded”, socially responsible approach; namely theory of knowledge; creativity, action, service; and an extended essay.

For Maths, the IB topic list and techniques for answering questions are around 95% similar to A-Level, and there are equally rigorous end-of-course exams. What’s a little different is their frequent “Investigations”, “International mindedness”, “Developing inquiry skills”, and “TOK” (Theory of Knowledge) sections, all encouraging students to creatively “look beyond” the curriculum. For instance:

Investigations; for a Pool Party Invitation, as part of Permutations and Combinations: how many different ways could three images be arranged for the invitation card? (Answer: 3! = 6)

International Mindedness: Where did Numbers come from? (Answer: many answers such as India and Sumeria and Egypt). And where does the Word Asymptote come from? Answer: the Greek word “Asymptotos” meaning “not falling together”. (Note: your author, long before being aware of IB, was including similar etymological references in my Maths tuition materials such as “al-jabr,” meaning “restoration of broken parts” the Arabic origin of algebra).

Developing Inquiry Skills. With pieces of spaghetti, construct a circle with radius one spaghetti length. What is the circumference of your circle in spaghetti units?

Theory of Knowledge TOK): Is Mathematics a Language? Why do we call Pascal’s triangle Pascal’s triangle if it was in use before he was born? Is it possible to know things about infinity, of which we have no experience? (Author’s note: this TOK is not one half of TikTok)

A good example of how IB maths is, let’s say, more intellectual, even ethereal, than A-Level Maths is that in the middle of some fairly standard A-Level fare on quadratic equations’ discriminants, there is suddenly a section on “the fundamental theory of algebra” referring to “the existence of complex zeros of a polynomial” (no me neither, at first!)

How is IB viewed at university?

Because UK Universities increasingly attract international students, they usually include IB required grades in their offers. For instance, an IB HL grade 7 is equivalent to A* in A-Level. A typical Oxbridge offer would be A*A*A or IB 42 points with grades 7,7,6 in the Higher Level choices.

Where can I study IB in the U.K.?

There are over 5000 “IB world” schools internationally, and around 100 schools in the UK offer the IB. Most but by no means all are in the UK Independent sector. They range from those offering the complete IB programme, including Year12-13 IBDP, as above, and also Primary and Middle Year IB; through to schools offering mainly A-Level but IBDP as an alternative.

There is more information in this article, in which the featured IB school is the new Fulham School, which your author was intrigued to find has opened up in the same road which our family used to live in, before moving to Twickenham. Who’d have thought!

How does Tutoring fit in?

Zoom or MIcrosoft Teams mean that tutoring doesn’t have to be local, or even national, especially since the “on-line” course text-book material is so technically advanced. Using this, I do international IB tutoring, and my approach is to pick out a few of their sample exam questions for each sub-topic which the student is currently doing – such as Binomial Expansion – and ask the student to try on their own. I then let them access official model answers, which I also supplement and add value to with my own additional workings, comments, and if necessary alternative methods and good ways of explaining.

Although my approach is fundamentally to “teach to the test”, to help the student get through their end-of-topic tests, mocks and major IB exams, I might also throw in a few challenging questions on the same topic from other advanced Entrance Boards like Cambridge TMUA or Oxford MAT; or Maths Challenges with a similar focus on “out-of-the-box” problem solving like the UKMT Senior Maths Challenge.

In summary

Although IBDP in general offers more breadth than A-Level (six subjects instead of three), it actually offers less breadth when you look at individual subjects. For instance, the IBDP in Maths has no mechanics, and less statistics; but arguably it has more depth in the subjects it does cover, and the exam questions may be fractionally harder.

Like the new technical T-levels (more on that in a future blog), the IBDP in general offers a minority but viable alternative for those who want something different out of their Sixth Form Years; namely more focus on soft skills, less specialism since both Arts and STEM subjects are compulsory, and most important I believe, it is a universally recognised qualification and comparable across multinational countries. It is suitable for those candidates who are comfortable with continuous assessment tasks, are aiming high academically across a variety of subjects, are intrigued by the philosophy as well as content of their subject and anticipate an international University placement or future career abroad.

Update after initial posting: the Economist magazine, no less, has run an article on the IB, emphasising its’ role in encouraging community service projects and keeping a spectrum of arts and STEM/sciences going through a Sixth Former’s years. It also speculates on an English Baccalaureate (but would we spoil it?!)

2022 GCSE results – a national and personal tutoring perspective

The 2022 GCSE are now out so what’s my take from a personal tutorial point of view, and a national perspective.

My pupils

Well first of all, let’s be relived the exams happened at all. Think back a year and some were questioning the very continuation of these qualifications.

From a personal perspective I’m very happy with the GCSE results my pupils managed. All had school interruptions during the two year programme but pulled it together for the exams. For the one who needed a top grade 9 for his new school sixth form entry – yes, he got it. For those who simply wanted high grades , several got 7’s and 8’s, one got 6’s.  And for those who simply wanted a pass, and took Foundation, they got the maximum possible 5. 

The exams were unusual this year – not just because they were the first to be actually sat since 2019.  The syllabus was narrowed down so that pupils were given advance warning of what would and would not be in the exams. Typically about 10-15% of topics were removed. My strategy was to examine these lists in great detail and make sure that pupils revised what they needed to, and eliminated what they didn’t. And it was possible to even narrow down accurate predictions from Papers 1 to 2 for Science, and 1,2 and 3 for Maths. I issued Mocks with several typical questions per included topic and several pupils said they did indeed crop up.  

I think this approach especially helped some pupils with whom I only had a few lessons from Easter onwards. If my time with a Pupil is limited, and indeed all pupils’ own time is spread amongst other topics, then focus on what’s important is crucial.   

However, if we assume this advance warning is not carried through to next year, will this “focused topic” approach still be appropriate? Well, aspects of it, yes. For instance I examined past papers in detail  and it was obvious that the Core Practicals formed the basis, every year, of detailed exam questions. So I found a series of excellent short videos on each, issued links, advised pupils to re-read their lab experiment books, and told them precisely what examiners wanted with the 6-mark “how would you design an experiment to…”   questions. This advice will always be relevant in science. And across all my subjects – Science, Maths, Business  – the fine details and nuances of what’s in Foundation, Higher, Combined, Triple, Paper 1 paper 2 , Long question etc can be so important to emphasise with pupils.      

 The national picture

A lot of focus is on lockdown induced grade inflation, from pre-Pandemic levels. So let us start there. For A level, the grade inflation between 2019 and 2021, coinciding mainly with teacher assessment, was around 20%. The grade A or higher numbers of entrants jumped from 26% to 45%. By 2022 this % had dropped, as expected, and by an amount that was anticipated by examiners. The A-Level inflation reduced by around half, so that the 36% for 2022 brought us almost exactly half way back to the pre-Covid levels.

For GCSE the grade inflation also fell, but in a different way. First, the inflation from 2019 to 2021 was not as high as A Level ; for instance the % of pupils getting grade 4 or above in GCSE inflated by around 10% from 67% to 77% ; in 2022 this figure was 73% , a drop of 4%,  so just less than half the 10% grade inflation has been eliminated.   Similarly, for the percent getting grade 7 or above, the figure jumped from 20% to 28% and back this year to 25%.

In theory, by 2023, grade boundaries and these percentages should return to pre-Pandemic i.e. 2019 levels – but who knows! First, will more unusual events happen, and second will the examiners give more time for settling down?

Other ways of looking at the results include:

  • the attainment gap between boys and girls continued, with girls being about 7% higher, though the gap has narrowed fractionally.       
  • Independent and especially state selective schools as expected got the highest percentage results, though it should be noted that independents showed the highest drop of all ownership categories 2021-2022 i.e. are eliminating grade inflation fastest.
  • London schools continue to outperform the rest of the U.K. For instance around 32% of London pupils scored 7 or higher grade, compared to 22% in the North East.   
  • For Maths, and Combined Science and Business, the distributions of grades was a typical normal distribution with the most common being 4 and 5, with tail-offs above and below those. But for the individual Triple sciences, all three had heavily skewed distributions towards the higher grades – almost all grades in Triple Biology, Chemistry or Physics were grade 5 and above, with very few below grade 5. So if a teacher thinks you are good enough to do Triple versus Combined, its probably the right decision
  • What I cant find out, and would be fascinating, is this : for those who took Foundation exam in Maths , the maximum grade is 5, a reasonable pass is 4, and below that means a re-sit; so what proportions of pupils in the end passed, or had to re-sit, and how does the re-sit figure compare to those who took Higher? This might shed light on the conundrum of which exam a pupil who is on the cusp of Higher or Foundation should take. From my own limited sample, those who opted for Foundation did indeed get grade 5.

    Below are a series of graphics and infographics illustrating for GCSE the above points. Note that one good thing to emerge from the Pandemic was the use of highly visual means of displaying dull or complex statistics, particularly trend graphs. Though I say it myself, I helped start off this approach with award winning publications and software applications almost 20 years ago!

2022 GCSE exam content changes : from the modest to the severe


As anticipated the exam Boards such as Edexcel and AQA have published their “advance information” changes to assessment content for the 2022 exams including GCSE. If you recall, the purpose is to offset the difficulties pupils have endured due to the Covid disruptions. The indication is this is just for 2022.

I myself would have kept the content pretty much the same but made the questions easier by making them more on-syllabus, and less obtuse and wordy; but anyway we now have the Boards’ pretty specific topic list of what will or won’t be assessed, and I have taken a quick look at my specialities for Edexcel Maths and AQA Triple and Combined Science (see also web links at the end of the article which cover all subjects). I am sure teachers will be explaining these to pupils and parents alike, but here is my immediate take, initially on Higher.

Towards the end of this document, I also include a little on grade boundaries, formulae sheets and Mock exams and finish with some overall conclusions and take-aways. Also I have included an update on topic-targeted mocks I’ve created.

But let’s start with what is in (the “main focus areas”) and what is out.

Maths Edexcel

For Higher Pearson Edexcel Maths, the amount of content reduction is very low, so most topics are still in there – about 90 topics are listed as “main focus areas” i.e. are “in”. It looks like a few difficult ones like Quadratic Sequence, Completing the Square, Congruence, Volume of cone and sphere, Proofs, and Iteration are excluded from assessment now.

Sometimes there is some ambiguity: compound interest is mentioned in the formula sheet but not in the list of included assessed topics so perhaps will be needed for growth, decay, depreciation; while for Angles the easier parallel line topic seems excluded while the more difficult polygon and circle theorem topics are included.  

Mostly the topic list is precise enough to revise from but not so specific so as to tell you the question – this is as it should be.  But sometimes the description is so specific that you can almost anticipate the question – such as capture recapture, and equation of a tangent to a circle.  

Overall the Maths changes are fair. About 90% of topics remain included. Any exclusions are spread fairly evenly across the main headings of Algebra, Geometry etc.

Ideally (like science below) a list of exclusions (as well as inclusions) would have been stated by Pearson, but hopefully my pointers above will help and no doubt teachers will firm up on these in due course. The implied exclusions will reduce revision time slightly, but note the preamble does ask teachers to teach the full content anyway.  

Science AQA

For AQA science the picture is different from Edexcel Maths; from modest exclusions for Chemistry to almost the opposite for Biology i.e. very few Biology inclusions (Bizarre, I know!). Let me explain.

First Triple. For Chemistry the content at first sight seems to remain largely untouched. There are only two minor “not to be assessed” exclusions listed – nanoparticles and (strangely considering their importance) greenhouse gases.

There are a large number of topic headings listed as “main focus areas of assessment” such as Periodic Table (section 4.1.2). So far so good.

But then you think, what about 4.1.1?   This is the all-important atomic and electronic structure section – which helps you understand 4.1.2 Periodic table – yet is not listed in the inclusions. Similarly, section 4.8 is not mentioned at all – Chemical analyses such as Chromatography and Flame tests – and yet the core Practical involving Flame tests IS included.

(And although I have not looked at Foundation in detail, strangely there are MORE listed topics in Foundation than Higher; so while atomic structure is not listed in Higher, it is included in Foundation. My take on that is this: in Higher there won’t be a specific question on, for example, atomic structure; but pupils would be advised to learn it anyway because it informs so many other parts of the syllabus from Periodic table onwards. I wonder if the Examiners have thought the communication of this through! I think maybe teachers will agree with me and err on the side of caution and continue to teach fundamental topics like this anyway)

I think there is some clarification needed on what needs to be revised. In the preamble to the lists (for all Sciences) the Board indicates that topics not specifically listed as “in assessment” may still be included in “low tariff or linked questions” which confirms my view that pupils should still revise most of the syllabus to be on the safe side.  

On balance I think the list of Chemistry “in topics” does indeed help and is sometimes very specific , like section 4.10.4 (Haber process/NPK fertilisers – so there’s almost certainly a question on this- and it links to another inclusion on Reversible reactions) ; although sometimes less specific (like 4.4.3 Electrolysis). I think they are trying to pinpoint the particular questions likely to be asked.  For all the sciences the devil may be in the detail: the specific numbered subsections may sometimes give the game away.  Myself and teachers will no doubt be trying to second guess these questions!

Note that for Chemistry and all Sciences the Board emphasise that the type of question will not change and the general scientific methods including maths skills and practical experiment interpretation are still needed. The specific core practical list (a bit reduced ) is well pinpointed and I strongly recommend pupils revise the short videos available on these; high chance of specific questions on these practicals.

 For Physics the list of inclusions is narrowed down considerably to essentially Particle Model, Energy, Forces, Momentum, Pressure, Waves and Space.

And unlike Chemistry above, the list of “exclusions from assessment”  is very long and specific. So out go most of Electricity, most or all of Radioactivity and Atomic Structure, and Magnetism altogether. And yet there is some ambiguity to resolve. Section 4.2.4 energy transfer is included and this includes Power, Current and Voltage i.e. electrics; and yet the basics of that, namely amps, potential and circuits from 4.2.1 to 4.2.3 are specifically excluded.

Some of these exclusions are topics which have been a staple for pupils at school since Year 7 and before and it seems actually unfair on pupils to exclude the basics of electricity and magnetism which for some would have been easier than let’s say Space. I suppose you can’t have it both ways: since broad education is meant to be more important per se than the exams themselves, in a sense it does not matter if they are examined on a topic. On the other hand, to “waste” five years work with just a few month’s notice may annoy many pupils, who having already finished the topic by now and would be quite happy to be examined upon them.  

For Biology triple, like Physics there are considerable reductions; the inclusions are narrowed down to Cell Structure, tissues, organ systems, diseases, antibodies, nervous systems, hormones, reproduction, parts of ecosystem.

There are a long list of exclusions, for instance the whole of staples like Evolution won’t be assessed. And again there are ambiguities: nothing from the large section on Section 4 Bioenergetics is included; and yet only a small part ( Taking Exercise) is specifically excluded. Bioenergetics describes the core biology fundamentals of Photosynthesis and Respiration and pupils have learned these no doubt from year 7 and they have featured in almost every past paper. To not test pupils on this seems perverse.  But since very little has been specifically excluded from section 4, should pupils after all revise it anyway? My take is that there won’t be a specific question on section 4 Bioenergetics, but it would be prudent to still revise as it infuses the remainder of the syllabus and there may be a “linked” or low tariff” question on this core topic.

Similarly, 4.5.2 Nervous System is a main focus area, but from it 4.5.1 (structure function), 4.5.2 (brain) and 4.5.3 (eye) are excluded. This is useful as it leaves only 4.5.4 (temperature), implying a specific question. But it would be unwise to ignore the introductory 4.5.1 as it informs 4.5.4.

The list of required Biology practicals, as for other sciences, is reduced but still very specific. So the staple Quadrat and Mass of Potato chips practicals are included as ever and the fact they have survived points very clearly to a question this year (as almost every year) and their video should be watched, understood and learned.

In Combined Science (Higher) the picture is similar as for Triple;

Combined Chemistry lists several very specific inclusions, similar Included content to Triple Chemistry,  and almost zero exclusions mentioned.  

For Combined Physics a focus on Energy and particles as with Triple, but this time including Radiation and Motor Effect and EM Waves (so Combined has more extensive content than Triple!) And again ambiguity: series and parallel circuits are excluded as an assessment topic, yet the required practical on these is Included. Similarly 6.7.2 the Motor Effect – which has its roots in magnetic fields –   is included, yet 6.7.1 the basics of magnetism is excluded.

For Combined Biology, a very short specific list of inclusions and very long list of exclusions. The list of inclusions is slightly different to Triple, for instance Photosynthesis is included.

Discussion on science lists.

There is some ambiguity to be resolved, by the AQA Board or perhaps by teachers. If something is neither included in assessment, nor specifically excluded from assessment, should it still be revised, to be safe, in case “linked or low tariff” questions arise? I think in some cases a topic can be eliminated altogether, but in others it would pay to revise just in case; so some detailed analysis will be required to make that call. If the Exam Boards’ “exclusion lists” are taken too literally, some precious revision may be missed which in fact may contribute to “linked” questions.

For English, if a set book is excluded that presumably can safely be put aside. But for chemistry, if “atomic structure” is not to be assessed, then it would be a mistake to simply not revise it, because it informs so much of the surviving other topics.  

Grade Boundaries
The Boards have indicated that boundaries will be set somewhere between normal, and the last two years.

Mock exams
Many schools have already penciled in exams for after half term in late February 2022. The dilemma for teachers is, shall we complete the syllabus testing as normal to encourage a full learning experience; or shall we adjust them to exclude the “not being assessed” topics, in order to avoid wasted revision time? No doubt teachers will be crawling through the fine detail of today’s lists, just like I have done above!

Formula sheets
For Physics, as before the formulae are extensive. For Maths, intriguingly, some of the few formulae which were given last time are not this time (for spheres and cones) confirming their probable absence from assessment. While formulae like quadratic formulae and sin and cosine rule are included now, indicating their probable inclusion in assessment.

In conclusion

The Boards have rightly kept their promise to publish by February 7th

The timing of the announcement seems about right; earlier, and some topics would not have been taught at all; later and some revision time would have been wasted.

The Exam Boards in their announcements and preambles have stressed they still want as much of the content to be taught and revised as possible. But with their list of exclusions, inevitably the precious, finite teaching and revision time will not be devoted to topics on the “not to be assessed”  lists.  This is useful , as long as care is taken when dropping topics.  

Maths is relatively untouched compared to the sciences and revision should still cover around 90% of topics. The basics are all still there and the exclusions are often niche standalones.  

Chemistry has very few specific exclusions, and a broad list of main inclusions, but gaps in this list indicate some additional topics will not be assessed.

Physics and Biology have long lists of exclusions and short lists of inclusions. The topics have been considerably reduced.  In my opinion reduced too much – some fundamentals have been eliminated.    

But for the Sciences the sub-section numbers listed from the specification which do survive as “included” can often give very specific pointers to the content of the question

A key phrase in the Sciences preamble is “Topics not explicitly given in any (main focus) list may (still nevertheless) appear in low tariff questions or via ‘linked’ questions, (but) topics not assessed (at all) either directly or through ‘linked’ content have been listed as “not to be assessed”.

Hence there is some ambiguity to be resolved in Science in terms of what topics to revise – there are three categories: first, about 70% are essential to revise; and then (15%) topics not listed as key focus areas, yet are fundamentals so may crop up in linked or low tariff questions, and so should probably be revised anyway; and finally (15%) those definitely excluded from assessment – only these can be truly de-prioritised.   

The type of science question is not altered i.e. could still include unusual applications, maths calculations, and practicals: the core practicals listed are very specific and may indicate precise questions – so have high revision priority.

I think the above lists will be communicated and ambiguities resolved for pupils in the coming weeks. If any parent or pupils have questions please don’t hesitate to ask your teachers, or myself as I believe I can help.  


Pearson Edexcel web link to changes in 2022 assessment

AQA web link to changes in 2022 assessment

Update March 7th 2022

I have created Mock exams featuring two or more questions on every one of the Paper 1 , 2 and 3 Higher and Foundation maths Pearson Edexcel inclusion lists. Their specific topic list for each paper is very useful, for instance: in Higher Maths the highly niche topic of Capture Recapture appears only in paper 2 and likewise Frequency Polygon only Paper 3, and a quick refresh just before those exam dates would pay dividends.

I also created topic targeted Mocks for AQA Triple and, separately Combined science, and together with Maths these proved very useful to pupils in their actual Mocks especially as I added my own explanatory notes over and above the sometimes rather bare official mark schemes. I also managed to get some of the very latest exam Board questions in too.

I have also begun to research the 2022 topic lists for the specialist qualifications like Further Maths, iGCSE, and OCR FSMQ and also the Edexcel Sciences.

UKMT Maths Challenge – benefits for pupils and tutors

UKMT is the United Kingdom Maths Trust which on foundation in 1996 brought together a trio of similar pre-existing Maths challenges at three different age groups, the Junior, Intermediate and Senior tests. Dr. Tony Gardiner is the name most associated with driving these competitions forward and now tens of thousands of pupils a year take part in the three competitions, which cover Years 8 and below, Year 11 and below, and Year 13 and below.

The format is very similar in each – 25 questions of increasing difficulty each with 5 multiple choice answer options. Clearly the standard of questions increases through the age groups but not in the way you might think. I have studied the Intermediate and Senior papers in particular and the syllabuses do not vary greatly, rather it is largely the same topics, but with more challenging questions. You will see in the appendix my research,
that I have collated from past UKMT papers, the GCSE and A-Level individual topics that students need as a minimum to know to have a good chance of success in the UKMT competitions..

In order of most frequent first, Geometry, Number, Algebra, Trigonometry, Statistics, Probability (counting outcomes) and finally Ratio are the topics featured. You might think that calculus is included in the Senior challenge, but no, as I say, it sticks largely to GCSE topics but with more challenging questions, and set in a particular style which after a while becomes familiar. Both competitions challenge pupils in two ways especially; working at speed and doing problem solving, which is something the UKMT wishes to encourage.

The benefits to pupils are of the following kind. Most obviously, more exposure to subjects which will feature in their GCSE and A Level exams – for instance Pythagoras and Similarity feature extensively.   Second, learning to work fast in terms of reading a problem, understanding what to do and executing the solution all within a few minutes (and without a calculator, thus developing mental arithmetic skills). Third, managing an exam – how should I proceed if my answer is not listed, when guessing a wrong answer may carry penalties, and which if any questions should be missed out? Fourth, the problems help you to think in a different way about Maths, imaginatively. out of the box if you like. And lastly, especially for those who are successful, it can add to your UCAS personal statement.

Just entering shows ambition, and there are further possible rewards for high scores, such as Gold,Silver,Bronze, Kangaroo (I’ll let you research that one!), and a national olympiad. There is also a team competition, which I am pleased to say my old school Newcastle Royal Grammar School won a few years back. 

Do you have to be really good at school Maths for high scores? Well it helps of course, but the questions do encourage intuition and feeling for Maths rather than (just ) rewarding technical revision.

Shown below are some typical geometry questions, then number questions, from each of the three age group competitions, showing yes the progression and but also continuity. You will see that knowing some Maths formulae and definitions is a minimum essential – but that alone does not guarantee success, as intuition and for instance ability to quickly sketch, plan solutions, create equations or compile tables is needed too.

Typical medium difficulty UKMT Geometry questions

Typical medium difficulty UKMT Number questions

How do you enter? Well, the school usually helps with the administration. Remember the Junior, Intermediate and Senior competitions are typically in April, February and November respectively, with deadlines for entries a few weeks before each. A practice really is needed!

For tutors the benefit of helping pupils is that most tutors will have to stretch themselves to accurately and quickly answer the difficult questions; often there is more than one way to approach them and the challenge is to see the relative benefits of different methods; and learn to think in different ways about Maths problems beyond the confines of conventional exam requirements. My own approach to coaching UKMT is to start by going through topic by topic and set questions relevant to that subject from both UKMT and also GCSE past papers; and once any shortfalls are ironed out I begin to set full papers at first without time limits and finally within time constraints. Although model answers are available, they are sometimes a bit wordy, and I try to write out the solutions myself to force me to think through the problem and anticipate how a pupil may best understand an answer. I give tips on both managing the exam and also question-specific explanations and tips – for instance I point out that certain types of question such as circle/square combinations occur year after year.

In summary UKMT is a great initiative which encourages good Maths practices and techniques and I enjoy greatly helping pupils to become familiar with the challenging papers. More information is available through UKMT’s website

Appendix 1. List of Maths topics you need to know for Intermediate and Senior UKMT

Coronavirus, school and tutoring

Possible developments and updates

November 14th. It is now time to end this particular blog or else it will go on forever!. Schools did indeed return in September and in my view teachers and their representatives, and pupils and parents have all done a great job in keeping the show on the road, at the time of writing, in difficult circumstances At this stage exams in England are going ahead, delayed a little to June or July, but it seems inevitable some changes such as reduced syllabus or exam questions options will be introduced. What is clear is that one aspect of education has changed forever, namely the use of on-line technology, which surely will be a permanent part of the mix even when things return to normal.

August 17th. At this stage its is likely that schools will return in September but still not certain, with Case numbers creeping up. But the real story is A- Level results and the move to stick with Teacher grades. Comparing these to previous year actual outcomes versus predictions indicates significant grade inflation will therefore take place. The infamous algorithm actually did its’ job in bringing the broad sweep of grades back to where they should be. However: two problems. First, when applying correction factors, the algorithm produced some ridiculous individual results such as fails when no exam was taken. And second, it seemed to favour smaller class sizes, which are more common in private than state schools.

July 7th Various announcements have been made that schools will indeed go back full time in September for all Years which is good news. The emphasis will be on hygiene, from washing hands to cleaning surfaces, and minimising contact through staggered timetables, one way systems etc. Rather than a strict 2m rule throughout school, though avoiding 1m still seems required. This will be difficult, but the alternative of further virtual schooling may be worse. I think it will happen, but with nuances like cutting back on aspects of the syllabus content, shorter exams and perhaps still some virtual learning (after all, some of it has been very fruitful)

One aspect of the lockdown not much talked about is the loss for Year 11 and 13 of the “going into school to get results” day, and the leaving events like Proms, and so many end-of-school holiday trips have been cancelled. It is so sad for that generation.

June 19 Primary Schools have been back since June 1, years 1 and 6 at least. Years 10 and 12 have just begun to return, a few 2-hour lessons per week on face to face, mostly focussing on core subjects. Its is a slow start but we’re getting there. Some schools are really pushing on-line work rigorously, others less so. One school I am in touch with are setting exams at end of June for Year 10’s, not far off mock GCSE standard that’s good. I can see that the on-line novelty will wear off and we need to find a way of getting children back to school, safely of course but with an attitude of “we’re gonna do this”. If not for this school year then certainly in September. I think year 10 parents are the most worried the GCSE’s will be affected and why demand for Year 10 tuition remains very high.

For year 11’s (the forgotten year) two things are happening. First, yes we know their predicted grades will be formulated into actual grades in August. Some surveys have suggested they will be half a grade higher than last year. Perhaps the final examiners will bring them back down a touch but it seems reasonable. The issue for me is that children need four go’s at really learning a topic but Year 11’s missed out on the final pre exam revision push.

So that means that the if they take a topic forward to A Level they will have missed out on that final embedding of knowledge which forms the beginning of AS Level. Which is why – the second happening – it is a great thing that schools are beginning to use the June/July hiatus for Year 11’s to begin year 12 AS Level, even if its is with videos and on-line learning. (And why I am running Maths for A Level science courses for Year 11’s! )

Today we had the publication of plans for NTP the National Tutoring Programme and it certainly seems to have had a lot of thought put into it. The website is up and running and the aims and resources are clear. I think we should wish them well in trying to do the catch up of lost time, and maybe even at the other end of the programme providing a permanent means for disadvantaged pupils to keep up.

My tuition for International students continues about the same level but there’s just a hint that some are hesitating as to whether the British international schools will be open in September. We shall see.

May 11 The beginning of the end. Or the end of the beginning. The Prime Minister announced that some restrictions will be eased and said he hoped first and last year of primary schools could open from June, with secondary perhaps seeing some face to face teaching July. But I think it will take a lot to persuade parents and teachers alike to believe it is safe. I believe it is 50:50 whether any schools reopen before September – or at least more than they are now because we shouldn’t forget technically they are open to a small number of vulnerable pupils and those of front line workers.

May 8. Still full. I lost my first Chinese pupil whose parents understandably were hesitant to continue lessons in the uncertainty about resumption. But the place was quickly filled by an extra UK lesson. Zoom works well on Waiting Room but slightly annoyingly when 1 person is Waiting and 2 are in the lesson that counts as 3, which means maximum 40 minutes so you sometimes have to restart. I have found a way of helping with student’s school web tasks but feeding the questions back into a mix of past paper questions to check they can do them without help. I’m also extending Maths for A-Level Biology to Maths for A-Level Chemistry.

Still no sign of at-school restart : safety has to be guaranteed, so if not straight after half term, that would mean end of June earliest – and what would be the point for a few weeks. Are we into Alice Cooper territory? Schools Out for Summer. Schools Out Forever? The lyrics are eerily appropriate.

April 24 The first full week after Easter and it looks like all the pupils in my schedule have returned for on-line lessons. I have adjusted Zoom to include a password and the excellent waiting room feature. For GCSE students the Maths for A Level Biology programme seems to be working well; while continuing GCSE work is useful just in case resits are needed and to keep a learning focus, I’ve offered a programme which looks forward rather than back.

Still no sign of the plans for restart: these could vary for a phased resumption before half term on geographic and yeargroup basis, to a more widespread resumption immediately after half term, to a wait till September. My instinct is for the middle option, but we shall see. Years 10 and 12 will probably be a priority.

April 3 The second week complete and all my pupils have now used Zoom with me successfully , albeit I’ll adjust some settings during Easter. Some schools now looking forward rather than back, beginning A-Level introduction early for GCSE students rather than continuing GCSE work for which there’s no exam and its now become clear today that current work will not count towards GCSE because “schools have also been told not to set extra work to inform the predictions, because young people may not be able to do themselves justice if they are incapacitated by illness or have a difficult home environment”. Likewise with some of my GCSE students I will begin “Maths for A-Level Biology” early.

March 28 The first week of shutdown has completed and Zoom is working pretty well for my remote tuition. There is a boom in Zoom round the world it seems. Schools have been using Microsoft Teams, Google Classroom, Show My Homework, Hegarty Maths, Kerboodle among others to set on-line homework tasks which vary from watching videos to answering questions and entering answers. It looks like Year 13 A-Level students’ tasks do indeed still count towards final grade; with Year 11 GCSE it is a little less clear how important their continued diligence is.

March 20: schools have shut down. Some clarity received from Government that cancelled exams will NOT mean that GCSE s and A Levels are not awarded: rather that the criteria for allocating grades will be determined by predicted grades, mocks, and coursework which teachers will collate and inform examining boards of their recommendation. These grades will be awarded earlier than usual in July and so appeals may be received and possibly an optional Autumn term exam will be arranged. What is not quite clear is whether tasks submitted on line over the next few weeks will count towards grades. Until informed otherwise we have to assume they will.

For year 10’s who are not yet taking exams the objective must be to take on- line tasks, teaching and tuition seriously and diligently to ensure the prolonged absence does not adversely affect their chances at GCSE next year

Today’s various announcements marked a Rubicon so from now I will be doing on-line tuition only till further notice, which some of my UK pupils have already started with me using Zoom. My Chinese students already do this and it works well.

March 19 : update: schools beginning to shut down and set up homework and revision material on the web systems. Some are timetabling the issue of new material to when their normal lesson times would be and some are planning to run live webinar lectures at lesson times. I am beginning to do on line tuition to UK students in the afternoon (already plenty of Chinese in the morning) and finding so far Zoom better than more well known Skype.

Still no word on decision of what might replace exams as a qualification.

March 18: update: announcement that all schools will close Friday and that exams will not take place in May/June. An announcement will be needed as to whether this means postponement till September, or waive through on Precited Grades. PM’s phrase “pupils will get qualifications” could indicate the latter. I am beginning to see how schools will keep their pupils busy: good on line portals like GCSE Pod or Show My Homework are places to set tasks.

A thought: one of the world’s most valuable Apps in moral terms is “Nextdoor” where you can find out what is happening locally, and who knows what its now worth in financial terms. Other Apps whose time has come include Zoom and Skype.

March 17 : update: Teddington has moved to closing most of the school but keeping Year 11/13 open. The reason is associated with shortage of staff, self isolating or on sickness.

Similarly Waldegrave is closing except for Year 7, 11 and 13 which remain open and Orleans Park is open for years 7,9,11,12 and 13 only.

This leaves keeps things moving for GCSE and A Level and leaves open the possibility of completing those exams but of course things are fast moving and may change.

Parents from year 10 are beginning to ask about possible extra tuition.

March 16

My personal opinion is that after this weekend the chances of UK schools having to close due to Coronavirus have moved from below 50% to over 50%. Whatever the science says, peer pressure may become irresistible. If closure happens, the length could be perhaps 4 weeks, 2 of which luckily are at Easter holiday; all the way up to 6 months including summer holidays.

With a short stop, perhaps pupils in Year 11/13 who would be most affected could receive remote schooling, reassemble for exams, and examiners might lower the grade boundaries. But for an extended outage, the question would then be, what about qualifications for 6th form and University, assuming that no exams would be possible in May unless on-line exams were mobilised quickly?  I don’t believe that everyone repeating their year would be an option; firstly I do not believe pupils would want that, and second the capacity is not available unless you roll all the way back to nursery and delay the very first year of schooling.

Even a half way house of taking GCSE/A Level in September would be problematic as it would mean starting the next Year after Christmas, and requiring pupils to maintain “mental fitness” all over this summer. So an interesting alternative compromise is nearby Teddington’s plan to close the school except for Year 11/13, which at least keeps things moving.

If exams were to be cancelled altogether and yet pupils progress to the next level, that then implies that coursework and predicted grades at GCSE and A Level would come into play, as a means of determining 6th form and College admissions. But this is speculation. We shall see. Currently isolation for over 70’s seems to be the focus, but certainly schools are beginning to plan – for instance my school at Waldegrave is encouraging pupils to take more books and equipment home each day in case a sudden instruction comes.

As a tutor, whatever happens, I will offer options to parents of continuing as normal, or moving to on-line, or (and I hope not) stopping altogether. Note that better than Skype for on-line is a purpose built free programme called Zhumu, which I already use extensively with my morning Chinese students and remote Europeans and the tutoring works very well using this system. Needless to say we have already introduced handwashing.


The Biology of Coronavirus is interesting to say the least; at GCSE level we know that viruses, despite causing so much grief, are not actually living, as they do not have enough of the MRSGREN characteristics (more on that in future updates); they only live when a host is found, where they can rapidly replicate; and antibiotics do not work, instead a vaccine is needed to prevent infection rather than cure ; and at A Level you would know that the reason that soap and water is so effective is that the hydrophobic part of the soap can rupture the lipid membrane of the virus (see below)

On a lighter note

Regular readers will know that a pop song is never far away. Let’s hope the outcome is less of John Lennon’s “hold you in his armchair you can feel his disease” in Come Together, or Depeche Mode’s “you know how hard it is for me to shake the disease”; rather Paul McCartney’s “Its getting better all the time” (he always was more optimistic), a song which originated when Ringo fell ill in 1964, and was temporarily replaced with drummer Jimmy Nichol, who played five concerts before Ringo was well enough to return. During Nicol’s tenure John and Paul constantly asked him how he was coming along, to which he always replied, “It’s getting better,” In 1967 Paul made this into a song for Sergeant Pepper.

Medical advice might be, as the Police say, “Don’t Stand So Close to Me” (and that was actually at school) or remain as X-Ray Spex would say, a Germ Free Adolescent.

As events develop I will update this blog. Auto updates are possible if you complete the subscription form

The school science of the Apollo 11 moon landing

50th anniversary

On July 20 1969 The Apollo 11 Lunar Module touched down on the surface of the moon and Neil Armstrong and Buzz Aldrin began their walk. Many (including me) judge this to be mankind’s greatest single-event achievement so far. Outlined below are the many aspects of this story which provide learning opportunities and potential exam questions across the three GCSE Sciences, particularly Physics.

The take-off

Despite the enormous sound and visual fury of the launch, the fuel used by the Saturn rockets powering the mission was mainly not fossil fuel, rather it was a mixture of liquid oxygen and hydrogen. Normally gaseous, very low temperatures are required to liquefy them, -219 C and -253 C respectively. Being liquid rather than gas is safer, and occupies much less space because
volume = mass / density and liquid density is higher. Saturn had sections which as fuel was used up were jettisoned to just leave the lunar and command modules. The enormous power was needed to enable the modules to reach the required speed to exit the earth’s atmosphere and escape the main gravitational pull.

Saturn V launches Apollo 11

The journey there

The distance from the earth to the moon is about 240,000 miles and the maximum speed was just over 24,000 miles per hour as it left earth’s orbit. So a “time = distance / speed “ calculation indicates a ten hour journey time and yet it took 3 days, so what happened to this slow-coach! Well, maximum speed does not mean average speed, and after the Saturn rockets were jettisoned, gravity slowed down the un-powered Module , as required, in order not to fly straight past the moon as it approached. Also, the journey included an orbit of the earth and several of the moon before descending to the moon so the distance was much higher.

The journey there..and back

Fuel Cells

If the rockets were jettisoned, how did the modules get to the moon without their powerful fuel? Well, once the modules were propelled out of earth’s orbit at high speed, less force was acting upon them since air resistance was zero. There was still a backwards gravitational pull of earth but it became smaller and smaller.  So Newton’s Law would suggest they just carry on in the direction they were pointing, namely towards the moon, even without Saturn rockets’s major fuel source, albeit gradually decelerating from initial 24,000 mph. Small amounts of fuel were needed for lighting, communication and landing/leaving the moon, and these were a mixture of conventional fuels and fuel cells developed in Cambridge University, which were the early versions of the fuel cells we learn about in Physics GCSE. Namely hydrogen plus oxygen combining through electrodes to produce water,and release energy as electricity. The maximum power was around 2000 Watts and the water was not wasted – it was drunk by the astronauts!

A fuel cell was used on Apollo 11 mission

“In space, no one can hear you scream”

As the advert for the science fiction classic confirmed, sound cannot travel in space because the longitudinal sound waves, whose vibrations are parallel to the direction of travel, need particles such as air to vibrate – but there is no air in a vacuum. So how come we could hear the astronauts? 

Sound waves don’t travel in space …but radio waves do

As David Bowie memorably told us in Space Oddity, a conversation was possible between Major Tom and Ground Control. Well, the answer is that communication was achieved by Radio waves, which are not sound waves but Electromagnetic waves which as transverse waves vibrate at right angles to the direction of travel. Just like other parts of the spectrum – like light waves from the sun – radio waves can travel through a vacuum at the speed of light namely 300 million meters per second. Since the 240,000 miles is around 360 million meters, then using time = distance / speed, the time for a radio signal to travel from the moon to the earth is only 1.2 seconds.  Hence the only-slight delay between Houston asking a question and the astronauts answering.

Note however that Michael Collins, alone in the Command module while Armstrong and Aldrin walked on the moon, could not be contacted on the far side of the moon as radio contact was lost, as expected. Perhaps this was why Bowie’s Major Tom  lost contact at the end of the record – “can you hear me Major Tom?”

Ground Control could hear Major Tom …at first

The physics of an orbit

When the lunar module had jettisoned its rockets it performed an orbit of the earth before heading to the moon. How does this work? If the module is set in forward motion at just the right speed then the force at right angles to its motion – namely gravity – pulls it towards earth and the net result is a bisecting direction along the path of the orbit.

The speed of the orbit remains constant at 25,000 miles an hour but the velocity is constantly changing. How can this be? Well, it’s because velocity is a vector and speed is a scalar quantity and as Vector tells Gru in Despicable Me, a vector has magnitude as well as direction. So the velocity is constantly changing because the direction in a circular path is constantly changing. When a force creates a circular motion, this is a centripetal force. (Gravity is a non-contact force while other centripetal forces are contact forces – the friction when a motor bike turns, and the tension in the spokes of the London Eye)

The diameter of the earth is about 8000 miles and the Module initially orbited the earth at around 100 miles up. So the diameter of the orbit around the centre of the earth was 8200 miles, giving a circumference of approximately 25,000 miles using Pi. At almost 25,000 miles per hour, the initial orbit took 1 hour.

The Moon Landing

When Armstrong and Aldrin’s lunar module separated from Collins’s Command Module above the moon, it reduced its speed but slightly overshot the landing site in the Sea of Tranquility in order to avoid landing in a crater. Armstrong took over control from the Module computer to achieve this ( a computer with less processing power than an I Phone incidentally).  Less than 30 seconds of fuel remained, so this was where both of the astronauts’ flying experience, including  dog fights with Russian MIG’s in the Korean War, proved invaluable. They stayed impossibly cool, while Houston’s control centre personnel famously were so tense they almost “turned blue”.

Armstrong’s heart beat stayed normal at 70 beats per minute, almost until the “Eagle has landed” but even he succumbed at touchdown to the fight or flight adrenaline hormone at touch down, when his heartbeat reached 150.

After Armstrong stepped down off the ladder – “one small step for man, one giant leap for mankind” – Aldrin soon followed him and began, as the Police would later sing, while Walking on the Moon, to take “giant steps” with his “feet hardly touching the ground”. Why is this? Well ,gravity there is only a sixth of the earth’s gravity ( g is 1.6 rather than 10). So it was easy to hop around. And why is the gravitational force lower? Because the force is proportional to the mass of the two objects, and the moon is lighter than the earth, even if the man has the same mass. So a person of 50 kg faces a gravitational downward force of 500 N on earth but only 80 N on the moon.

The Police …drums on the side of a Saturn

They collected rocks and when later analysed they were found to contain the chemical lelements silicon, iron, aluminum, calcium, magnesium, titanium and oxygen. No carbon or nitrogen, so not enough ingredients for biological life.  Years later however , hydrogen and iced water were found at the moon’s poles and this opens the possibility, with the presence of hydrogen and oxygen, of creating fuel cells using electrolysis which could mean that the Moon could be used as refuelling stop on the way to Mars. 

The journey back

After taking off from the moon, the lunar module docked with the orbiting Command Module and together they returned to earth.  Long before the mission, Aldrin had written a thesis on docking in space based on his experience as a scientist and Air Force pilot in Korea. As the Module approached the earth atmosphere the frictional force – this time a contact force – caused the heat shield to reach high temperatures and gradually melt – as planned.


A parachute slowed the Module down further, with air resistance offsetting the weight of the Module, which floated down at a leisurely terminal velocity to the sea.

The crew were kept in quarantine for several days in case they had caught viruses on the moon.  A virus – unlike bacteria – is counted as non-living but nevertheless can contain DNA. It is worth recalling that DNA was discovered by Watson and Crick at Cambridge University only 16 years before the Apollo 11 mission.

Further Physics work

All of the above science should be readily understandable by anyone taking Physics or Maths GCSE – if not it’s a definite revision topic! For those carrying on with Physics, the A Level and Physics Aptitude Test for Oxford will contain more advanced Space concepts like eclipses, Kepler’s Laws for orbits and what many consider to be one of the all-time great equations; namely Newton’s formula for the Force exerted by gravity on two objects, of mass m1 and m2: F = Gm1m2/r^2 where r is the distance between the masses and G is the universal gravitational constant. 

Scientists are still not sure what Gravity truly is, yet in the 1700’s Newton could already quantify it, and in a sense invented the science behind Apollo.

What to expect in the 11-plus

What to expect in 11 plus entry exams

I have just completed some Maths tutoring for two excellent students hoping to join a grammar or independent school in South West London.  Their approach was exemplary, their Maths was already well in advance of Year 6, and they wanted to get even better, being prepared to work very hard in lessons and at home. One full practice paper was not enough for homework, they coped with two a week.  Their parents hoped for a free or reduced fees place, but if not I have no doubt they would try to find a way to sacrifice to pay fees.

With the recent news about possible expansion of grammar schools, it made me think about what would happen if my two students did, or didn’t, make the grammar schools, and also how the various entry exams compared to each other, and to traditional year 6 SATs standards.  In other words, what should pupils expect in their exam?  Let’s start with this.

The entrance exam

My focus was upon my local South West London schools, 10 fee paying private independent schools and 8 free, state, selective grammar schools.  I drew broad conclusions about the latest exam processes, likely to be reasonably applicable outside London too. The first thing to say is that in these 18 Schools, it is very difficult to find free sample papers or even sample questions on their websites.  This is to avoid advantaged children “buying” their entrance through expensive “teaching to the test” tuition.  However, for some of the Surrey schools typical common entrance papers can be purchased, some schools just outside this area do publish sample papers, and of course national publishers like CGP and Bond make practice papers available.

So you can piece together what the typical test will look like.  Maths rather than English is my speciality so here are some of features of the typical Maths entrance paper.

The number of questions will be between 25 and 50, students have 45 minutes to 75 minutes to complete, so at 1.5 to 2 minutes each these are short sharp questions.  But the complexity varies significantly from beginning to end, so you should expect to spend 30 seconds on the easy ones and perhaps 3 minutes on the difficult ones. The ability to work fast is almost as important as the ability to answer the question.  The paper typically divides, in order of questions, into what I’ll call the four quartiles of difficulty.   Remember that the higher the reputation of the school, the higher the demand for places, the higher proportion of questions in quartiles 3 and 4, as follows:

1st quartile  – simple KS2 topics
Number : Addition, subtraction, multiplication, division (always without calculator)
Fractions, percent and decimals, number lines
2nd quartile – tricky KS2 topics
Number and measurement: clock times, square and prime numbers, ratios, units of measure
Algebra: graph coordinates, sequences, simple algebra expressions,
Geometry:, Angles along straight lines, at a point and in triangles, areas and perimeters of regular shapes, recognise 2D and 3D shapes, simple translation and reflections.
Data : Mean (average),Tables, Pictograms, Bar Charts, Pie Charts, Line graphs
Problems: Inverse Logic problems such as “what number did I start with”
3rd quartile – still KS2 but highly developed problems
 Factor pairs, place list of fractions and decimals in ascending order
Algebra: Solving linear equations, Create equations from areas and perimeters, including odd shapes;  substitution of numbers in equations
Geometry: Combination of angles rules in one problem, Nets, angles round a clock-face circle Rotations, Symmetry, Mirror (e.g. what would “WINTER SALE” be on a window’s other side
Problems: Speed x times = distance problems, Number reasoning, Railway timetables, Time-zones

4th quartile – Beyond KS2 to KS3 and KS4 GCSE, and Puzzles
: Exchange rate conversions, Fibonacci sequence, Prime factor trees, Ratio problems such as cake recipe; HCF and LCM; powers.
Algebra: simultaneous equations created from e.g. prices of burgers and soft drinks, Multiply double brackets using grid or FOIL
Geometry Parallel line angles, enlargements and scale factors, 3-D cuboids
Data: Venn diagrams, Probability, Mode, Range and Median
Problems: Sudoku-like magic number puzzles, Shapes representing operations, number machines Shortest route problems such as through the streets of New York; full page multi-paragraph problems featuring combination of numeric and verbal reason logic culminating in for example, which of five children got a present, which of five animal lives on which island?
This last, 4th quartile frequently goes well beyond KS2 in two respects. Firstly, what I’ll call “puzzles” – which ironically will never resurface in secondary exams. Secondly, school syllabus content stretching well into KS3 Year 8 and 9 even in rare cases up to KS4 GCSE level (yes!). This last quartile contains the differentiator questions, the ones you have to be able to do to be really confident of gaining entry. When tutoring an 11 plus pupil followed by a GCSE pupil I sometimes find myself using the same sample questions.

Most of the school websites say, to be politically correct, that the questions should be suitable for any KS2 student (only one admitted that some questions may stretch to KS3). Parents should not be fooled. With demand outstripping supply by 4 or more to 1, the higher reputation schools do throw in the puzzles and year 7-11 level questions to identify the brightest pupils.


How many exams?

The table below shows, for the 8 grammar schools sampled in SW London, most have 2 stages, although the Sutton set start with the common SET test. The 10 independents all have just one stage except St Pauls, which starts with the common ISBE test, and most have an interview to confirm selection. Most schools feature Maths, English and either a separate verbal reasoning test or similar questions within English. What is noticeable is that Non Verbal Reasoning is becoming quite rare now (thank goodness – awfully difficult to teach!)


Maths English Non Verbal
Comments Sample Maths available
Tiffin Boys  Y Y  N 2 stages,  and stage 1 counts 10% each Maths and English, Stage 2 counts 40% each Maths and English  for entry. No
Tiffin Girls  Y Y N 2 stages, and stage 1 is Maths and English OMR multi choice, passing gets you to Stage 2 Maths and English which alone determines entry No
Below are the Sutton Grammars taking  common SET
Nonsuch High for
 Y Y N 2 stage, 1st  English and Maths common SET multi choice, then joint second stage Maths and English with Wallington High School for Girls No but SET samples can be ordered
High for Girls
 Y Y  N 2 stage, 1st English and Maths common SET multi  choice then joint second stage Maths and English with NonSuch High School for Girls As above
Greenshaw High  Y Y  N 1 stage only Maths and English common SET multi choice. Pass for eligibility for  60 places. As above
Sutton Boys  Y Y  N 2 stages, first is common SET English and Maths multi choice , to get you to second stage Sutton specific English and Maths. 1st and 2nd stage tests all affect final entry, ratio is 2:2:3:3 As above
Wallington County  Y Y N 1 stage only, Maths and English common SET, pass to be eligible for  place As above
Wilson’s Sutton  Y Y N 2 Stage , first is common SET Maths and English, second Maths and English. Count in ratio 2:4:4. As above
Maths English Non Verbal
Comments Sample Maths available
Hampton  Y  Y  N 1 stage, 3 exams : English, Words and Reasoning, Maths and an interview A few questions
Halliford Y Y Y 1 stage Maths, English, Verbal and Non Verbal reasoning No
Lady Eleanor Holllis Y Y Y 1 stage tests in Maths, English, VR, Non VR followed by Interview No
St Catherine’s Y Y N 1 Stage tests in Maths and English then interview No
Y Y N 1 Stage tests in Maths and English then interview. Note : it confirms some KS3 material will be tested. Yes full paper
Y Y N 1 stage tests in Maths and English Plus write a personal statement No
Kingston Grammar Y Y N 1 stage English Maths and verbal  reasoning followed by an interview Yes most of a sample paper
Reeds Y Y N 1 stage tests Maths English and Verbal Reasoning No
Y Y N 1 stage test Maths English and Verbal Reasoning Yes a full paper
St Pauls Y Y Y 1st stage ISBE / GL Multiple Choice in English, Maths, Verbal and non Verbal reasoning. 2nd stage is English and Maths and interview No but ISBE sample papers can be ordered

Grammars – the pros and cons.

Through the lens of my two students, if they started Year 7 even in the best of the local state schools, they would be so far ahead that they would, to be honest, be bored and held back. Like many bright children they need the challenge. The supply of free grammar schools is limited. At many of our local grammars the ratio of applicants to places is 4 to 1 and at some even higher, where queues around the block form at the start of exam day. (Some now phase exams through the day to avoid this).  In business, if supply is limited and demand is high, you increase prices or create more capacity – in this case by creating more grammar schools, because prices are fixed at zero.

However the downside is of course that if the brightest pupils are creamed off from state schools, the overall standard must surely fall. This is detrimental to the remaining pupils, who lose the chance to learn from the approach and abilities of high achieving pupils, and dispiriting for teachers who enjoy challenging them and getting a positive can-do response. Some teachers would surely jump ship. Some Headteachers have said this would recreate “secondary moderns”.

One compromise – which one of our local state schools already employs – is to offer a limited number of exam-selective places, while mainly offering free places for local pupils.  The question then is, do you sprinkle the selected pupils among the classes, or “set” from the start.  The problem with the first approach is that schools are constrained by the national curriculum which prescribes certain content for certain years, so the brighter pupils would be constrained by the pace of the slowest.  The alternative is to “Set” from year 7 and effectively teach the top set Year 8 or 9 level content from age 11, and take all GCSE’s  (not just Maths) a year early.  This “grammar stream” approach is advocated by former UCAS Chief Executive Mary Curnock Cook Or go further (as my old school used to do) and identify the brightest year 7 pupils and to remove them at year end from Year 8 and place them straight into Year 9 (we were called “removes”).

Is tutoring needed?
As noted above, the questions definitely stretch beyond standard KS2 (whatever schools say). The question is, how do you get access to, and practice these.  In theory, purchase of Bond or CGP practice books can do the trick, but the risk is that the pupil will miss the personal explanation and without homework being set, may not practice enough, and even these excellent publications don’t include the outrageously tricky questions which do crop up.  Note also that while common entrance papers like SET the Selective Eligibility Test can be purchased, frequently these are only for Stage 1 permission to sit the really challenging Stage 2 papers which are not formally available. So structured learning, and exam tips are needed over and above school provision. Parents might provide this but many would struggle with the vital end of paper questions. Extra tutoring is your insurance policy (but not a guarantee) and this can come in several forms, including private one to one,  or exam centre cramming.     

What is tutoring providing?

What you are trying to do is this: First make sure the basics of KS2 are in place. Second, introduce the pupil to a selection of KS3 topics which may crop up. Third, help the pupil work at speed. Fourth, teach exam techniques. Finally set a sufficient quantity and quality of challenging tasks from which gradual improvement instils confidence – the “more I practice the luckier I get”.  What is difficult to teach is the natural mathematical abilities such as puzzle solving and spatial awareness, and my guess is that is why such puzzles are included – there may be disadvantaged pupils who cannot afford tutoring yet have that innate mathematical ability which money can’t buy.

In conclusion

The 11 plus is highly challenging. A good KS2 performance – an 11 plus “pass” – will probably not be enough to get through. There are many pupils and parents willing to take up that challenge, to achieve that extra level of excellence. Schools, the State and Tutors all have a part to play in meeting that demand.

Chinese Maths in English schools

News that Chinease Maths techniques are to be introduced to English schools needs some explanation and examination.


Initially to be piloted in around half of our primary schools, the technique involves learning techniques more by rote,  asking one child to answer a question, then asking the remainder of children to repeat the answer. The class does not move on until all the class has “got it”. The brighter children avoid being held back because they have a role in leading the other children with the first answer.   There are some similarities with Kumon, namely keep practising by repetition until “mastery” of a topic is achieved to an advanced level, but differences too: Chinese Maths emphasises the role of the respected teacher at the front of class, Kumon relies more on self learning through worksheets.

Chinsese children themselves are believed to be 2-3 years ahead by the time they move to Year 11; so 16 year olds in China are already at the same level of maths as an 18 year old A level student in the UK.

There is a view that culturally some British pupils are not ready for this and our cultural diversity and child centred participation doesn’t sit easily with chanting and learning by rote which is common and part of the educational ethos in China. The benefits are not at all questioned.

Chinese Maths versus English real world approach

More important I believe is this. The direction in Maths and Science in England is to introduce more “real world” relevance to exam questions, not just at GCSE KS4 but also at earlier KS3 and KS2 as well.

So while introducing a “back to basics” learning approach in Maths is very good, not least because we are slipping down the international educational league tables, I wonder if joined up thinking is taking place in Government in terms of the following two factors:

If teaching methods move in the direction of focusing upon  purely numerical excellence, and yet examiners insist on setting real world applied questions where the maths technique is merely a small means to an end, do we risk the recent Biology GCSE “drunken rat” exam problem ? By this I mean that the children aim to learn the syllabus and technical methods to the best of their ability, and they put a lot of effort into mastering the knowledge and technique required in the syllabus, but meanwhile the examiners smother the questions in “real-world” unfathomable words and situations.  So the child learns the techniques but can’t do the exam questions because they haven’t been schooled in the methods of deciphering them, or applying the technical knwledge they have acquired.

An example in Maths itself is the 2015 GCSE question that went viral. The question involved two techniques rarely seen together: algebra, and probability. One can imagine pupils achieving high levels in these two topics individually using Chinese techniques of practising lots of examples, but being unbable to piece together the required jigsaw which requires a different sort of skill altogether.

Mile long and centimeter deep

One other phrase associated with Chinese Maths is interesting: their criticism of the British Maths syallabus is that it is a “mile long but a centimetre deep”.   There is something in this.  For GCSE Maths there are five basic topics such as Number and Algebra but within those there are many sub-topics making around 80 in all. One wonders if all of these are necessary, for instance frequency density histograms are beloved by specification setters but in practice are never used by businesses. Could some topics be left out allowing time for in-depth understanding of the core?

But we are where we are: my philosophy as a tutor is to “teach to the test”, whether GCSE exams or earlier end-term tests. Because that’s what parents want. And the last thing a child wants is to open an exam paper and find there are topics they don’t even recognise. So you have to teach the whole syallabus, not just the mathematic principles but the ability to understand and answer increasingly inscrutable questions.

Measuring success

In summary there will almost certainly be benefits and we need somehow to catch up on global competitors. An intangible benefit may be a cultural change, to make Maths excellence expected rather than optional. But ultimately, the acid test is this: will the programme lead to better GCSE results, either higher marks, or the same marks at a younger age? This may depend on whether the new techniques are compatible with the direction of Maths exam question designers. Sound learning of fundamentals is essential and surely must be improved – so we have to start somewhere; but it may be only the first base-camp stage in achieving the summit of maths mastery. We may not be able to judge success for half a decade.

Drawing graphs – Top 180 pop records example

In GCSE Science and Maths you are often asked to draw or interpret graphs – representing and visualising data are the technical terms. Often it depends on whether the data is discreet or continuous.

Continuous data can be almost anything – a temperature measurement for instance – and line graphs are generaly used – whereas discreet tends to be categories that can only have certain values and bar charts are best. As an example here is an assessement I did for my hobby – assembled the top 3 pop singles each year for the last 60 years. I used a bar chart to show which artists had appeared more than twice. Not suprisingly the Beatles, Elvis and Michael Jackson were at the top. If you are pop rock and soul fan you can see the full list and how they they were chosen in this link. 



graph6As part of my tuition I run through each of the types of graphs you can see here including scatter, line, Pie, box plot, bar, cumulative frequency, histogram. These are becoming ever more important to understand with the new GCSE’s coming next year with Maths.



Another favourite with the examiners expecially with science is the concept of independent and dependent variables. Independent variables are the things you change deliberately e.g. the size of the pellets in a chemcial reaction, and these normally go on the x-axis. These “cause” a change in the dependent variables which are the “effect” i.e.they tend to be continuous, could be the reaction rate, and are usually on the y axis of a graph.  Finally the “control variable” is something you keep the same to be fair, such as as room temperature or weight of pellets.

There is often a cross over between Maths and Physics so if you learn about Distance Time graphs in Maths you will also see efectively the same graph in Physics.

And often you will be asked to interpret a graph about which you know nothing such as the drunkne rat biology question – the key is not to panic and instead apply the pronciples you have learned about graph interpretaton.

And don’t of course forget algebra graphs , classic y against x, straight lines or quadratic curves, measuring gradients, shading inequalities for instance.

All in all graphs pop up everywhere in Maths and Science GCSE not to mention Business Studies!

Would seeing an exam beforehand really help?

News today that the Department for Education inadvertently but helpfully posted a SATS test on a practice paper website some time before the real thing (not a good week for the department, the National Audit Office found holes in their accounts). This made me think, how much would it really help to see an exam before?

The answer is, if you didn’t know it was going to be the real thing, then it wouldnt help that much. It would be easy to forget the solutions, especially if time passed.

However, if you did know it was going to be the exam, you would take extra care to remember the methods and solutions.

In practice the chances of this happening are almost zero. Or are they? In the following sense this does happen.

Certain questions occur time after time in pretty much the same form – just with different numbers. Actually this tends to happen more in A-Level than GCSE, but consider these examples:

June 2015 : Expand and simplify (t +2)(t + 4)     
November 2014 Expand and simplify (2x + 3) (x – 8)
June 2013 Expand and simplify (m + 3) (m + 10)

(Answers below)

They are in effect the same question, same technique, but with different numbers.

Will esentially the same question occur in 2016? We shall find out soon. You could look at it in two ways. Either, it occurs so often it’s time for a break: or it’s a staple question, it will occur agan. Second guessing the examiner’s mind is impossible in terms of exact questions, but broadly you can predict the type of question.

What’s clear is that this type of algebra, whether “expand the brackets”, or perhaps the reverse – “factorise”, introduce the brackets, and solve the quadratic – is likely to crop up.

Therefore if you have done your past paper practice, and it does reappear, then in effect you have seen the question before. At least the method, which you have practiced and mastered. If you turn over the paper and see this type of question, you think “joy, I know how to do this”.

Of course not every question is a “repeat” question, but broadly quite a large proportion have similarities. As a back up to learning the methods, past paper practice, with access to worked answers, is so incredibly useful ! And why my tutoring homework always includes some real (on paper, not PC ) past paper examples.


June 2015 : Expand and  simplify (t +2)(t + 4)    t² + 6t + 8   
November 2014 Expand and simplify (2x + 3) (x – 8)   2x² – 13x – 24
June 2013 Expand ans simplify (m + 3) (m + 10)   m² + 13m + 30

West Indian cricket wins Maths question

The start of the new English cricket season reminds me of that moment a few weeks ago when England were about to win the T20 World Cup.  West Indies batsmen had a mountain to climb from their last over and Ben Stokes, England’s expert “death” bowler, was ready (Stokes had won the game for England in the semi final in similar circumstances). However (and this is a personal opinion) I think Stokes was already imagining his celebration, particularly to his nemesis Marlon Samuels, and his concentration wavered.

Carlos Brathwaite, West Indian batsman, had other ideas and England’s hopes disappeared in a blaze of sixes. His achievement lends itself to a form of GCSE Maths question proving popular with examiners. Namely the “reverse mean” question where pupils have to calculate not the average of a given set of numbers, rather the number needed to change an old mean to a new mean.

England cricket team had an average of 7.75 runs from their 20 overs. West Indies after 19 overs had averaged 7.21 runs per over. How many runs did they need from the last over to win the match ? (i.e. exceed England’s total by 1 run)  (See below for answer)

Although West Indian cricket has struggled of late, the win was eventually going to happen as they have a tremendous competitive spirit. As can be see in this fascinating BBC article about the use of gamification in Jamacan classes. A small company, Edufocal, has set up computer aided classrooms for core subjects like Maths which reward the children for scoring right answers. The company is growing and results are improving. Sponsorship from Virgin’s Branson Centre of Entrepreurship is helping.  Some of my pupils use CGP Mathsbuster which has a similar philosophy – bronze, silver, gold trophies are awarded as pupils move through the questions.  But in Edufocal’s case the prizes are real – cinema tickets etc ( funded by subscription).

And just to keep the Jamaican theme going, one of my favourite artists and songs is Bob Marley’s One Love, the video here being not in Jamaica but London, with a yound Suggs and Paul McCartney.

So, returning to the cricket, the final was featured in the “Cricinfo” website which specialises in statistical coverage of cricket matches and includes graphs which, while not exactly the same as in GCSE, do show the power of using visual techniques to bring numbers to life.

Carlos Brathwaite perhaps wasn’t thinking of solving a GCSE puzzle as he awaited Stokes’s first ball (a glance at the scoreboard may have been easier!) But if he was. here is what he would be calculating:

England’s average (mean) of 7.75 runs per over from 20 overs meant they scored 7.75 x 20 =155 runs in total. So West Indies needed to score 156 to win. But after 19 overs, their average was only 7.21 per over so they had scored 7.21 x 19 = 137 runs.  So from the last over they needed 156 minus 137 equals 19 runs to win. (In fact they scored 3 sixes from 3 balls, and another from the next for good measure, to win with 2 balls left. Bravo!) 

Big data helps Maths GCSE revision

Big data is a term used increasingly to describe the use of large amounts of data gathered electronically to determine insights otherwise lost in the detail. It is often characterised as the 3 V’s, Volume ( e.g. terrabytes); Variety (e.g. social media insights as well as surveys) and Velocity (fast data transfer and processing). A famous early example was use of location-specific Google searches on flu medicine to predict and track the spread of a flu virus through America quicker than conventional methids.

How can this principle help revision? Well, a subset of Big Data is simply “more data than usual” – big data light to coin a phrase – and I have done this with Maths past papers. Not just answers and methods are available on line for all past papers – that is well known – but also examiners’ comments are available question by question.

erInitially I have looked in detail at 4 past papers, 100 questions, and captured the comments from each, 130 in all, for which the examiners highlighted common causes of lost marks from tens of thousands of entries. Then I grouped them and tallied them GCSE style in a frequency table and chart as seen left. This sheds light on general areas for revision, with (lack of) “basic maths skills” ferquently bemoaned by examiners, as well as subtle tips such as “read the question very carefully and make sure you show working”.

Then, further I picked out twenty very specific examples of errors that seemed to occur – this time syallabus technical content rather than functional categories above – and wrote and illustrated a list of “20 things examiners do and don’t like to see”.  A typical one is shown. I recently took some examiner marking training and I can assure you this is true. If a question asks you to “express a number as a product of its prime factors”  then merely listing them, with commas, will lose you a mark, if the “times” sign is missed out. Even if the numbers are riight as above.

I have put these and other tips together into an Easter/Summer Term special lesson covering:
– reminder of key basic maths skills, especially the ones that get overlooked
– exam technique :  start, during and end of exam
– problem solving techniques for difficult, wordy, end of paper high mark questions
– active revision methods
– the twenty things examiners do and don’t want to see.

With half time biscuits covering the Jack Black “school of rock” Math video.

misAnother phrase used in the Big Data field is “wisdom of the crowds”.  This is being applied superbly by the excellent on-line Maths tutor “MrBartonMaths” (he is also a real teacher). One of the blog pages he runs is “Diagnostic Questions – Guess the Misconception” where students are invited on-line to answer a multiple choice question and give their reason (a typical weekly question is shown). Typically around a thousand students vote (hence the “crowd”) and reveal what errors are often being made (in the example A is correct of course, C was the most common error). The misconceptions are both the students’ errors, and tutors’ sometimes incorrect expectations of what errors might be most frequent.

A lot of data is available out there on-line – the key is to process and present it in the best way to understand and hence help students.


Gangnam Style Exam Cramming

News that Psy’s worldwide hit “Gangnam Style” has exceeded 2.5 billion video views is astonishing. That’s two thousand five hundred million (like when my football team loses 8-0, the teleprinter helpfully adds “eight”).  A Maths GCSE question could be:

Write 2,500,000,000 in standard form : Ans. 2.5 x 10 to the 9th 

Gangnam_Style_Official_CoverBut where or what is Gangnam? Well, the Economist reported recently from Gangnam itself in Seoul, South Korea, where just to get into the best private tuition after-school study groups, children have to pass exams; the children are cramming for crammers. These are the Hagwon schools and the best are called Sekki (cub) – most of them in fashionable Daechi-dong in stylish Gangnam (yes that one). Students work at a level up to 5 years ahead of their age group syllabus and often arrive home tired and late after a double day in education. A law is now being proposed to ban children from studying in private tuition after 10 pm.

Children also spend their free periods at school doing extra homework for Hagwon. Parents spend 0.8 % of GDP (or a tenth of all household income)  on private education, which puts South Korea top on the Private Tuition World League (Britain is 8th with 0.4% of GDP). But few parents actually admit to enrolling.

But this is what we in the West are up against – huge achievement in South East Asia.  Demand for tuition is so high (sigh!) in Seoul, South Korea that no advertising is needed.

But does this have a measurable impact upon results? Well, yes. according to the latest PISA study (not the leaning tower, rather the international education benchmark for 15 year olds in 72 countries). Korea is in the top ten for Maths and reading and 11th for Science (Singapore as ever dominates). While the U.K. has climbed to 15th in Science it has dropped to 27th in Maths. A sobering thought. Should the U.K. strive to match SE Asia by copying their “learning by wrote” mastery techniques, or push on with our strategy of “real world” syllabus questions perhaps more relevant to the workplace. That’s for a future blog!

Gangnam is a fashionable district of Seoul in South Korea described as affluent and the equivalent of Beverley Hills or Chelsea. Psy wrote “Gangnam Style” as a slightly ironic social comment on Gangnam residents lifestyle.

First ever on-line national Maths test

News perhaps lost over Christmas was that national tests are to be introduced by the Goverment for times tables. up to times 12 by age 11. Momentous not so much for the fact that “3R’s back to basics” are being tested –  it seems to makes sense to do so – but for the first time ever a national test is to be conducted on-line with results available immediately.  It is another test for teachers to organise, so more workload, but hopefully the automation minimises administration and marking (provided the iT works !)

timesNo doubt someone will beaver away analysing where the hotspots and coldspots are ( will x7 prove the most difficult, except in Sevenoaks? Will x2 prove the easiest, especially in Twice Brewed?). A benefit of “Big Data” analysis is that it reveals “Wisdom of the Crowds”, or “Bulk Crime” as Police would call it, where when you are able to easily consolidate data, patterns emerge, which can lead to actions being addressed.




We are all getting used to using on-line Maths coaching and testing, there are scores of websites. My own favourites are CGP Mathsbuster, BBC Bitesize, AQA AllAboutMaths, .

And last but not least where he uses “Essential Skills” diagnostic Maths quizzes with the ingenious requirement to add a few lines on “why you believe the answer is correct”, which on compilation reveals the top reasons why pupils get a particular question wrong e.g in BIDMAS. And so “Wisdom of the Crowds” helps tutors and teachers identify problem areas with the certain knowledge that a large number of other pupils also find a topic difficult.

In conclusion, how relevent is the story for GCSE? Well, the national on line test is another step on the road to automation (how far will it go?) and while Times tables will clearly not be asked directly in GCSE, many steps in GCSE questions do require a thorough knowledge of the basics, especially the non-calculator exam, otherwise slow or incorrect answers will result.





The Maths in Greg Rutherford’s garden long-jump pit

Athletics has had a bad press recently, rightly so. But let’s celebrate one of Britain’s greats, Greg Rutherford, rightly nominated this week in the twelve for BBC Sports Personality of the Year

Greg Rutherford’s fantastic long jump win at the World Championships meant he joined the select band of Brits holding the four major athletics titles at once. It was all the more fascinating because he has built a long- jump training pit in his back garden, as you can see below.

And a genuine GCSE Physics or Maths Higher tier question might be this: end of paper “tricky”, but in line with the emphasis on “real world problem solving”.

Question: Greg builds a long-jump run up and pit in his back garden.  He typically accelerates evenly from 0 to 10 metres per second in 4 seconds, then runs for 2 more seconds at 10m/s before take off. The world record leap is then approximately 9 metres and he allows another 3 metres for landing.  What is the minimum length Greg’s garden must be, from beginning of run up to end of landing?

Answer: in the first phase the word “evenly” implies a straight line velocity versus time graph from 0 to 4 seconds, and the distance covered is the area under that graph, namely half the base (2 seconds) times the height (10 m/s) i.e. 20 m.

The second phase at constant speed is simply speed x time equals distance i.e. 2 seconds x 10 m/s equals 20m.

The sand pit must be 9+3 = 12 m so the total minimum length is 20+20+12 equals 52m.

Finally, back to those awards: why no cricketer?! (Joe Root, genuine personality, Ashes winner, record number of international runs in a year!)

Foornote May 2016: Greg has actually announced a world class competiition in hos own back garden using the afore-mentioned long jump pit!

Origin of the word Google – it’s Maths!

The Economist googlemathsthis week speculates that we are running out of combinations of letters for company names, and mentions the best and worst examples of made up names. One of the best is Google, which lead me to research its origin.

The good news is, there is a Maths angle.

The word Google comes from the googol,  namely 10 to the power of 100, or 1 followed by one hundred zeros.

The founders of the company used the googol to represent the search engine idea of identifying an extremely large number of options.  But the story goes that googol was
mis-spelled as google and the rest is history.

A nice GCSE question, in the new mode of “challenging”, might be:

A googol is 10 to the power 100

(a) What is a googol divided by ten to the power 98
(b) Write in standard form 15 googols

These could be seen as frightening, yet easy at the same time:

(a)  answer = 10² = 100
(b) answer 
1.5 x ten to the power 101

The word googol itself was invented by a nine year old (why am I not surprised?) in the 1920’s.  The nephew of American mathematician Edward Kasner.  To get an idea of what a googol “looks like” it is similar to the ratio of the mass of an electron to the mass of the whole visible universe.

The word google in fact was mentioned before the company invention by an unlikely author, Enid Blyton. Not in “A very large number of people go the smuggler’s top” but in the term “Google Bun” in Faraway Magic Tree. Also (much more likely)  Douglas Adams used the term Googleplex in the Hitchhiker’s Guide to the Galaxy, while Google itself uses “Googleplex” as the name for it’s HQ.

back-to-the-future-part-iii-2Googleplex is in fact the term for 10 to the power googol ( ten to the ten to the 100)  which is a very large number indeed, perhaps to infinity and beyond. The mind boogles. I mean boggols. I mean boggles. in “Back to the Future 3″ the Doc says about future wife Clara ” She’s one in a billion. One in a Googleplex!”

The word googol surfaced again when it was the £1 million question in 2001 in Who Wants to Be a Millionaire?, the one where Charles Ingram was revealed to have used an accomplice.

Google (the word) is often in the news. It was the subject of an imaginary merger of the future with Amazon and subsequent war with Microsoft in (the Epic 2014 Googlezon wars).

It has officially become a verb (to Google, to search). Ironically Google the company doesn’t like this use, because it has come to mean “to search the whole web”, not just using their search engine, although most people do actually use Google as their primary search tool.

Google has been translated for instance into Chinese


After a financial reorganisation, Google the company name, has technically become “Alphabet” (a combination of word search and alpha-bet, the best algorithm choices). Personally I don’t think “Alphabet” will stick – the word will never catch on!

Finally, the Economist rated Google one of the best company names (becoming a verb clinched it). The worst? A large consultancy expensively renamed itself “Monday”, a name judged so bad that it did not last to the Friday, when it was taken over.

Headmaster suspended for letting pupil take exam early

A headmaster in Wolverhampton has been suspended, and then reinstated after an enquiry, for allowing a pupil to take a GCSE English exam a day early. The reason seemed a little lax, namely to allow the pupil to go on holiday with their parents.

One assumes the enquiry involved checking his phone records and those of his friends in the few hours after the exam!

It reminds me of another “exam made easier” story from June when the answer to one GCSE question was helpfully supplied in another question, in the same paper. An AQA Chemistry paper contained the following:

2a. Fill in the blank. Limestone is mostly calcium ————
5b Limestone is made mostly of calcium carbonate…

In terms of making exams easier, let’s finish on a more serious note, well slightly more serious; allowing computers in exams.

googlemathsThe head of the OCR exam board suggests that Google be allowed in exams. The responses have varied from “ridiculous” and “rubbish” to “it would test resourcefulness and initiative rather than just your memory”.

Another proponent of the use of computers in exams is Dr. Sugata Mitra who conducted the famous experiment to place a computer in a hole in the wall adjacent to an Indian slum and found 7- year old children very quickly picked up skills with no assistance. It is a topic that won’t go away. But that is for another blog!

One Direction’s Maths Song – it’s good!

One Direction were in the news yesterday for postponing a concert, but the Mathemateer is more interested in the group’s Maths song.  Yes there is one, and it’s good !
As described below – can you do the mental Maths? !  Hear it here. 


One Direction were in the news earlier as they are rumoured to be taking a break in 2016. Recalling the excellent parody of their own song “What Makes You Beautiful” on Radio 1, the band wrote and recorded “Maths Song” whose main chorus is “Your Maths Skills = Terrible”

It features a series of quick, simple, mental maths tasks whose eventual answer is 130.  At GCSE level this would not constitute a genuine question but on the other hand the lost art of mental maths should not be underestimated. As a warm up exercise before a test you could do worse than follow this through.  Well done 1D as I think I should call them!