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
Number: 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
Number : 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!)
| School (State selective) |
Maths | English | Non Verbal Reasoning |
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 Girls |
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 |
| Wallington 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 |
| School (private) |
Maths | English | Non Verbal Reasoning |
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 |
| Radnor House |
Y | Y | N | 1 Stage tests in Maths and English then interview. Note : it confirms some KS3 material will be tested. | Yes full paper |
| Surbiton High |
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 |
| Claremont Fan |
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.