11+ maths: everything you need to know

Is your child applying for 11 plus entry to a grammar school or a selective independent school? Most 11 plus exams include a maths test.

Keep reading to find out everything you need to know about 11 plus maths. In this article, we'll cover:

• The key topics your child needs to know

• The types of maths questions used by major exam boards

• How your child can revise and prepare effectively

• Plus, sign up for Atom's free 11+ course and get a full-length 11+ maths practice paper!

When are 11 plus maths exams?

If your child is applying to a grammar school, they will take their 11+ exams in September in Year 6.

11 plus exams for entry to independent schools tend to take place a little later – usually between December and January in Year 6. If your child is taking the ISEB Common Pre-Test, they will probably sit the exam in November.

What are the key 11+ maths topics?

Most 11+ maths exams include the topics taught on the national curriculum up to the end of Year 5. Some 11 plus exams include content taught in early Year 6. 11+ tests are meant to be challenging, so it's normal for your child to come across questions they're not familiar with.

Key Stage 2 maths covers these topics:

1. Number – number and place value
2. Number – addition and subtraction
3. Number – multiplication and division
4. Number – fractions (including decimals and percentages)
5. Measurement
6. Geometry – properties of shape
7. Geometry – position and direction
8. Statistics

We've broken down these topics into more detail below.

1. Number: number and place value

By the end of Year 5, your child should be able to:

• read, write, order, compare and round numbers up to 1,000,000
• count backwards and forwards with positive and negative numbers (including through zero)
• count backwards and forwards in steps of 10 for any number up to 1,000,000
• interpret negative numbers in context
• read Roman numerals up to 1,000 (M) and recognise years written in Roman numerals

Take a look at an 'ordering' question from an Atom Learning 11 plus mock test below.

2. Number: addition and subtraction

By the end of Year 5, your child should be able to:

• add and subtract numbers mentally, using increasingly larger numbers
• use formal written methods (columnar addition and subtraction to add and subtract whole numbers of more than 4 digits
• use rounding to check their answers and work out levels of accuracy when solving problems
• decide whether to use addition or subtraction when solving multi-step problems

The question below shows a situation where your child would need to use addition, subtraction, and rounding to solve a problem.

3. Number – multiplication and division

By the end of Year 5, your child should be able to:

• identify multiples, all the factor pairs of a number, and the common factors of two numbers
• understand and use the vocabulary of prime numbers, prime factors and composite numbers
• work out whether a number up to 100 is prime
• recall prime numbers up to 19
• use long multiplication when multiplying numbers up to 4 digits by a 2-digit number
• use short division when dividing numbers up to 4 digits by a 1-digit number
• solve multiplication and division problems using knowledge of factors, multiples, squares and cubes
• multiply and divide numbers mentally
• multiply and divide whole numbers, and numbers involving decimals, by 10, 100 and 1,000
• recognise and use square numbers and cube numbers
• solve problems using multiplication and division, including scaling by simple fractions, and problems involving simple rates

The long division question below is from an 11 plus maths practice test on Atom.

4. Number – fractions (including decimals and percentages)

By the end of Year 5, your child should be able to:

• compare and order fractions whose denominators are multiples of the same number
• multiply proper fractions and mixed numbers by whole numbers
• identify, name and write equivalent fractions
• add and subtract fractions with the same denominator(s)
• read and write decimals as fractions
• compare numbers with up to 3 decimal places, and round numbers with 2 decimal places, to the nearest whole number
• recognise mixed numbers and improper fractions and convert from one form to the other
• recognise the per cent symbol (%) and write percentages as a fraction with the denominator 100, and as a decimal

The question below is an example of a multi-step fractions problem your child might see in the 11+ maths test.

5. Measurement

By the end of Year 5, your child should be able to:

• convert between different units of metric measure (such as centimetres and metres, or litres and millilitres)
• use approximate equivalences between metric and imperial units
• measure and calculate the perimeter of rectilinear shapes using metres and centimetres
• calculate and compare the areas of rectangles
• estimate the area of irregular shapes
• estimate volume
• use standard units, square centimetres and square metres

The question below is an example of when your child would need to calculate perimeter.

6. Geometry: properties of shape

By the end of Year 5, your child should be able to:

• identify 3D shapes from 2D representations
• learn how to compare and estimate acute, obtuse and reflex angles
• draw angles and measure them in degrees
• understand rectangle properties to deduce facts and find missing lengths and angles
• distinguish between regular and irregular polygons

The question below is taken from an 11 plus maths mock test on Atom. Your child would need to use their knowlegde of angles and degrees to solve the problem.

7. Geometry: position and direction

By the end of Year 5, your child should be able to:

• reflect shapes and lines
• identify, represent and describe the position of shapes following a reflection or translation

Take a look at the question below. To answer this, your child would need to use their understanding of coordinates and positioning.

8. Statistics

By the end of Year 5, your child should be able to:

• complete, read and interpret statistical information in tables (including timetables)
• use line graphs to solve comparison, sum and difference problems

Here's an example of the type of statistics question your child might see on their 11+ maths test.

What is the format of the 11 plus maths exam?

11 plus maths exams look a bit different depending on who creates your child's exam. Some schools use maths tests created by exam providers, while others create their own bespoke tests. 11 plus maths exams are usually non-calculator.

Take a look at the typical structure of 11+ maths exams below.

CAT4

The CAT4 – a cognitive abilities test – is used as an 11 plus exam for entry to some independent schools. State secondary schools also often use the CAT4 to 'stream' pupils into sets in Year 7.

The CAT4 can be taken online or on paper and it is non-adaptive. It consists of three parts, which are broken down into smaller individually-timed sections. The questions are multiple-choice and focus on reasoning and problem-solving.

Cambridge Select Insight

Cambridge Select Insight is used by some independent schools. It is taken online and is non-adaptive. It used to be known as CEM Select.

There are six sections in the Cambridge Select Insight test. The general maths section consists of 30 questions. These are usually in a drag-and-drop or multiple-choice format.

FSCE

FSCE (Future Stories Community Enterprise) supplies 11 plus exams to a few UK grammar schools. This exam is taken on paper and is not adaptive.

The format is similar to GL Assessment exams – your child will have a question booklet, and will need to write their answers on the answer sheet provided. There is a combination of free- response questions and multiple-choice questions.

GL Assessment

GL Assessment 11 plus exams are used by most UK grammar schools and some independent schools. These tests are taken on paper and are not adaptive.

Questions in GL Assessment 11 plus tests are multiple-choice. Your child will be given a question booklet and an answer booklet. They will need to shade in the correct answer for each question in their answer booklet, which is then marked electronically.

ISEB Common Pre-Test

The ISEB Common Pre-Test is used by some independent schools in the UK. This is an online and adaptive test.

There are four sections in the ISEB Pre-Test. The maths section has a time limit of 40 minutes and consists of multiple-choice questions. Your child will be allowed a pen and paper to jot down any calculations or notes that they want to make, but this won't be marked.

Quest Assessments

Many independent schools use entrance exams by Quest Assessments. This is an online and adaptive exam – the questions become more challenging depending on how your child is performing.

It's up to the school to decide whether to include a maths section, and if so, how long it should be. All questions in a Quest Assessment exam are multiple-choice. Your child will have scrap paper and pencils to help them work through the problem.

How is the 11 plus maths test marked?

Each maths question will have a different number of marks. Most 11 plus maths exams have easier 1-mark questions to start, with more challenging questions towards the end. More difficult questions usually involve lots of steps, with more marks available.

Some exam boards reward pupils with marks for showing their workings. It's a good idea to make sure your child gets into the habit of writing down their problem-solving.

When your child's test is marked, the examiner will add the marks together to create a raw score. Many exam boards then use a process called standardisation to create a 'standardised age score'. This takes into account your child's age in years and months at the time of taking the exam, and the number of correct answers. This process ensures that children born at the end of the school year aren't disadvantaged.

With an Atom Home subscription, your child can take unlimited 11+ practice tests. Get instant data, including their standardised age score, and performance compared to other children applying to the same school!

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