Key Stage 2, Key Stage 3, Key Stage 4

 11+ Entrance Exam and 13+ Entrance Exam Topics



Key Stage 2 Topics


Addition and subtraction
Introduce various methods of addition and subtraction.

Introduction to multiplication as repeated addition.

An introduction to division.

Addition and subtraction of fractions
Addition and Subtraction of fractions.

Common fractions
An introduction to common fractions.

Decimal addition and subtraction
Addition and subtraction of fractions.

Decimal fractions
An introduction to decimal fractions.

24 hour time
To introduce the concept of digital (24 hour) time.

Analogue time
An introduction to telling and reading time on an analogue watch.

Data handling
A basic introduction to tallying raw data and drawing up a bar graph.


To introduce the concept of addition of positive and negative numbers.

Introduction to integers
To introduce the concept of numbers less than zero.

Introduction to Multiples as repeated Multiples.

Number patterns
Receive an introduction to number patterns.

Place value
Introduction to the place values of numbers.

Prime and composite numbers
Identifying, testing for and listing prime numbers.

Ratio is a comparison of two numbers by division.

3D shapes
Introducing 3D shapes and corresponding terminology.

Discovering the formula for area of rectangular and square shapes.

Discovering the formula for perimeter of rectangular and square shapes.

An introduction to the properties of various polygons.


An introduction to volume.



Key Stage 3 Topics

Triangle Types
Learn how to recognise and name different types of triangles.

Angle Types
Learn how to recognise different types of angle - acute, obtuse and reflex.

Angle Measure 1: Acute and Obtuse
To be able to construct and measure acute and obtuse angles.

Angle Measure 2: Reflex
To be able to construct and measure reflex angles.

Learn how to name and draw 3-dimensional shapes, such as cylinders, cones, tetrahedrons, prisms and pyramids.

Understanding Rotation
Understand and use the language associated with rotations.

Rotational Transformations
Learn to transform shapes by rotation using a compass, ruler and protractor.

Learn how to name polygons and how to draw lines of symmetry on a variety of shapes.

Axial Symmetry
Learn about axial symmetry and the difference between the axes.

Planes of Symmetry
Understand how to find planes of symmetry on common solids.

Understand how to locate points in a 2-dimensional plane using co-ordinates.

Cartesian Plane
Understand how to read the co-ordinates of points plotted on the Cartesian plane.

Plotting Points in a Quadrant
Learn to plot points on the Cartesian plane using co-ordinates.

Learn how to replace numbers with letters called variables.

Learn how to simplify collections of terms called "expressions".

Multiplication of Variables
Understand how to multiply variables and terms in expressions.

Learn how to contain terms in brackets.

Algebraic Fractions
Understand how to use fractions when the numerators and denominators contain algebraic expressions.

Linear Equations

Learn how to recognise a linear equation.

Simultaneous Equations
Learn how to solve simultaneous equations using the elimination method.

Bisecting Lines
Learn how to bisect lines and angles using a compass and a straight edge.

Pythagoras' Theorem
Learn how Pythagoras' Theorem can be used to solve problems with right-angled triangles.

Trigonometric Ratios
Understand that the trigonometrical ratios are ratios of triangle sides.

Finding Angles From Ratios
Learn how to use a scientific calculator to find angles when given a trigonometrical ratio.

Multiplying by 10, 100...
Learn how to multiply and divide numbers using powers of 10.

Summing Decimals
Learn how to add and subtract numbers that have up to 2 decimal places.

Ordering Decimals
Learn how to order whole numbers and numbers with up to two decimal places.




Key Stage 4 Topics

Simultaneous Equations
To understand what simultaneous equations are and learn how to solve simultaneous equations and problems, using simultaneous equations.

Solving Quadratic Equations
To understand how to define, factorise and solve a Quadratic Equation.

Solving Quadratic Equations by Formula
To understand how to use a formula and solve any possible Quadratic Equation which has real solutions.

Factors 1
To understand how to extract common factors and how to factorise simple terms and quadratics.

Factors 2
To understand how to extract common factors from four terms and how to factorise complex quadratic equations and squares.

Area of Triangle
To be able to understand the rule for the area of a non right-angled triangle and apply the rule for the area of a triangle to simple and complex problems.

Pythagoras' Theorem
To be able to identify when Pythagoras' Theorem can be used, and how to solve right-angled triangle problems.

The Sine Rule
To understand how to apply the Sine Rule to a simple triangle and to more complex problems, and how to use compass directions to solve problems.

Triangle Basics
To understand how to identify right angle, adjacent, opposite and hypotenuse sides in right-angled triangles, and describe the ratio of sine, cosine and tangent.

Triangles with Angles > 90 Degrees
To understand how to find the value of an angle if given the Sin, Cos or Tan for an angle between 90° and 360°, inclusive.

To understand the circumference, arcs, cyclic quadrilaterals and tangents to circles.

Equation of the Line
To understand how to find the equation of the line linking any two points, and how to draw any line from the equation of the line.

To understand the slope formula and how to apply it to calculate slopes of parallel and perpendicular lines.

Triangle Theorems
To understand triangle ratios, equiangular triangles and Pythagoras' Theorem.



11+ (Year 7) Entrance Exam Topics

This paper checks basic numerical skills , tackle real-life and theoretical problems contained within National Curriculum Attainment Targets Ma2 to Ma4. Questions are generally aimed at Levels 4 and  5 with some elements of Level 6.

Questions may be set on the followings topics:

Addition and subtraction of integers and decimal;

Long multiplication of integers or division by one or two digit integers;

Subtraction and multiplication of simple decimals;

Making sensible estimates of everyday objects;

Simplifying fractions and finding fractions of quantities;

Simple percentage;

Use simple imperial or metric units in context, know to convert one metric to another and know the rough metric equivalents of imperial units in daily use;

Recognising number patterns;

Knowing prime number to 20 and square number up to 10 x10;

Cartesian co-ordinates;

Using simple formulae;

Understand the meaning of factor and multiple;

Use correctly of symbols< , > and = ;

Understand the use of brackets to determine the order of operations;

Recognise the angles on a straight line total 180˚ and the sum of the angles of a triangle is 180˚;

Simple 2D and 3D shapes, visualise 3D shapes from 2D drawings;

Reflective, rotational symmetry and translation;

Finding perimeters, area or simple volumes and angles;

Use units of time – seconds, minutes, hours, days and weeks and know the relationship between them;

Interpretation of statistical diagrams ( bar charts, line graphs ,pie charts, etc);

Estimation of probability on the scale of 0 to 1;

Mean, mode, median and range of a set of data.




13+ (Year 9) Entrance Exam Topics

This paper checks basic numerical skills and gives candidates the opportunity to tackle real-life and theoretical problems contained within National Curriculum Attainment Targets Ma2 to Ma4. Questions are generally aimed at Levels 5 and 6, with some elements of Level 7. Material contained in the 11+ (Year 7) paper is assumed. No calculators are permitted.


Questions may be set on the following topics:

The four basic operations applied to fractions; ratios, calculations with decimals, use of estimation to check calculations;

Generating sequences using formulae;

Co-ordinates in all quadrants;

Solving simple equations or inequalities;

Simplifying algebraic expressions; substituting numbers into a formula. Solving a pair of simultaneous equations either graphically or by elimination. The graphical representation of simple linear equations.

Understanding the meaning of square, square root, cube and cube root;

Use index notation and know the laws for multiplying and dividing positive integer powers.

 2D and 3D shapes; area of plane shapes or volumes of simple solids; types of quadrilaterals;

Pythagoras’ Theorem;

Find an exterior or interior angle of a regular polygon;

Transformations: Rotation, Reflection, Translation and Enlargement; 

Probability; outcomes of combining two independent events;

Have a basic understanding of correlation and be able to use a line of best fit.