Syllabus

Numbers and their operations

• primes and prime factorisation

• finding highest common factor (HCF) and lowest common multiple (LCM), squares, cubes, square roots and cube roots by prime factorisation

• negative numbers, integers, rational numbers, real numbers, and their four operations

• calculations with calculator

• representation and ordering of numbers on the number line

• use of the symbols <, >, ⩽, ⩾

• approximation and estimation (including rounding off numbers to a required number of decimal places or significant figures and estimating the results of computation)

• use of standard form A × 10n, where n is an integer, and 1 ⩽ A < 10

• positive, negative, zero and fractional indices

• laws of indices 

Ratio and proportion

• ratios involving rational numbers

• writing a ratio in its simplest form

• map scales (distance and area)

• direct and inverse proportion 

Percentage

• expressing one quantity as a percentage of another

• comparing two quantities by percentage

• percentages greater than 100%

• increasing/decreasing a quantity by a given percentage

• reverse percentages 

Rate and speed

• average rate and average speed

• conversion of units (e.g. km/h to m/s) 

Algebraic expressions and formulae

• using letters to represent numbers

• interpreting notations

• evaluation of algebraic expressions and formulae

• translation of simple real-world situations into algebraic expressions

• recognising and representing patterns/relationships by finding an algebraic expression for the nth term

• addition and subtraction of linear expressions

• simplification of linear expressions

• use brackets and extract common factors

• factorisation of linear expressions of the form ax + bx + kay + kby • expansion of the product of algebraic expressions

• changing the subject of a formula

• finding the value of an unknown quantity in a given formula 

• factorisation of quadratic expressions ax^2 + bx + c

• multiplication and division of simple algebraic fractions

• addition and subtraction of algebraic fractions with linear or quadratic denominator

Functions and graphs

• Cartesian coordinates in two dimensions • graph of a set of ordered pairs as a representation of a relationship between two variables

• linear functions (y = ax + b) and quadratic functions (y = ax^2 + bx + c)

• graphs of linear functions

• the gradient of a linear graph as the ratio of the vertical change to the horizontal change (positive and negative gradients)

• graphs of quadratic functions and their properties

• sketching the graphs of quadratic functions

• graphs of power functions of the form y = ax^n, where n = −2, −1, 0, 1, 2, 3, and simple sums of not more than three of these

• graphs of exponential functions y = ka^x , where a is a positive integer

• estimation of the gradient of a curve by drawing a tangent 

Equations and inequalities

• solving linear equations in one variable

• solving simple fractional equations that can be reduced to linear equations 

• solving simultaneous linear equations in two variables by

∗ substitution and elimination methods

∗ graphical method

• solving quadratic equations in one unknown by

∗ factorisation

∗ use of formula

∗ completing the square for y = x + px +q 2

∗ graphical methods

• solving fractional equations that can be reduced to quadratic equations 

• formulating equations to solve problems

• solving linear inequalities in one variable, and representing the solution on the number line 

Set language and notation

• use of set language and the notations

• union and intersection of two sets

• Venn diagrams 

Matrices 

• display of information in the form of a matrix of any order

• interpreting the data in a given matrix

• product of a scalar quantity and a matrix

• problems involving the calculation of the sum and product (where appropriate) of two matrices 

Problems in realworld contexts 

• solving problems based on real-world contexts

• interpreting and analysing data from tables and graphs, including distance–time and speed–time graphs

• interpreting the solution in the context of the problem 

Angles, triangles and polygons

• right, acute, obtuse and reflex angles

• vertically opposite angles, angles on a straight line and angles at a point • angles formed by two parallel lines and a transversal: corresponding angles, alternate angles, interior angles

• properties of triangles, special quadrilaterals and regular polygons (pentagon, hexagon, octagon and decagon), including symmetry properties

• classifying special quadrilaterals on the basis of their properties

• angle sum of interior and exterior angles of any convex polygon

• properties of perpendicular bisectors of line segments and angle bisectors

• construction of simple geometrical figures from given data (including perpendicular bisectors and angle bisectors) using compasses, ruler, set squares and protractors, where appropriate 

Congruence and similarity

• congruent figures and similar figures • properties of similar triangles and polygons

• enlargement and reduction of a plane figure

• scale drawings

• determining whether two triangles are

∗ congruent

∗ similar

• ratio of areas of similar plane figures

• ratio of volumes of similar solids

• solving simple problems involving similarity and congruence 

Properties of circles

• symmetry properties of circles

• angle properties of circles

Pythagoras’ theorem and trigonometry

• use of Pythagoras’ theorem

• determining whether a triangle is right-angled given the lengths of three sides

• use of trigonometric ratios (sine, cosine and tangent) of acute angles to calculate unknown sides and angles in right-angled triangles

• extending sine and cosine to obtuse angles

• use of the formula 1/2 ab sin C for the area of a triangle

• use of sine rule and cosine rule for any triangle

• problems in two and three dimensions including those involving angles of elevation and depression and bearings 

Mensuration

• area of parallelogram and trapezium

• problems involving perimeter and area of composite plane figures

• volume and surface area of cube, cuboid, prism, cylinder, pyramid, cone and sphere

• conversion between cm2 and m2 , and between cm3 and m3

• problems involving volume and surface area of composite solids

• arc length, sector area and area of a segment of a circle

• use of radian measure of angle (including conversion between radians and degrees)

Coordinate geometry

• finding the gradient of a straight line given the coordinates of two points on it

• finding the length of a line segment given the coordinates of its end points

• interpreting and finding the equation of a straight line graph in the form y = mx + c

• geometric problems involving the use of coordinates 

Vectors in two dimensions

• use of vector notations

• representing a vector as a directed line segment

• translation by a vector

• position vectors

• magnitude of vectors

• use of sum and difference of two vectors to express given vectors in terms of two coplanar vectors

• multiplication of a vector by a scalar

• geometric problems involving the use of vectors 

Problems in realworld contexts 

• solving problems in real-world contexts (including floor plans, surveying, navigation, etc.) using geometry

• interpreting the solution in the context of the problem

Data analysis

• analysis and interpretation of:

∗ tables

∗ bar graphs

∗ pictograms

∗ line graphs

∗ pie charts

∗ dot diagrams

∗ histograms with equal class intervals

∗ stem-and-leaf diagrams

∗ cumulative frequency diagrams

∗ box-and-whisker plots

• purposes and uses, advantages and disadvantages of the different forms of statistical representations

• explaining why a given statistical diagram leads to misinterpretation of data

• mean, mode and median as measures of central tendency for a set of data

• purposes and use of mean, mode and median

• calculation of the mean for grouped data

• quartiles and percentiles

• range, interquartile range and standard deviation as measures of spread for a set of data

• calculation of the standard deviation for a set of data (grouped and ungrouped)

• using the mean and standard deviation to compare two sets of data 

Probability

• probability as a measure of chance

• probability of single events (including listing all the possible outcomes in a simple chance situation to calculate the probability)

• probability of simple combined events (including using possibility diagrams and tree diagrams, where appropriate)

• addition and multiplication of probabilities (mutually exclusive events and independent events)