New stage 1 New stage 2

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1 iv New stage 1 New stage 2 1 Integers and powers 1.1 Integers and place value 1 2 Reading, writing and ordering NA2a integers and 1.2 Calculating with negative 2 4 The four operations with NA2a/3a numbers negative numbers 1.3 Rounding to one 4 5 Estimating by rounding all NA2a/3h/4a/b significant figure numbers in a calculation to 1 s.f. 1.4 Rounding to a number of 5 6 Rounding whole numbers and NA3h/4b significant figures to up to 5 s.f. 1.5 Squares, square roots, 6 7 Squares, cubes and roots to NA2b/3g/i cubes and cube roots learn by heart 1.6 Index notation 7 8 Evaluating expressions given NA3g in index form; solving equations such as 6 x Index laws 8 9 Simplifying expressions using NA2b the index laws for multiplication and division 1.8 BIDMAS 9 10 The order of operations NA3b 1.9 Reciprocals Finding the reciprocal of NA3a integers, and 1.10 LCM, HCF and prime Writing numbers in prime NA2a/3a factor decomposition factor form and hence finding HCF; finding LCM by comparing lists of multiples Mixed exercise Summary of key points Fractions, and percentages 2.1 Improper and Converting improper NA2c mixed numbers to mixed numbers and vice versa 2.2 Equivalent Simplifying by NA2c dividing the HCF of the numerator and denominator 2.3 Ordering 18 Ordering by writing NA2c them as equivalent with the same denominator 2.4 Adding and subtracting 19 Adding and subtracting NA3i and mixed numbers 2.5 Multiplying and dividing Multiplying and dividing NA3i and mixed numbers

2 v 2.6 Multiplying and dividing Multiplying and dividing NA3i by powers of 10 by 10, 100, Ordering Ordering by NA2d comparing digits with the same place value 2.8 Adding and subtracting Written methods and mental NA3i/4a calculations for numbers with one decimal place 2.9 Multiplying and dividing Multiplying whole numbers NA3i/k decimal numbers and using place value adjustment; changing calculations involving to calculations with whole numbers by multiplying the powers of Converting between Fraction to decimal conversion NA2d/3c and and vice versa; terminating and recurring 2.11 Ordering and Ordering by converting all to NA2d/3c 2.12 Appropriate degrees of Rounding up or down in the NA3o/p/4a/b accuracy context of the problem 2.13 Using a calculator to Using a calculator for NA3o/p evaluate expressions calculations involving brackets, powers, roots and times 2.14 Percentages, Equivalent, NA2e and and percentages 2.15 Finding a percentage of Working out percentages of NA2e a quantity amounts Mixed exercise Summary of key points Index notation and standard form 3.1 Zero, negative and 37 Index notation for reciprocals NA2b/3g fractional indices and roots; meaning of x Writing numbers in Using standard form; entering NA2b/3h/p standard form numbers in standard form in a calculator and interpreting the display 3.3 Calculations using Calculating with numbers in NA3i/m/4b standard form standard form, using the index laws 3.4 Estimating and Using standard form and NA3m/4a/b checking 1 s.f. approximations to estimate answers Mixed exercise Summary of key points 45

3 vi 4 5 Essential algebra 4.1 Basic rules of algebra 46 Simplifying terms, products NA5a/b and sums 4.2 Expanding brackets 47 Multiplying a single term NA5b over a bracket 4.3 Factorising Factorising completely; NA5b single brackets 4.4 Simplifying expressions Expanding brackets and NA5b involving brackets collecting like terms 4.5 Multiplying two Expanding double brackets NA5b expressions with brackets 4.6 Factorising quadratic Factorising by taking out a NA5b expressions common factor, or into two brackets 4.7 The difference of two Factorising quadratic NA5b squares equations of the form x 2 a Cancelling common Simplifying algebraic NA5b factors by dividing numerator and denominator by common factors 4.9 Adding and subtracting Writing equivalent NA5b algebraic with a common denominator 4.10 Multiplying and dividing Simplifying first by cancelling algebraic common factors NA5b Mixed exercise Summary of key points Coordinates and graphs 5.1 Coordinates in all four Reading and plotting NA6b/SSM3e quadrants coordinates in all four quadrants 5.2 Coordinates to complete Finding the coordinates of the SSM2a/3e shapes final point to make a given shape (parallelogram, square, etc.) 5.3 Mid-points of line Using the formula to find the SSM2a/3e segments coordinates of the mid-point D, 2-D or 3-D? 65 Identifying 2-D and 3-D SSM3e shapes; using 3-D coordinates 5.5 Graphs of straight lines Graphs of x c and y c NA6b parallel to the axes 5.6 Straight lines passing Graphs of y ax for positive NA6b through the origin and negative a 5.7 Graphs of linear functions Graphs of equations of the NA6b form y mx c, with y given explicitly or implicitly Mixed exercise Summary of key points 74 75

4 vii 6 Sequences 6.1 Term to term rules Generating sequences; NA6a finding term to term rules 6.2 The nth term of a Finding the nth term of NA6a sequence arithmetic series 6.3 Sequences of shapes Finding the nth term and NA6a number of matchsticks, tiles, etc. in shapes in a sequence Mixed exercise Summary of key points Properties of shapes 7.1 Polygons Definitions and names of SSM1e polygons with different numbers of sides 7.2 Properties of triangles Special triangles SSM2b 7.3 Angle properties of Equilateral and isosceles SSM2e triangles triangles; interior and exterior angles 7.4 Properties of Special quadrilaterals SSM2c quadrilaterals 7.5 Parallel lines, alternate Angles formed by parallel SSM2a and corresponding angles lines 7.6 Proof in geometry Proofs of angle properties SSM2a of a triangle 7.7 Bearings Drawing and calculating SSM4a bearings Mixed exercise Summary of key points Properties of circles 8.1 Circle parts Names and definitions of SSM2h parts of a circle 8.2 Tangents to circles Solving geometry problems SSM2h using tangent facts 8.3 Drawing regular 106 Drawing polygons by SSM2h polygons dividing a circle into equal sectors Summary of key points Measures 9.1 Using suitable units 108 Converting all NA4a/SSM4a measurements to the same unit before doing a calculation

5 viii 9.2 Metric and imperial Converting measures from NA4a/b/SSM4a equivalents metric to imperial and vice versa 9.3 Accuracy Maximum and minimum NA4b/SSM4a possible values and possible error 9.4 Speed Using the formula for speed NA4a/b/SSM4a 9.5 Density 114 Using the formula for NA4a/b/SSM4a density 9.6 Changing units Changing units for speed NA4a/SSM4a and other compound measures 9.7 Using estimates Estimating answers when NA4b/SSM4a an accurate answer is not required 9.8 Comparing Better buys, and comparing NA4a/SSM4a measurements measurements by converting them to the same units Mixed exercise Summary of key points Perimeter, area and volume 10.1 Area of plane shapes Area of triangle, SSM4d parallelogram, trapezium 10.2 Surface area and volume Calculating surface area SSM4d of cuboids and volume of different cuboids 10.3 Fitting boxes into larger Working out how many SSM4d boxes small boxes will fit into a larger box 10.4 Surface area of simple Calculating the area of SSM4d shapes different faces and adding together 10.5 Volume of prisms Using the formula for SSM4d volume of a prism Mixed exercise Summary of key points 131 Examination practice paper Stage 1 (multiple choice) Practice questions Stage 1 (multiple choice) Formulae sheet 140 Answers