List of NEW Maths content
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1 List of NEW Maths content Our brand new Maths content for the new Maths GCSE (9-1) consists of 212 chapters broken up into 37 titles and 4 topic areas (Algebra, Geometry & Measures, Number and Statistics). See below for more details. Contents ALGEBRA... 2 GEOMETRY & MEASURES... 5 NUMBER... 7 STATISTICS
2 ALGEBRA Algebraic manipulation Simplifying algebraic expressions Expanding brackets Expanding brackets (Higher only) Common factors Factorising quadratics Factorising quadratics (Higher only) Simplifying quotients (Higher only) Completing the square (Higher only) Algebraic fractions (Higher only) Calculators Using a graphics calculator (Core) Using a graphics calculator (Extended) Use of a graphical calculator Calculus Turning points Applications Equations Linear equations in one unknown Quadratic equations that factorise Quadratic equations (Higher only) Factor theorem Simultaneous equations, linear only Proportion (Higher only) Simultaneous equations, linear and quadratic (Higher only) Trial and improvement Using iteration (Higher only) Linear inequalities Inequalities (Higher only) 2
3 Formulae Substitution Formulating problems algebraically Rearranging formulae Rearranging formulae (Higher) Standard formulae Matrices Matrices (Extended) The Language of Algebra Notation and conventions Domain and range Vocabulary Proof Proof (Higher only) Functions Functions (Higher only) Linear graphs Coordinates Graphs through the origin y = mx + c Gradient Gradient (Higher only) Area under graphs (Higher only) Solving equations Tangents to circles (Higher only) Inequalities with two variables (Higher only) Sequences Term to term rules Position to term rules Special sequences 3
4 Linear sequences Geometric progressions Special sequences (higher only) Quadratic sequences Quadratic sequences (higher only) Cubic sequences Non-linear graphs Quadratic graphs Reciprocal graphs Exponential graphs (Higher only) Cubic graphs Other graphs Trigonometric graphs (Higher only) Circles (Higher only) Gradient (Higher only) Area under the graphs (Higher only) Transformations of graphs (Higher only) Quadratic graphs part 2 Asymptotes Absolute value function Logarithmic function Other graphs (harder) Cubic graphs (Extended) The Trapezium Rule (Higher Only) 4
5 GEOMETRY & MEASURES Matrices Matrices Language and Conventions Coordinates Vectors 2D shapes Circles 3D shapes How to use a pair of compasses and a protractor Using compasses and a protractor to draw accurate diagrams Trigonometry Pythagoras theorem Trigonometry in right-angled triangles Exact values Sine rule (Higher only) Cosine rule (Higher only) Area formula (Higher only) 3D trigonometry (Higher only) Accurate drawing Scale diagrams Maps and bearings Constructions Loci 2D representations of 3D shapes Angles Angles around points Angles in parallel lines Angles in polygons 5
6 Circle Theories (Higher only) Circles and tangents (Higher only) Congruence and similarity Transformations Enlargement Transformations (Higher only) Vectors (Higher only) Congruence Similarity Area and volume (Higher only) Length, area and volume Triangles Quadrilaterals Composite shapes Circles Parts of circles Prisms Dimensions Other 3D shapes Properties of shapes Triangles Quadrilaterals Symmetry 3D shapes Proofs Proofs (Higher) Units Standard units Compound units Conversion between metric units Imperial units Converting between units 6
7 NUMBER Integers Factors and multiples Primes Prime factorisation Highest common factors and lowest common multiples Fractions Ordering fractions Fractions of a given number Adding and subtracting fractions Multiplying fractions and cancelling Dividing fractions Links with ratio Powers and roots Squares and square roots and higher powers and roots Estimating powers and roots (Higher only) Reciprocals Laws of indices Fractional indices (Higher only) Manipulating surds (Higher only) Rationalising denominators (Higher only) Growth and decay Iterative processes (Higher only) Percentages Finding percentages Comparing using percentages Percentage change Reverse percentage change Simple interest Ratio and proportion 7
8 Simplifying ratios Sharing in a given ratio Solve proportion problems involving ratio Direct proportion Inverse proportion Decimals Ordering decimals Adding and subtracting decimals Multiplying decimals Dividing decimals Standard form Calculation Adding and subtracting whole numbers Multiplying whole numbers Dividing whole numbers The order of operations Negative numbers Counting Combinations Accuracy Ordering integers Place value Rounding Estimating Exact calculation and answers Limits of accuracy Upper and lower bounds (Higher only) Rounding to significant figures Decimals and units Money 8
9 Converting Converting to percentages Converting to fractions Converting recurring decimals (Higher only) 9
10 STATISTICS Sets Venn diagrams Collecting Data Sampling Collecting and collating data Questionnaires Testing a hypothesis Two-way tables Representing Data Categorical data Discrete data Stem and leaf diagrams Continuous data Other representations Time series data Cumulative frequency graphs (Higher only) Histograms (Higher only) Box plots (Higher only) Analysing Data Averages Estimating averages Measures of spread Measures of spread (Higher only) Percentiles Bivariate data Use correlation Interpreting graphs Single event probability Measuring probability Calculating probability 10
11 Relative frequency Equally likely outcomes Combined events Calculating probability Tree diagrams Conditional probability (Higher only) Probability/Number (Higher only) 11
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