| Topic | Foundation | Higher |
| Ratio and Proportion | Sharing in a ratio, and problems involving this
Simplifying a ratio Best buys Relate ratios to fractions Calculate percentages and percentage change Calculate reverse percentages Calculate compound interest |
Form and solve equations using ratios
Interpret graphs that illustrate direct and inverse proportion Compares lengths, areas and volumes of similar shapes Describe direct and inverse proportion using an equation Find the instantaneous and average rate of change from a graph |
| Pythagoras, Trigonometry and Vectors | Know and use Pythagoras’ Theorem
Find distances between points Use trigonometric ratios to find missing sides and angles Know the exact values of sin, cos and tan for certain sizes of angle Write column vectors Add, subtract and find multiples of column vectors |
Use Pythagoras’ Theorem and trigonometric ratios in 3D shapes
Use the sine and cosine rules Use the sine formula for the area of a triangle Calculate with vectors and use them in geometric proofs |
| Factors, Multiples, Indices, Roots and Standard Form | Calculate factors and multiples
List the prime factors of a number as a product Calculate the HCF and LCM of numbers or expressions Calculate powers and roots Use the three laws of indices Change between normal notation and standard form Calculate with numbers in standard form |
Use the laws of indices for fractional and negative powers
Simplify surds and expressions involving surds Rationalise the denominator of fractions Perform harder calculations with numbers in standard form |
| Sets and the Probability of Combined Events | Use Venn diagrams to record outcomes and calculate probabilities
Know and use the set theoretic notation associated with Venn diagrams Construct possibility (sample) spaces and use them Use probability tree diagrams to calculate the probability of independent or dependent events |
Calculate and interpret conditional probabilities |