Definition: Surface area is the total area of all faces of a 3D shape Vocabulary: Total surface area of a cube = 6x², where x is the length of one edge Example: For a cube with surface area 150cm², the edge length is 5cm and volume is 125cm³

Definition: A Venn diagram shows relationships between different sets Vocabulary: B' (complement of set B) contains all elements not in set B Example: Odd numbers and square numbers are represented in different regions of the Venn diagram

Example: If a 20% increase equals £240, the original price can be calculated by finding 10% (£120) and multiplying by 10 Highlight: Working backwards from the percentage increase to find the original amount

Definition: The point of intersection of two lines represents the solution to simultaneous equations Example: The equations 2-2y=x and 2y=3x-22 are solved graphically Highlight: The solution can be verified by substituting coordinates into both equations

Vocabulary: Terms with the same variables and powers can be combined Example: (6x²y³)² is expanded using the power rule Highlight: Final answer must be in the form ax^b y^c where a, b, c are integers

Definition: Direct proportion means y = kx where k is the constant of proportionality Example: Using y = 24 when x = 1.5 to find k, then calculating y when x = 5 Highlight: All working steps must be shown to demonstrate understanding

Definition: Perpendicular lines have gradients that are negative reciprocals of each other Example: If one line has gradient m, the perpendicular line has gradient -1/m Highlight: The solution requires solving equations to find the value of k

Example: Rearranging y = 4$2x-7$/$5x+3$ to isolate x Highlight: Multiple steps of algebraic manipulation required

Example: 5 starters × 12 main courses × x desserts = 420 combinations Highlight: Real-world application of counting principles

Definition: A tangent is perpendicular to the radius at the point of contact Example: Using circle theorems to find angle ADC Highlight: Multiple circle theorems must be applied sequentially