This question explores the relationship between surface area and volume of a cube, requiring reverse calculation from surface area to find volume.

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

This question tests understanding of Venn diagrams and probability concepts using sets of numbers with specific properties.

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

This question involves reverse percentage calculations in a real-world context of holiday pricing.

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

This question tests graphical solution of simultaneous equations using line intersections.

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

This question involves expanding brackets and combining like terms in algebraic expressions.

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

This question tests understanding of direct proportion relationships and calculations.

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

This question explores the relationship between gradients of perpendicular lines.

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

This question tests ability to make x the subject of a complex formula.

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

This question involves applying multiplication principle in a restaurant menu context.

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

This question tests knowledge and application of circle theorems.

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