Essential GCSE Maths Problem Practice
Foundation Level Problem-Solving Methods Step-by-Step Solutions GCSE Resit Preparation
Learning Objectives - WALT
We Are Learning To solve percentage problems using multiplication We Are Learning To find nth terms in arithmetic sequences We Are Learning To calculate probabilities from given data We Are Learning To work with scale and ratio problems We Are Learning To apply area and perimeter formulas
Problem 1: Percentage Calculation
Question: Work out 135% of 160 Method: Convert percentage to decimal 135% = 135 ÷ 100 = 1.35 Calculate: 1.35 × 160 = 216 Answer: 216
Problem 2: Arithmetic Sequences
Sequence: 29, 25, 21, 17, 13 Find the pattern: 29 - 25 = -4 (common difference) Formula: nth term = first term + (n-1) × common difference nth term = 29 + (n-1) × (-4) Simplified: nth term = 29 - 4n + 4 = 33 - 4n
Problem 3: Probability Calculation
Given probabilities: Red = 0.42, Blue = 0.3 All probabilities must sum to 1 White probability = 1 - (0.42 + 0.3) White probability = 1 - 0.72 Answer: White probability = 0.28
Problem 4: Scale and Distance
Scale: 1:50,000 means 1cm = 50,000cm Map distance: 10cm Real distance: 10 × 50,000 = 500,000cm Convert to kilometers: 500,000cm ÷ 100,000 = 5km Answer: 5 kilometers
Problem 5: Circle Area
Formula: Area = π × r² Given: radius = 9cm Substitute: Area = π × 9² Calculate: Area = π × 81 Answer: 81π cm²
Problem 6: Percentage Profit
Cost price: £250,000 Selling price: £263,750 Profit = £263,750 - £250,000 = £13,750 Percentage profit = (profit ÷ cost price) × 100 Percentage profit = (13,750 ÷ 250,000) × 100 = 5.5%
Problem 7: Ratio Sharing
Ratio: Molly : Paige : Demi = 4 : 2 : 1 Total parts = 4 + 2 + 1 = 7 parts Total sweets = 42 Each part = 42 ÷ 7 = 6 sweets Molly: 4 × 6 = 24, Paige: 2 × 6 = 12, Demi: 1 × 6 = 6
Problem 8: Currency Exchange
Exchange rate: £1 = €1.12 Amount to exchange: £350 Method: Multiply pounds by exchange rate Calculation: £350 × 1.12 Answer: €392
Problem 9: Rectangle Perimeter
Given: Length = 8cm, Width = 5cm Formula: Perimeter = 2 × (length + width) Substitute: Perimeter = 2 × (8 + 5) Calculate: Perimeter = 2 × 13 Answer: 26cm
Problem 10: Rectangle Area
Given: Length = 7cm, Width = 4cm Formula: Area = length × width Substitute: Area = 7 × 4 Calculate: Area = 28 Answer: 28cm²
3 more slides available after you open the deck.
Download all 15 slides