Mathematical Reasoning and Problem Solving
Overview
Mathematical Reasoning and Problem Solving is assessed across all CCEA GCSE Mathematics content. Questions place familiar mathematics in unfamiliar or multi-step contexts and reward clear communication: identifying information, choosing a method, showing working and interpreting the answer.
Core rules
- Read the whole question before calculating; identify what is given and what is required.
- Break a multi-step problem into stages and label each result with its meaning and units.
- Use “hence” to mean “use your previous answer”; “show that” requires every step of a proof or derivation.
- Estimate by rounding each value to 1 significant figure, then check whether the exact answer is reasonable.
- Convert units before calculating: 1 m = 100 cm, 1 km = 1000 m, 1 hour = 60 minutes, 1 m/s = 3.6 km/h.
- When a question asks to explain or compare, finish with a sentence that answers it directly.
Worked example
A car travels 84 km in 1 hour 10 minutes. Find its average speed in km/h. Convert the time: 1 hour 10 minutes = 70 minutes = 70/60 = 7/6 hours. Speed = distance ÷ time = 84 ÷ (7/6) = 84 × 6/7 = 72 km/h. Check: 72 km/h for 7/6 hours gives 72 × 7/6 = 84 km, as required.
Traps
Using 1.1 hours for 1 hour 10 minutes; stopping at an intermediate value without answering the actual question; rounding too early; giving a bare number when the question asks for a conclusion; mixing units such as minutes and hours in the same calculation.