Reasoning questions ask you to explain or justify rather than just calculate. They use phrases like "show that", "prove that", "give a reason for", or "explain why".
"Show that" questions: Work through the calculation fully. Don't just write the final answer — the marker needs every step. If the target answer is given in the question, that's your cue to be extra careful.
"Prove that" questions: Start from known facts and build logically towards the result. Each line must follow from the last. You cannot assume what you're trying to prove.
"Give a reason" (geometry): Quote the theorem by name. Writing just a number isn't enough — you need "angles on a straight line sum to 180°" or "alternate angles are equal". See Angle facts and Circle theorems for the ones to learn.
Algebraic proof — useful tools:
- Even number: $2n$
- Odd number: $2n + 1$
- Consecutive integers: $n$, $n+1$, $n+2$
- Consecutive even numbers: $2n$, $2n+2$, $2n+4$
Expand and simplify fully — your final line should make the conclusion obvious.
Example: Prove that the sum of any two consecutive odd numbers is divisible by 4. $$\text{Two consecutive odd numbers: } (2n+1) + (2n+3) = 4n + 4 = 4(n+1)$$ This is a multiple of 4. $\square$