Why are the questions difficult?
- They combine topics such as calculus, trigonometry and vectors
- They present familiar mathematics in unfamiliar contexts
- They require a non-obvious starting point
- They expose gaps in earlier GCSE or A-Level foundations
Step 1: Deconstruct the question
- Read twice and note command words
- Highlight given values, variables and conditions
- Write down the exact outcome the question asks for
Step 2: Formulate a plan
- Recall connected formulas or theorems
- Break the problem into smaller steps
- Try a different representation if the first route stalls
Step 3: Show working clearly
- Write numbers and variables legibly
- Show each meaningful step
- State assumptions
- Use correct mathematical notation
Step 4: Check and reflect
- Ask whether the result is reasonable
- Reread the required outcome
- Check algebra, signs, units and substitutions
Step 5: Practise deliberately
- Use later questions from past papers
- Target weak areas such as specific calculus or proof skills
- Get feedback from a teacher or tutor
- Keep an error log and redo the question
Final thought
Deconstructing, planning, showing working and checking can turn an intimidating question into a sequence of manageable decisions.