Module 5: Exam Skills, Formulae & Command Words
Master Exam Technique, Official Formulae & Command Words
Knowing mathematical content is only half the battle. Exam technique, precise working layout, and understanding command words are what separate grade 7 students from grade 9 students.
1. Decoding GCSE Maths Command Words
| Command Word | What the Examiner Expects | Common Trap |
|---|---|---|
| "Work out / Calculate" | Perform mathematical operations and give a numerical answer with working. | Writing down final answer without showing working (loses method marks). |
| "Show that..." | Provide a complete, unbroken logical chain of proof leading to the stated answer. | Using the target number inside the calculation itself. |
| "Write down / State" | Direct recall or reading a value from a graph. No working required. | Wasting time performing long calculations for a 1-mark question. |
| "Give a reason for your answer" | Write the formal geometric/statistical theorem rule in plain English. | Using informal slang like "Z-angle" instead of "Alternate angles are equal". |
| "Estimate" | Round every number to 1 significant figure BEFORE performing calculation. | Calculating exact answer first and rounding at the end (scores 0 marks!). |
2. Must-Memorise Formulae Sheet
Formulae You MUST Memorise (Not Provided in Exam)
- Area of Circle: Area = π r²
- Circumference of Circle: Circumference = 2 π r = π d
- Area of Trapezium: Area = ½ (a + b) h
- Speed, Distance, Time: Speed = Distance ÷ Time
- Density, Mass, Volume: Density = Mass ÷ Volume
- Pressure, Force, Area: Pressure = Force ÷ Area
- Pythagoras Theorem: a² + b² = c²
- Trigonometric Ratios: sin θ = O/H, cos θ = A/H, tan θ = O/A
Paper 1 Non-Calculator Tip: Practice multiplying fractions, converting decimals to fractions, and using prime factor trees mentally. Speed on Paper 1 frees up time to double-check multi-step questions!
3. Time Management & Exam Day Strategy
- Pacing: You have 90 minutes for 80 marks. Aim for approximately 1 minute per mark, leaving 10 minutes at the end for checking.
- First Pass: Complete all questions you find easy first. If stuck on a multi-step question for more than 3 minutes, circle it and move on!
- Never Leave Blanks: Even if you cannot finish a 5-mark question, write down relevant formulae, state variables, or perform initial conversions to secure 1–2 method marks.
- Check Realism: Does your answer make real-world sense? (e.g. A person cannot run at 120 mph, and a probability cannot exceed 1.0!).
Frequently Asked Questions
Major exam boards provide formulae for: (1) Volume of a sphere (4/3 π r³) & surface area (4 π r²), (2) Volume of a cone (1/3 π r² h) & curved surface area (π r l), and (3) Kinematics / quadratic formula (on Higher tier). You MUST memorise areas of circles, trapeziums, trigonometry, and Pythagoras!
'Show that' means the final answer is already given in the question prompt. You MUST write down every single line of working out clearly step-by-step to prove how that value is reached. Never start your calculation with the target answer!
Label each line of working (e.g. 'Step 1: Calculate hypotenuse', 'Step 2: Calculate shaded area'). Keep units clear, and underline your final answer at the bottom right of the answer space.