Mastering the syllabus is only half the battle; the rest is strategy. Exams are a specific skill in their own right, and how you execute on the day often determines the difference between a good grade and a great one.
Below is a comprehensive collection of the most effective strategies I have compiled over years of teaching. These techniques are designed to help you command the paper, manage your time ruthlessly, and ensure your final grade reflects your true ability.
Practice past papers under timed, no-note conditions. This helps you get used to the pace and spot where you need to speed up or slow down.
Know exactly which formulas are provided in the booklet and which you must know by heart. Dedicate time to memorising essential formulas and practice applying them until they become second nature. OCR provides a list of these here.
The exam will provide the specific data you need for calculations. However, you are expected to be familiar with its context, variables, and limitations to answer written interpretation questions. Here are summaries of the data sets for each exam board:
Familiarise yourself with command words. These provide instructions and hints for how to write your answer.
Calculate / Find / Solve / Evaluate
Obtain the final answer. While a correct answer can sometimes yield full marks on its own, you are strongly advised to show your working. If you make a small error without working, you score zero. You may use your calculator, but write down the equation to secure method marks (in case you make an input error).
Determine
Obtain the final answer, but you must provide justification or show the specific steps/calculation used to reach it.
Exact
Give the answer as a fraction, surd, or in terms of π, ln, or e. Never use rounded decimals in your workings.
Estimate
Use the provided information or a mathematical model (e.g. trapezium rule, Newton-Raphson, small-angle approximations) to find an approximate value. Do not try to calculate the exact answer.
State / Write down / Give
No working out is required. The answer should be obvious from the question, a graph, or your calculator.
Identify
Select the correct answer from a list, a set of options, or a graph.
Prove
A formal, rigorous argument. You must clearly define any variables used, show clear logical steps, and finish with a formal concluding statement.
Show that
You are given the answer; your job is to prove it is true. You must show every single step of the derivation; do not risk skipping lines of algebra just because you can do them in your head. You must finish with a concluding statement.
Show detailed reasoning
You must demonstrate the detailed analytical method used to solve the problem. You may use a calculator to check values or perform arithmetic, but the logical steps must be fully written out on the page.
Verify
Substitute a value into an equation to demonstrate that it works.
Hence
You must use the result found in the previous part of the question. Any other method, even if correct, typically scores zero marks.
Hence or otherwise
You should use the previous result (it’s usually faster), but other valid methods are permitted.
Deduce
Use a previous result to find the answer with a little thinking. Minimal working is required.
Explain
Provide a concise written answer using correct mathematical vocabulary. If relevant, support your explanation with a calculation.
Interpret
Translate a mathematical result into a written statement about the real-world context (e.g. "The gradient represents the cost per item").
Comment on
Analyse your results. This often involves comparing your calculated value to a real-world fact or judging if a model is realistic/valid.
Compare
State a similarity or difference between two things. You must explicitly mention both items in your answer.
Sketch
Draw the general shape of the curve without graph paper. You must label key features such as axes intercepts, turning points, intersections and asymptotes (using dashed lines).
Plot
Mark specific points accurately on a grid and join them if required.
Draw
Create a diagram with appropriate accuracy. Include any labels, annotations, lengths or angles as these may justify marks.
Read more here:
Start from the beginning and work your way through. Early questions are easier and can boost your confidence. Label each section (e.g. (a), (b), (c)) so examiners can easily follow your work.
Don't get bogged down on a single question. If you are stuck, place a star ✱ next to it and move on. Returning to the problem later with a fresh perspective is more effective than staring at it for five minutes without progress. You will maximise your marks by maintaining your momentum.
The number of marks should guide your timings. Sticking to this pace gives you a 20-minute 'safety buffer' at the end to check your work and return to the hard questions you starred.
The mark allocation indicates the expected complexity and depth of your solution. Use it to guide how much you write.
1 Mark: Write the answer. These are usually “state” or “write down” questions. Typically, no workings are required. If the calculation feels complex, re-read the question: you’ve likely missed a shortcut.
2-4 Marks: Show your working. Method marks are often awarded even if the final answer is incorrect, so make your steps clear.
5+ Marks: A short answer here is a red flag. It suggests you have oversimplified the problem or relied too heavily on your calculator. These questions demand a rigorous, logical chain of reasoning.
A big, clear diagram can help simplify complex problems: vectors, coordinate geometry, trigonometry, normal distribution, force diagrams, etc. Visuals make it easier to process and understand all the information.
Answers without working may not gain full credit. Even if you can do it in your head, write it down. Always quote the formula you are using before you use it. Even if your final answer is wrong, you can still earn method marks.
If you can’t answer part (a), you may still be able to answer the other parts. You can still earn follow-through marks, even if you suspect your earlier answers are incorrect. If part (a) is a “show that” and you can’t prove it, assume the result is true and use it in (b).
Questions often build on one another, even without the word "Hence". If you are stuck, review your previous work. The result from part (a) is sometimes the key to unlocking part (b).
For complex, high-mark questions, you rarely see the full path to the solution immediately. Do not stare at the blank page. Instead, write down a relevant formula, draw a diagram, or perform any logical calculation with the given values. This momentum helps you secure early method marks and often helps reveal the rest of the path as you work.
If the question gives you a value, a diagram, or any extra condition, it’s likely there for a reason. If you’ve finished but haven’t used all the information, you’ve probably made a mistake. Pause and ask: Why did they tell me this? Unused information is often a clue that your method, interpretation, or model is incomplete.
For commands like "Find", "Calculate", "Evaluate" or "Solve", you may use your calculator’s advanced functions (e.g. polynomial solver, inequality solver, simultaneous equation solver) to save time. However, always write down the equation you are solving first. This acts as your "working out" and secures method marks if you make an input error.
However, you must show full algebraic working if:
The question contains “show all stages of your working” or requests “detailed reasoning”.
The command words are “Prove”, “Show that”, “Determine”, or "Solve algebraically".
The question asks for an “Exact value” (your calculator may not give you the exact answer).
In these cases, use your calculator only to check your final answer. A correct answer without a supporting method will likely score zero marks.
Also, for Edexcel:
"Solutions relying entirely on calculator technology are not acceptable" means your calculator is an assistant. You can use it for "grunt work" (arithmetic, evaluating logs, roots), but you cannot use it to completely bypass the actual method being tested.
"Solutions relying on calculator technology are not acceptable" means your calculator is banned. Your work must look as if you do not own a calculator.
The question’s specific wording often tells you how many answers are required.
“Find the value...” / “Estimate the root...”
Expect a single answer. If you find two, check if one needs to be discarded.
“Find the values...”
Expect multiple answers. If you only find one, you may have missed a solution (e.g. by dividing by a variable instead of factorising).
“Find the set of values...” / “Find the range of values...”
Expect an inequality.
“Find the coordinates...”
Don’t just find x and stop! Find the corresponding value of y and write the answer as a pair (x,y).
Correct algebra can produce answers that are mathematically impossible or contextually wrong. You must explicitly reject these to gain full marks.
Constraints:
Restricted Domain: Is the solution in the domain of the function?
Logarithms: You can only log numbers greater than 0.
Square Roots: You can only root numbers greater than or equal to 0.
Denominators: A solution that makes the denominator 0 is undefined (asymptote).
"Ghost" Solutions:
Squaring: If you squared both sides to solve, you may have created extraneous solutions. Check them in the original equation.
Modulus Equations: You may have found extraneous solutions. Check them in the original equation.
Out of Bounds:
Trigonometry: Is the solution inside the given interval (e.g. 0 < x < 360)?
Small Angle Approximations: Is the answer small and in radians?
Binomial Expansion: Is the input x valid for the expansion range?
Geometric Series: Is -1 < r < 1 for the series to be convergent?
Context:
Physical Quantities:
Time, mass, distance, and speed are scalar quantities and cannot be negative.
Displacement, velocity, and acceleration are vector quantities and can be negative.
Probability: Must be between 0 and 1.
Models: Is the answer sensible in the real-world context?
Check your mode before every problem.
If you see a π symbol, you’re in radians, and if you see a ° symbol, you’re in degrees.
For differentiation and integration of trig functions, you MUST be in radians.
Indefinite integrals always include a “+c”.
Rooting an equation produces positive and negative solutions: if x² = 4, then x = ±2.
However, evaluating a square root yields only the positive result: √4 = 2.
Exact form or decimal? Do they want set notation? Do they want a specific equation form (e.g. ax + by + c = 0)? Column vector or i and j vector notation? Degrees or radians?
Ensure all units are consistent before calculating (e.g. matching km/h with hours).
Check if the question requires a specific unit for the final answer.
Missing or incorrect units can lose a mark, even if the numerical value is correct.
Always check the required level of accuracy (e.g. 1 decimal place).
When no specific degree of accuracy is stated, three significant figures is normally acceptable for final answers.
Avoid rounding until your final answer.
If a question asks to find an equation linking variables H and t, you must use them in your final answer. Writing a generic equation like y = mx + c instead of H = mt + c will lose the final accuracy mark.
Check the variable’s scale: "population P, measured in thousands" means that if the question gives you 5,000 people, you must substitute P = 5 into the equation.
Check how the variable is defined:
Relative wording: If t is defined as "years after 1990", then for 2005, use t = 15, not t = 2005.
Cumulative wording: If a model gives you the “total sales after t months” but asks for sales specifically “in the 5th month”, you will need to find the difference between t = 5 and t = 4.
Ask yourself: Does this make sense? A car going 400mph? A coefficient of friction of μ = 9.2? A negative variance? If something looks wrong, go back and check your workings.
To fully define a function, you must state its domain. When finding f⁻¹(x), always state its domain, even if not explicitly asked. This is often worth a mark.
Tip: The domain of the inverse is the range of the original function.
In statistics, remember to relate your answers to the context. When interpreting answers, critiquing assumptions, or concluding hypothesis tests, ensure your response relates back to the real-world scenario.
Keep the full calculator values throughout your workings by using the ANS or STO functions, and round only at the end to avoid introducing errors. In mechanics, use g = 9.8 m/s² unless the question specifies otherwise, and make sure any final answers that rely on this value are rounded to three significant figures.
Sometimes examiners are very strict with “show that” questions. Your final answer should match the given form exactly: same structure, letters, and order. If they want “S=½Mgcotθ”, then concluding with “S=½cotθMg” can (unfairly) lose you a mark. Be precise in your final step.
Misreading or misinterpreting questions are common pitfalls; take your time to read and understand what’s being asked carefully. Work through the problem one step at a time, pausing regularly to review your reasoning and calculations. Before moving on, double-check your answer to confirm you’ve addressed every element of the question.
Recalculate tricky expressions.
Use the powerful functions on your calculator to double-check quadratic/cubic equations, quadratic inequalities, simultaneous equations, definite integrals, derivative evaluations, and summations.
Substitute your solution back into the original equation to confirm it holds true.
On the CG50, you can check the solutions to sinx = tanx by graphing y = sinx and y = tanx and finding their intersections.
At the end, go through your paper with fresh eyes. Confirm that every part is answered, and the calculations are accurate. If time allows, redo tricky questions without looking at your original solution: you're unlikely to make the same error twice.
If you realise you have made a mistake, draw a single, neat diagonal line through the work.
If you replace it: Examiners will ignore the crossed-out work and mark the new attempt.
If you do not replace it: Examiners will mark the crossed-out work (provided it is legible).
Do not scribble it out completely: You may need to refer back to it, or you may realise it was actually correct!
Don’t overwrite: Never turn a "3" into a "5". Cross out the old number and write the new one clearly alongside.
Always clearly cross out attempts you do not want marked. If you leave two attempts uncrossed:
Edexcel: Marks the final attempt that is most complete.
AQA: Marks the best attempt (but may withhold marks if the answers contradict each other).
OCR: Marks the last attempt (unless it is substantially less complete).
💤 Sleep: Prioritise 8 hours of sleep over late-night cramming. A tired brain makes calculation errors.
🎒 Equipment: Pack your clear pencil case: spare black ballpoint pens, sharp pencils, ruler, eraser, highlighter. A compass is useful for accurate circle sketches.
💧Water: Pack a clear water bottle with the label removed.
📟 Calculator: Remove the lid and check the battery/charge.
🆔 ID: Pack your student ID card.
🍳 Nutrition: Eat a slow-release energy breakfast (porridge, oats, eggs, toast).
👕 Clothing: Exam halls are unpredictable. Wear a t-shirt with a hoodie/jumper over it so you can adapt to the AC or heat.
📟 Calculator: Ensure "Exam Mode" is active (e.g. FX-CG50, Numworks). Set to Degrees mode for Statistics and Mechanics.
🥪 Afternoon Exams: Eat a proper lunch. Stick to light revision only: flashcards and formulas.
⏱️Arrival: Arrive early to avoid stress, and visit the bathroom before entering.
🕰️ Clock Visibility: Locate the clock. If it's not visible, tell the invigilator.
🪑 Wobbly Desk: If your desk wobbles, ask for a folded sheet of paper.
🧠 Brain Dump: Once the exam starts, flip to the first blank page and write any formulae not provided that you typically forget.