GCSE Maths revision,
one topic at a time.
By Topicly, operated by Knowledge Quay · Updated
A whole exam paper can feel like a lot to fix at once. Start with one skill: understand a worked example, try a question without looking, then check the exact step that needs more practice.
This guide explains six starting points, with original examples and practice answers. Use your school’s topic list and exam-board specification to plan the rest of your revision.
Find the step that went wrong.
Use a recent class question, homework task or marked practice paper. “I’m bad at algebra” is too broad to act on. “I forget to divide both sides of an equation” gives you something specific to work on.
- Try the question without notes.Keep your working, even if you cannot finish. If you do not know how to start, write down what the question gives you and what it asks you to find.
- Compare the method, not just the answer.Find the first line where your working differs from a correct solution. Was it a method choice, an arithmetic slip, a notation problem or a misunderstanding of the question?
- Name one skill.Write a short target, such as “use a common denominator” or “identify the hypotenuse”. Check an earlier skill first if it is causing the difficulty.
- Practise, then revisit.Try a similar question on your own. Later, mix it with questions on other topics so you have to choose the method yourself.
Where does your topic fit?
GCSE Maths in England covers six broad areas. These examples show how to turn an area into a smaller revision target.
- Number
- For example, adding fractions rather than “all number work”.
- Algebra
- Solving a two-step equation rather than “all algebra”.
- Ratio, proportion and rates of change
- Finding one part when sharing an amount in a ratio.
- Geometry and measures
- Choosing which side is the hypotenuse before using Pythagoras.
- Probability
- Counting all the equally likely outcomes.
- Statistics
- Choosing between the mean, median and mode for a question.
The subject areas follow the Department for Education’s GCSE Maths content. Check your own qualification and specification with your school.
How do you add fractions with different denominators?
Find a common denominator, rewrite the fractions as equivalent fractions, add the numerators and simplify. Keep the common denominator when adding: it tells you the size of the equal parts.
Worked example
Calculate 3/4 + 2/3. Give your answer as a simplified fraction or mixed number.
- Choose a common denominator. The lowest common multiple of 4 and 3 is 12.
- Multiply the numerator and denominator of 3/4 by 3: 3/4 = 9/12. Multiply both parts of 2/3 by 4: 2/3 = 8/12.
- The parts are now the same size, so add the numerators: 9/12 + 8/12 = 17/12.
- There are 12 twelfths in one whole. 17/12 = 1 5/12 (one and five twelfths).
Check your answer. Both starting fractions are greater than 1/2, so their sum should exceed 1. An answer of 1 5/12 makes sense.
A mistake to avoid
Adding the denominators gives 5/7, which is incorrect. You are adding quantities of equal-sized parts, not changing the size of those parts.
Try it yourself
Calculate 2/5 + 1/4 in its simplest form.
Show the answer and method
13/20. Use twentieths: 2/5 = 8/20 and 1/4 = 5/20. Add 8 + 5, keeping the denominator 20.
How do you calculate a price after a percentage decrease?
Calculate the percentage of the original price, then subtract that amount from the original price. A percentage is a number of parts out of 100; the discount and the final price are different amounts.
Worked example
A jacket costs £80. Its price is reduced by 15%. What is the sale price?
- Find 10% of £80 by dividing by 10: £8.
- Find 5% by halving the 10% amount: £4.
- The 15% discount is £8 + £4 = £12.
- Subtract the discount from the original price: £80 − £12 = £68.
Check your answer. After a 15% reduction, 85% of the price remains. The multiplier method gives the same result: 80 × 0.85 = 68.
A mistake to avoid
£12 is the discount, not the sale price. Also, subtracting 15 from 80 treats a percentage as a fixed number of pounds.
Try it yourself
A ticket costs £64. Its price increases by 12.5%. Find the new price.
Show the answer and method
£72. 12.5% is 1/8, and 64 ÷ 8 = 8. Add the £8 increase to £64. Alternatively, 64 × 1.125 = 72.
How do you solve a two-step linear equation?
Undo the operations in reverse order, applying each operation to both sides, until the unknown is on its own. Doing the same thing to both sides keeps the equation balanced.
Worked example
Solve 3x + 7 = 22.
- Undo the addition first. Subtract 7 from both sides: 3x = 15.
- 3x means 3 multiplied by x. Divide both sides by 3: x = 5.
- Write the value of the unknown clearly. The solution is x = 5.
Check your answer. Put 5 into the original equation: 3 × 5 + 7 = 15 + 7 = 22. Both sides match.
A mistake to avoid
Changing only one side breaks the balance. Dividing 22 by 3 straight away also leaves the +7 unaccounted for. Keep a line of working for each operation.
Try it yourself
Solve 4x − 9 = 19.
Show the answer and method
x = 7. Add 9 to both sides to get 4x = 28, then divide both sides by 4. Check: 4 × 7 − 9 = 19.
How do you share an amount in a given ratio?
Add the ratio parts, divide the total amount by that sum to find one part, then multiply by each person’s number of parts. A part-to-part ratio compares the shares.
Worked example
Share £84 between Aisha and Ben in the ratio 3 : 4.
- Find the total number of parts: 3 + 4 = 7.
- Divide the total money by 7 to find one part: £84 ÷ 7 = £12.
- Aisha gets 3 parts: 3 × £12 = £36.
- Ben gets 4 parts: 4 × £12 = £48.
Check your answer. £36 + £48 = £84, so all the money is shared. The ratio 36 : 48 simplifies to 3 : 4 when both numbers are divided by 12.
A mistake to avoid
Aisha’s share is 3/7 of the total, not 3/4. The 4 describes Ben’s parts; the whole has 7 parts.
Try it yourself
Share £90 in the ratio 2 : 3.
Show the answer and method
£36 and £54, in that order. There are 5 parts, so one part is £18. The shares are 2 × £18 and 3 × £18.
How do you use Pythagoras to find a missing side?
In a right-angled triangle, use a² + b² = c², where c is the hypotenuse: the longest side, opposite the right angle. Add the squares of the shorter sides to find c², or subtract a shorter side’s square from c² to find the other side’s square. Then take the positive square root.
Worked example
A right-angled triangle has shorter sides of 6 cm and 8 cm. Find the hypotenuse.
- The missing side is the hypotenuse, so add the squares of the two shorter lengths: c² = 6² + 8².
- Calculate the squares: c² = 36 + 64 = 100.
- Take the positive square root, because a length is positive: c = √100 = 10 cm.
Check your answer. The answer, 10 cm, is longer than either shorter side. Substitution also works: 6² + 8² = 10².
A mistake to avoid
6 + 8 = 14 does not use the theorem. Stopping at 100 also misses the final square root. Check that the triangle has a right angle before using this method.
Try it yourself
A right-angled triangle has a hypotenuse of 13 cm and one shorter side of 5 cm. Find the other shorter side.
Show the answer and method
12 cm. This time subtract to find the missing shorter side: b² = 13² − 5² = 169 − 25 = 144. Taking the positive square root gives b = 12 cm.
How do you calculate the probability of a single event?
When individual outcomes are equally likely, divide the number of outcomes you want by the total number of possible outcomes.
Worked example
A bag contains 3 red, 5 blue and 2 green counters. Each counter is equally likely to be selected. What is the probability of choosing a blue counter?
- Count all the counters: 3 + 5 + 2 = 10.
- There are 5 blue counters, so the probability is 5/10.
- Simplify the fraction: 5/10 = 1/2. This is also 0.5 or 50%.
Check your answer. Five of the ten counters are blue, so half the counters give the desired result. The probability lies between 0 and 1.
A mistake to avoid
There are three colours, but they are not equally likely. The counters are the equally likely outcomes, so 1/3 would be incorrect.
Try it yourself
A different bag has 4 red, 3 blue and 5 green counters, each equally likely to be chosen. What is the probability of choosing a counter that is not green?
Show the answer and method
7/12. There are 12 counters in total and 4 + 3 = 7 that are not green. You can also calculate 1 − 5/12 = 7/12.
A manageable next revision session.
Use this as a flexible 20-minute starting plan. Spend longer on a step if you need to; finishing quickly is less useful than knowing why the method works.
- Minutes 0–3: choose one target.Pick a specific skill from your marked work or school checklist. Try a short question to see what you remember.
- Minutes 3–8: explain a worked example.Read each step and say why it is allowed. Cover the solution and reconstruct the method in your own working.
- Minutes 8–16: practise independently.Try two or three relevant questions from your school resources. Check the method after each attempt and correct any mistake.
- Minutes 16–20: record your next step.Write what you can now do and what still needs help. Revisit the topic another day, including a question mixed with other topics.
If you still cannot explain a step, turn it into a question: “Why do we subtract the square of the shorter side here?” is more useful than “I don’t get Pythagoras”. Take that question to your teacher, or look for a published lesson that addresses the skill.
GCSE Maths revision questions.
Is this guide for Foundation or Higher?
These are introductory examples of selected GCSE methods. They do not cover either tier in full or assign a grade to a skill. Ask your school which tier you are taking, and use your exam-board specification to check the depth and range of content you need.
Should I revise by topic or do whole papers?
Use topic practice to work on a specific gap, then try mixed questions to practise choosing a method. Whole papers can help you practise timing and show which skills need another visit. Use papers for your qualification and tier, and review your working afterwards.
What if I can follow the example but cannot answer a new question?
Try covering the solution and explaining each step from memory. Then use a similar question with different numbers. If you get stuck, identify the first decision you could not make and practise that part before trying the whole question again.
How does a Topicly lesson fit into revision?
Topicly’s planned live GCSE Maths lessons focus on one topic at a time for learners in Years 9–11. A £5 booking is for one named learner in one lesson, with no subscription. Check the published GCSE Maths timetable for the topic, tier, prerequisites, date and booking availability. The examples on this page do not guarantee that a matching lesson is available.
Does Topicly offer A-level Maths?
A-level lessons are coming soon. They are not currently open for booking. This guide focuses on GCSE Maths.
Official curriculum references
The links below explain GCSE Maths content in England. The worked examples and practice questions on this page are original Topicly learning material.
- Department for Education: GCSE mathematics subject content and assessment objectives
- AQA GCSE Mathematics 8300: subject content and tier information
Use the specification for the qualification and exam board your school has chosen.