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1. Find out what they are working on

Ask which topic they are on this week, or look at their last piece of homework. Every GCSE Maths topic has a free page that sets out what the exam asks, where students usually lose marks, and how the questions tend to be worded. No account needed.

2. Use worked examples the right way

Each topic page has worked examples, one step at a time. Cover the working, let them have a go, then uncover one step at a time to check. Reading through a finished answer feels like learning; trying first and then checking each step is what makes it stick.

3. Eight mistakes that cost marks

These come up again and again. Each links to a worked example that shows the right method.

1. Taking a percentage off the price they were given, to find the price before a discount.

   The price they were given is what is left. After a 10% discount it is 90% of the original, so divide by 0.9. See the worked example

2. Adding percentage changes that happen one after another.

   A 20% rise then a 15% fall is not a 5% rise. Multiply the multipliers: 1.2 × 0.85. See the worked example

3. Adding the squares when the missing side is one of the shorter ones.

   Add to find the longest side (the hypotenuse); subtract to find a shorter side. See the worked example

4. Moving a number across the equals sign without doing the opposite operation.

   Do the same thing to both sides, and write each step down. See the worked example

5. Dividing by one number of the ratio when sharing an amount.

   Add the parts first: in 3 : 5 there are 8 parts, so one part is the total divided by 8. See the worked example

6. Adding probabilities when two things both have to happen.

   Both happening (AND) means multiply. Either one happening (OR, when they cannot both happen) means add. See the worked example

7. Dividing by the number of rows in a frequency table to find the mean.

   Divide by the total frequency: how many values there are altogether, not how many rows. See the worked example

8. Using the diameter where the formula needs the radius.

   The radius is half the diameter. Check which one the question gives before using a formula. See the worked example

4. A little and often beats one long session

Ten minutes of mixed questions on topics from a few weeks ago does more than an hour re-reading notes. Testing yourself, rather than re-reading, is one of the best-supported findings in research on learning. The free retrieval games are made for exactly this: fifteen quick questions per topic, with the method behind every answer.

5. Show the working, every time

Many GCSE Maths questions give marks for the method as well as the answer, so a wrong final answer can still earn most of the marks, and a right answer with no working can lose them. If they get it right in their head, ask them to write down how.

6. Practise without a calculator too

AQA GCSE Maths is three papers, and the first does not allow a calculator. Keep some practice calculator-free, especially percentages, fractions and working with negative numbers.

7. When to ask for more help

If the same topic keeps going wrong after a few goes, tell their teacher which topic and which mistake. Specific information is the most useful thing you can give them, and it is exactly what the list above helps you spot.

More for parents: Foundation or Higher? and a 12-week revision plan. Coming soon: a printed GCSE Maths workbook, with every answer and mark scheme in the back.