Stuck on a maths problem? What to do before you look at the memo

Being stuck is a normal part of doing maths. Even people who are very good at maths get stuck all the time. The difference is that they have a routine for getting unstuck, and they don't reach for the answer the moment it gets hard.

Looking at the memo too soon feels helpful, but it takes away the one thing that makes you better at maths: working out the next step yourself. In the exam there's no memo. Here's a routine to try first.

1. Read the question again, slowly

A surprising number of "I'm stuck" moments come from misreading the question. Read it again and underline:

• What you're given. Every number, equation and condition.
• What you're asked for. Exactly what the final answer should be.
• The key words. "Hence" means use the previous answer. "Show that" means you already know the answer and must prove it. "Determine" means work it out.

If the question says "hence", the method is almost always in the part before.

2. Write down what you know

Write the given information in maths, not words. "The graph passes through (2; 5)" becomes f(2) = 5. "The gradient at x = 1 is zero" becomes f′(1) = 0.

Seeing it written as equations often shows you the next step.

3. Ask: what does this remind me of?

Most exam questions are variations of questions you've done before. Ask yourself:

• Which topic is this from?
• What methods do I know for this topic?
• Have I seen a question with the same kind of ending?

If the question wants a turning point, you know tools for that: completing the square, the axis of symmetry formula or setting the derivative to zero. Try one.

4. Draw something

A sketch is often the fastest way to get unstuck, especially in functions, geometry, trigonometry and word problems. Draw the graph, the triangle or the situation. Label everything you know.

In geometry, mark equal angles and sides on the diagram as you find them. The next step often appears on the sketch.

5. Try a simpler version

If the problem is too complicated, make it simpler:

• Replace awkward numbers with easy ones and see what happens.
• Try the first few terms of a sequence by hand.
• Solve a special case first, like x = 0 or x = 1.

Once you see the pattern in the simple version, go back to the real one.

6. Work backwards

Start from what you need to find and ask: "What would I need to know to get this?" Then: "What would I need to know to get that?" Keep going until you reach something the question gave you.

This works especially well for "show that" questions and geometry proofs.

7. Take a short break

If you've tried properly for 10–15 minutes, step away for a few minutes. Your brain keeps working on problems in the background, and many people find the answer comes to them when they come back.

8. When you do get help, ask for a hint, not the answer

If you're still stuck, get help, but only as much as you need. Ask a friend, teacher or tutor for the next step, not the full solution. Then try to finish it yourself.

This is how Qondi works: snip the question and it asks what you've tried, then gives you just enough to take the next step. If you're really stuck, it shows a worked example of a similar question so you can still solve yours.

9. After you've solved it, look back

Once you've got the answer, spend one minute on this: what was the key idea that got you unstuck? Write it next to the question.

That one line is what you'll remember in the exam, when you see a question like it again.

A quick checklist

Next time you're stuck, work through this list before opening the memo:

1. Did I read the question properly and underline what's asked?
2. Have I written the given information as equations?
3. Which topic and methods does this remind me of?
4. Have I drawn a sketch?
5. Can I try a simpler version or work backwards?
6. If I need help, am I asking for a hint rather than the answer?