Finishing a past paper gives you a useful collection of questions to revisit. Checking the score is only one part of that work. For each question you missed, try to identify the first step that needs changing.

You can use this routine with a full paper, a topic set or a few questions from a lesson. Choose two or three mistakes to review carefully rather than attempting to repair everything in one sitting.

Look for the first wrong decision

Suppose a question asks you to factorise:

x2+5x+6

You write (x + 1)(x + 6). The numbers multiply to 6, which looks promising. But they add to 7, so the middle term is wrong. Expanding your answer makes the problem visible:

(x+1)(x+6)=x2+7x+6

The issue is specific: you checked the product but not the sum. Writing “bad at factorising” would not tell you what to do next. Writing “check both the constant term and the middle coefficient” does.

Repair the method

For a quadratic in the form x² + bx + c, look for two numbers that multiply to c and add to b. This shortcut applies when the coefficient of x² is 1.

Here, 2 and 3 satisfy both conditions: 2 × 3 = 6 and 2 + 3 = 5. Therefore:

x2+5x+6=(x+2)(x+3)

Expand the brackets to check: the four products are x², 3x, 2x and 6. Combining the middle terms returns the original expression.

Separate the kinds of mistake

When reviewing another question, choose a description that fits:

  • Method: I did not know how to start, or chose a method that did not fit.
  • Execution: The method was suitable, but a sign, calculation or algebra step went wrong.
  • Reading: I overlooked an instruction, unit or part of the question.

More than one description may apply. Use them to choose the next task. A method gap may need one explained example; a repeated sign error may need a few carefully written lines; a missed instruction needs a deliberate final check against the question.

Reattempt without the solution

  1. Correct the original question. Explain the change in a sentence.
  2. Close the worked answer. Solve a similar question independently.
  3. Return on another day. Reattempt the original or another question with different numbers.

For this example, try factorising x² + 7x + 10. Check both conditions before writing the brackets, then expand to verify them.

Check your reattempt

The numbers are 2 and 5: their product is 10 and their sum is 7. The factorisation is (x + 2)(x + 5).

Keep a short record of the question, the first wrong step and the check you will use next time. When you practise another paper, look for that same decision. The aim is to replace a repeated mistake with a method you can explain and use independently.