How to Check Your Answers in an IGCSE Maths Exam

Why Checking Matters

In IGCSE Mathematics, careless errors cost students more marks than lack of knowledge. A study of examiner reports for paper 0580 consistently shows that students lose marks not because they cannot do the maths, but because they make avoidable mistakes: sign errors, misread questions, arithmetic slips, and forgotten units.

Effective checking is a skill, not just a matter of “looking over your work.” It requires specific techniques and a systematic approach. The good news is that these techniques can be learned and practised.

How Much Time Should You Leave for Checking?

As a general guide:

• Paper 1 / Paper 2 (non-calculator): Aim to finish with 10-15 minutes to spare.
• Paper 3 / Paper 4 (calculator): Aim to finish with 15-20 minutes to spare.

If you cannot finish with this much time left, you may be spending too long on individual questions. Practise past papers under timed conditions to improve your pace.

Strategy 1: Substitution

This is the most powerful checking technique for algebra questions. If you have solved an equation to find x = 5, substitute x = 5 back into the original equation and verify that both sides are equal.

When to Use It

• Solving linear equations
• Solving quadratic equations (check both solutions)
• Solving simultaneous equations (substitute both values into both original equations)
• Finding the equation of a line (substitute a known point)

Example

You solved 3x + 7 = 22 and got x = 5.

Check: 3(5) + 7 = 15 + 7 = 22. Correct.

For simultaneous equations, suppose you found x = 3, y = −1 from the system:

2x + y = 5

x − 3y = 6

Check equation 1: 2(3) + (−1) = 6 − 1 = 5. Correct.

Check equation 2: 3 − 3(−1) = 3 + 3 = 6. Correct.

Both equations are satisfied, so the solution is correct. This takes 30 seconds and catches the most common errors in simultaneous equations.

Strategy 2: Estimation

Before accepting any numerical answer, ask yourself: does this answer make sense?

When to Use It

• Word problems involving money, distance, time, or measurements
• Percentage calculations
• Area and volume questions
• Probability (answers must be between 0 and 1)
• Any question where you can gauge a reasonable range

Example

A question asks for the volume of a cylinder with radius 3 cm and height 10 cm. You calculate 282.7 cm³.

Quick estimate: The cylinder fits inside a box of 6 × 6 × 10 = 360 cm³. A cylinder fills roughly 78% of its bounding box (since π/4 ≈ 0.785), so approximately 0.78 × 360 ≈ 281 cm³. Your answer of 282.7 cm³ is consistent. If you had accidentally written 28.27 cm³ or 2827 cm³, the estimation would immediately flag the error.

Red Flags to Watch For

• A person’s age coming out as 150 years
• A probability greater than 1 or less than 0
• A length or area that is negative
• A percentage discount that makes the price higher
• A speed of 500 km/h for a car journey

Strategy 3: Reverse Working

Work backwards from your answer to see if you arrive at the information given in the question.

When to Use It

• Percentage increase/decrease problems
• Ratio questions
• Algebraic problems where you can verify the answer independently

Example

A shop increases prices by 20%. The new price is RM 72. You calculated the original price as RM 60.

Reverse check: 20% of 60 = 12. Original price + increase = 60 + 12 = 72. Correct.

If you had mistakenly calculated 72 ÷ 1.2 = 58.33 (wrong), the reverse check would show: 20% of 58.33 = 11.67, and 58.33 + 11.67 = 70, which is not 72. The error is caught.

Strategy 4: Re-read the Question

This sounds obvious but is surprisingly effective. After solving a question, re-read it and check:

• Did you answer what was actually asked? If the question asks for the perimeter, did you give the area? If it asks for y, did you give x?
• Did you give the answer in the correct form? The question might ask for the answer “in terms of π,” “as a fraction,” “correct to 3 significant figures,” or “in standard form.”
• Did you include units? If the question involves measurement and does not say “state the units,” check whether units are expected.
• Did you give all the answers? A quadratic equation has two solutions. An inequality might need a range. “Find the coordinates” means both x and y.

Strategy 5: Use a Different Method

If time permits, solving a question a second way is the most thorough check possible. For example:

• Solve a quadratic by factorising, then verify using the quadratic formula.
• Find a gradient using the formula, then check by counting rise/run on the graph.
• Calculate a mean from raw data, then verify using a frequency table approach.

This technique is time-consuming, so reserve it for high-mark questions where you are uncertain of your answer.

Strategy 6: Check Your Calculator Work

Calculator errors are more common than students realise. The most frequent mistakes:

• Bracket errors: 5 + 3² is not the same as (5 + 3)². Make sure your calculator is evaluating the expression you intend.
• Negative number errors: (−3)² = 9 but −3² = −9 on most calculators. Use brackets around negative numbers.
• Mode errors: Ensure your calculator is in degrees mode for trigonometry, not radians.
• Transcription errors: You might press 56 instead of 65. Re-enter critical calculations.

A Systematic Checking Routine

When you finish the paper, do not just read through your work passively. Use this routine:

1. First pass (2-3 minutes): Scan every question to make sure you have not left any blank. Attempt any you skipped.
2. Second pass (5-10 minutes): For each answer, apply the most appropriate checking technique above. Prioritise high-mark questions.
3. Third pass (remaining time): Re-read questions you found difficult. Check that your final answers match the required format.

Do not change an answer unless you have a clear reason to. Your first instinct is often correct, and second-guessing without evidence can introduce new errors.

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