Common Exam Mistakes

Knowing the common mistakes that cost students marks on Edexcel GCSE Mathematics — and how to avoid them — is one of the fastest ways to improve your grade. This lesson catalogues the most frequent errors and gives you strategies to prevent each one.

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Mistake 1: Sign Errors

Sign errors (getting positives and negatives mixed up) are the single most common source of lost marks.

Where Sign Errors Happen

• Expanding brackets with negatives: −3(x − 4) = −3x + 12 (NOT −3x − 12)
• Collecting like terms: 5x − 3 − 2x + 7 = 3x + 4 (watch the signs on every term)
• Substituting negative values: If x = −2, then $x^{2} = (-2)^{2} = 4$x2=(−2)2=4, NOT −4
• Solving equations: When you move a term across the equals sign, the sign changes
• Negative coordinates: Misplotting (−3, 2) as (3, −2)

How to Avoid Sign Errors

1. Write out every step — do not try to do two operations at once.
2. When expanding a negative bracket, write the multiplication for each term separately.
3. When substituting, always put negative numbers in brackets: $(-2)^{2}$(−2)2 not $-2^{2}$−22.
4. After collecting like terms, re-check by substituting a simple value (like x = 1) into both the original and simplified expressions.

Worked Example 1

Question: Expand and simplify (x + 5)(x − 3) − 2(x + 1).

Step 1: $(x + 5)(x - 3) = x^{2} - 3x + 5x - 15 = x^{2} + 2x - 15$(x+5)(x−3)=x2−3x+5x−15=x2+2x−15 Step 2: 2(x + 1) = 2x + 2 Step 3: $(x^{2} + 2x - 15) - (2x + 2) = x^{2} + 2x - 15 - 2x - 2 =$(x2+2x−15)−(2x+2)=x2+2x−15−2x−2= $x^{2} - 17$x2−17

Common error: Forgetting to distribute the minus sign: writing −2x + 2 instead of −2x − 2.

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Mistake 2: Misreading the Question

Common Misreads

• Reading "simplify" when it says "factorise" (or vice versa).
• Missing "give your answer in its simplest form."
• Not noticing that a diagram is "NOT drawn accurately."
• Missing the word "NOT" — e.g. "Which of these is NOT a factor of 12?"
• Overlooking unit conversions required (e.g. the question gives cm but asks for m).

How to Avoid Misreading

1. Read the question twice before picking up your pen.
2. Underline or circle key words: the command word, the required form of answer, and any units.
3. After finishing your answer, re-read the final sentence of the question to ensure your answer matches what was asked.

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Mistake 3: Not Showing Working

This is especially costly because even if your final answer is wrong, method marks can rescue several marks per question.

The Rule

Always show your working, even if you can do it in your head.

Where This Matters Most

• Multi-step calculations.
• "Show that" questions (every step must be visible).
• Simultaneous equations (show the elimination or substitution method clearly).
• Questions worth 3 or more marks.
• Geometry questions (state which theorem or rule you are using).

Worked Example 2

Question (3 marks): Solve 5(2x − 3) = 25.

Full working (3 marks): 10x − 15 = 25 [M1: expanding] 10x = 40 [M1: rearranging] x = 4 [A1: correct answer]

Just the answer "x = 4" (1 mark): Only B1 if the answer is correct. If you wrote x = 5 with no working, you get 0 marks. With working, the method marks could still give you 1–2 marks.

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Mistake 4: Rounding Too Early

Rounding intermediate values can cause your final answer to be inaccurate, costing you the final A mark.

The Rule

Do not round until the very end of the calculation. Use the ANS button or memory functions on your calculator to keep full precision.

Worked Example 3

Question: Find the area of a circle with diameter 8.3 cm. Give your answer to 1 decimal place.

Wrong approach: $r = 8.3 \div 2 = 4.15 \approx 4.2 ($r=8.3÷2=4.15≈4.2(rounded too early) $A = \pi \times 4.2^{2} = 55.4 cm^{2} ($A=π×4.22=55.4cm2(WRONG)

Correct approach: $r = 8.3 \div 2 = 4.15 (keep$r=8.3÷2=4.15(keep exact) $A = \pi \times 4.15^{2} = \pi \times 17.2225 = 54.106$A=π×4.152=π×17.2225=54.106... = $54.1 cm^{2}$54.1cm2 (to 1 d.p.)

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Mistake 5: Forgetting Units

When Units Matter

• Any question involving measurement (length, area, volume, mass, time, speed).
• If the question gives units, your answer should include units.
• Pay particular attention to compound units (m/s, km/h, $g/cm^{3})$g/cm3).

Common Unit Errors

• Giving area in cm instead of $cm^{2}$cm2.
• Giving volume in $cm^{2}$cm2 instead of $cm^{3}$cm3.
• Forgetting to convert between units (e.g. cm to m, minutes to hours).
• Writing "meters" when you mean "metres" (not penalised on Edexcel, but be precise).

How to Avoid

Write the units next to your answer as you calculate, not as an afterthought.

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Mistake 6: Incorrect Use of the Formula Sheet

Errors

• Using a formula that is NOT on the sheet and getting it wrong from memory.
• Confusing which formula to use (e.g. using the volume of a cone when you need a sphere).
• Not checking the formula sheet at all and trying to remember everything.

Best Practice

1. At the start of the exam, flip to the formula sheet and spend 30 seconds reviewing it.
2. When you encounter a question involving a cone, sphere or prism, immediately check the sheet.
3. Know which formulae are NOT on the sheet (circle area, Pythagoras, trig ratios) and memorise those.

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Mistake 7: Not Checking Answers

Quick Checks That Catch Errors

Type of Question	Check
Equation solving	Substitute your answer back in
Factorising	Expand your answer and compare
Percentage questions	Estimate: is 15% of £200 roughly £30?
Probability	Is your answer between 0 and 1?
Area/Volume	Is the magnitude reasonable?
Angles in a triangle	Do they add up to $180°$180°?
Angles at a point	Do they add up to $360°$360°?
Simultaneous equations	Substitute both values into both equations

The 5-Minute Check Rule

Leave the last 5 minutes of each paper for checking. Prioritise:

1. Questions where you were unsure.
2. Questions worth the most marks.
3. Questions where you can quickly verify (e.g. substitution checks).

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Mistake 8: Copying Errors

Copying your own intermediate answer incorrectly from one line to the next or from one part of the page to another.

How to Avoid

• Write clearly and neatly.
• Keep your working organised — do not scatter calculations around the page.
• If a number appears in two places, double-check it matches.

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Mistake 9: Treating Diagrams as Accurate