Opening Maths Unlocked
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Opening Maths Unlocked
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GCSE MATHS REVISION
Many GCSE Maths errors are not caused by completely misunderstanding a topic. They happen because of a missed negative sign, an incorrect fraction rule, the wrong formula or a method that has been remembered slightly incorrectly.
Learning to recognise these mistakes can make your working more accurate and help you decide which skills need further practice.
The examples below show common errors, explain why they are wrong and give the correct approach.
Updated 5 October 2026
These are examples to watch for, rather than errors that every student makes.
Mistake
23 + 14 = 37
Why it is wrong: Fractions need a common denominator before their numerators can be added.
Correct approach
23 = 812
14 = 312
812 + 312 = 1112
Remember: Find a common denominator before adding or subtracting fractions.
Practise this skillMistake
−6 − 4 = 2
Why it is wrong: Subtracting a positive number moves further in the negative direction.
Correct approach
−6 − 4 = −10
Remember: Do not use the multiplication sign rules for addition and subtraction.
Practise this skillMistake
4 + 3 × 5 = 35
Why it is wrong: Multiplication is completed before addition.
Correct approach
4 + 15 = 19
Mistake
Increase £200 by 15%: 200 × 0.15 = £30
Why it is wrong: £30 is the increase, not the new total.
Correct approach
200 × 1.15 = £230
Alternatively, 15% of £200 = £30, then £200 + £30 = £230.
Mistake
6 ÷ 0.5 = 3
Why it is wrong: Dividing by one half asks how many halves fit into 6.
Correct approach
6 ÷ 0.5 = 12
Mistake
450,000 = 45 × 104
Why it is wrong: This has the correct value, but 45 is too large for the first number in standard form.
Correct approach
450,000 = 4.5 × 105
Remember: The first number must be at least 1 but less than 10.
Practise this skillMistake
3x + 4 = 7x
Why it is wrong: 3x and 4 are not like terms.
Correct approach
3x + 4 cannot be simplified further.
Mistake
3(x + 4) = 3x + 4
Why it is wrong: The 3 must multiply both terms inside the bracket.
Correct approach
3(x + 4) = 3x + 12
Remember: Multiply every term inside the bracket.
Practise this skillMistake
From 3x + 5 = 20, writing 3x = 25
Why it is wrong: Removing +5 requires subtracting 5 from both sides.
Correct approach
3x = 15
x = 5
Mistake
x3 × x4 = x12
Why it is wrong: Multiplying powers with the same base means adding, not multiplying, the indices.
Correct approach
x3 × x4 = x7
Remember: Add the indices when multiplying powers with the same base.
Practise this skillMistake
(x + 3)2 = x2 + 9
Why it is wrong: The two middle terms also contribute to the expansion.
Correct approach
(x + 3)(x + 3) = x2 + 6x + 9
Mistake
x + 4x = 4 (as a general simplification)
Why it is wrong: Terms joined by addition cannot simply be cancelled. The denominator also requires x ≠ 0.
Correct approach
x + 4x = 1 + 4x, for x ≠ 0.
Remember: Cancellation applies to common factors, not individual terms within a sum.
Practise this skillMistake
£80 shared 3 : 5 → 35 of £80
Why it is wrong: The ratio has eight parts altogether, not five.
Correct approach
3 + 5 = 8 parts
£80 ÷ 8 = £10 per part
The shares are £30 and £50.
Mistake
4 tickets cost £12, so 8 tickets cost £16.
Why it is wrong: Doubling the number of tickets doubles the cost; adding 4 to each quantity does not preserve the rate.
Correct approach
8 is twice 4, so the cost is twice £12 = £24.
Mistake
After a 20% increase the price is £120; £120 − 20% = £96.
Why it is wrong: The 20% increase was based on the original price, not £120.
Correct approach
120 ÷ 1.2 = 100
The original price was £100.
Mistake
A journey of 1 km in 2 minutes gives 1 ÷ 2 = 0.5 km/h.
Why it is wrong: The time is in minutes but the speed unit is kilometres per hour.
Correct approach
2 minutes = 130 hour
1 ÷ 130 = 30 km/h.
Remember: Convert to compatible units before calculating.
Practise this skillMistake
An 8 cm by 3 cm rectangle has area 22 cm2.
Why it is wrong: 22 cm measures the distance around the rectangle; area measures the space inside.
Correct approach
Perimeter = 2(8 + 3) = 22 cm
Area = 8 × 3 = 24 cm2
Remember: Area and perimeter have different units.
Practise this skillMistake
Area = base × height
Why it is wrong: A triangle has half the area of a rectangle with the same base and perpendicular height.
Correct approach
Area = 12 × base × perpendicular height
Remember: Use the perpendicular height.
Practise this skillMistake
Diameter 10 cm → area 100π cm2
Why it is wrong: The area formula uses the radius, not the diameter.
Correct approach
Radius = 5 cm
Area = π × 52 = 25π cm2
Mistake
Using a2 + b2 = c2 for a triangle that is not right-angled.
Why it is wrong: This relationship applies only to right-angled triangles; c is the hypotenuse.
Correct approach
For a right-angled triangle with shorter sides 6 and 8: 62 + 82 = 102, so the hypotenuse is 10.
Mistake
Using the same opposite and adjacent labels after changing the chosen angle.
Why it is wrong: Opposite and adjacent are defined relative to the angle being used.
Correct approach
Label the sides for the chosen angle before selecting sine, cosine or tangent.
Mistake
Length scale factor 3 → area scale factor 3.
Why it is wrong: Area depends on two dimensions, so the length factor is squared.
Correct approach
Area scale factor = 32 = 9
Higher: volume scale factor = 33 = 27.
Mistake
From 8, 2, 5, 11, 4, choosing 8 as the median before ordering.
Why it is wrong: The values must be put in numerical order before locating the middle value.
Correct approach
Ordered: 2, 4, 5, 8, 11
Median = 5
Mistake
For 4, 6, 8, 10: sum 28; mean = 28 ÷ 10.
Why it is wrong: The mean divides by the number of values, not the largest value.
Correct approach
28 ÷ 4 = 7
Mistake
Range = number of data values
Why it is wrong: The range measures spread between the extremes.
Correct approach
Range = highest value − lowest value
Mistake
Two variables are correlated, so one must cause the other.
Why it is wrong: An association alone cannot establish what causes it.
Correct approach
Correlation shows an association; it does not by itself prove causation.
Mistake
For unequal class widths, bar height always equals frequency.
Why it is wrong: Frequency is represented by the bar's area, so bar height is frequency density.
Correct approach
Frequency density = frequency ÷ class width.
Mistake
Five red and three blue counters: P(blue) = 35
Why it is wrong: There are eight equally likely counters altogether.
Correct approach
P(blue) = 38
Mistake
P(event) = 1.2
Why it is wrong: A probability cannot be greater than 1 or less than 0.
Correct approach
0 ≤ P(event) ≤ 1, equivalent to 0% to 100%.
Mistake
Adding P(A) and P(B) when A and B can overlap.
Why it is wrong: Simply adding overlapping events counts their shared outcomes twice.
Correct approach
For mutually exclusive events, P(A or B) = P(A) + P(B).
For example, 0.3 + 0.4 = 0.7.
Mistake
Adding probabilities along a single path.
Why it is wrong: A path combines successive events, so its probabilities multiply.
Correct approach
Multiply along a path. Add the probabilities of separate successful paths when appropriate.
Mistake
Assuming the same probabilities after an item is selected and not replaced.
Why it is wrong: The total number of items and possibly the number of desired items change.
Correct approach
Recalculate the probabilities after the first selection. Independent repeated events keep their probabilities unchanged.
Five quick checks of your reasoning. This is not a diagnostic test.
Sam writes 12 + 13 = 25. What has Sam done wrong?
Leah writes 4(x + 2) = 4x + 2. What has Leah done wrong?
A rectangle measures 7 cm by 4 cm. Noah says its area is 22 cm2. What has Noah calculated?
Mia says the probability of rolling a 7 on a fair six-sided die is 16. What is wrong?
Jack writes = 9. What is wrong?
Correcting a method matters more than copying the final answer.
Was it arithmetic, a forgotten method, incorrect notation, misunderstanding the question or choosing the wrong topic?
Work through the correct method and identify exactly where your solution changed direction.
Attempt a similar question independently rather than simply reading the correction.
Return to the skill after a gap to check that the corrected method is still secure.
These checks can catch some errors, but they cannot catch every possible mistake.
Does the size of the answer seem reasonable?
Should the answer be positive or negative?
Does the answer need cm, cm², cm³, kilometres per hour or another unit?
Have you answered what was actually asked?
Where appropriate, use the opposite operation to check the result.
There is no clean grade label for an error. Keep revisiting your underlying skills at the tier you study.
Prioritise accuracy with number, fractions, percentages, ratio, algebra and core geometry. Many longer Foundation questions depend on these fundamental skills.
Foundation RevisionKeep the core skills accurate while also checking algebraic manipulation, exact values, advanced geometry, statistics and probability carefully.
Higher RevisionMake time to revisit weaker skills.
Build a revision method that helps corrections stick.
Check paper-specific calculator habits.
Strengthen methods without a calculator.
Find broad areas that may need more practice.