CCEA GCSE Maths common mistakes
CCEA GCSE Maths · Understand the traps and how to avoid them.
Rounds a calculator display at every step, then uses the rounded value in the next calculation - for example writing 0.67 and using it to work out compound interest or a reverse percentage.
The calculator display is short, so candidates copy a truncated value instead of keeping the full value in calculator memory; they then treat the rounded number as exact.
What to do instead
Store intermediate results with the calculator memory or Ans key, write down the full expression, and round only the final answer. Check the final answer against a rough estimate and against any stated rounding requirement.
Evaluates -3² as 9, substitutes x = -2 into x² and gets -4, or drops brackets when substituting a negative number into an expression such as 5 - 2x.
The minus sign is treated as part of the number rather than as an operation with a defined order, and negative values are not bracketed when substituted.
What to do instead
Write negative substitutions in brackets: (-2)². Distinguish -3² = -(3²) from (-3)². Before calculating, rewrite the expression with brackets around every substituted value.
Expands (2x - 3)(x + 5) as 2x² - 15, missing the middle terms, or expands -(x - 4) as -x - 4.
The candidate distributes only the first term of each bracket, or applies the negative sign to the first term only; the structure of the expression is not checked.
What to do instead
Use a grid or draw arrows for every pair of terms, then collect like terms. For a leading minus, write each term with its sign changed. Check by substituting x = 1 into the original and expanded expressions.
Solves an equation such as 3(x - 2)/4 = 5x + 1 by multiplying only the fraction by 4, or moves +1 across the equals sign without changing its sign.
The candidate focuses on removing the fraction and forgets that every term must be multiplied, or applies inverse operations inconsistently to the two sides.
What to do instead
Multiply every term on both sides by the denominator, writing each line explicitly. Keep the balance method visible. Substitute the solution back into the original equation to verify it.
Uses “angle in a semicircle is 90°” when the angle is not subtended by a diameter, or assumes a tangent meets a radius at a right angle just because the diagram looks like it.
The candidate recognises the shape of the diagram rather than checking the conditions of the circle theorem; equal radii and right angles are assumed without evidence.
What to do instead
Annotate the diagram with only justified facts: equal radii create isosceles triangles, a diameter subtends 90°, and a tangent is perpendicular to the radius at the point of contact. State the theorem reason for each angle.
Converts 250 cm² to m² by dividing by 100, or uses 3 cm and 0.2 m in the same Pythagoras or trigonometry calculation without converting.
A single linear conversion factor is applied to an area or volume, and mixed units are used because the candidate does not notice the different units in the question.
What to do instead
Convert all lengths to the same unit before calculating. For area use the square of the length factor: 1 m² = 10,000 cm². For volume use the cube: 1 m³ = 1,000,000 cm³. Write the conversion as a separate line.
Reads the median from a cumulative frequency curve by taking the highest y-value or the x-value at the top of the curve, instead of going from n/2 across to the curve and down to the x-axis.
The axes are confused: cumulative frequency is on the vertical axis and the variable is on the horizontal axis, but the candidate treats the top of the curve as the median.
What to do instead
Find the total frequency n, draw a horizontal line at n/2 to the curve, then drop vertically to the x-axis. On a box plot, identify the median as the line inside the box, not the end of the box.
On a without-replacement tree diagram, keeps the first denominator for the second-branch probabilities, or adds probabilities along a branch instead of multiplying them.
The candidate confuses replacement with no replacement and mixes the rules for ‘and’ and ‘or’; the remaining totals after the first event are not updated.
What to do instead
Write the remaining totals on the second branches and update denominators. Multiply along a branch and add between mutually exclusive branches. Check that all final outcome probabilities sum to 1.
Gives a bare numerical answer after a multi-step problem - for example ‘12’ for a cost or ‘4’ for the number of packs - without units or a conclusion, and does not answer a question such as ‘Is there enough?’
The candidate stops as soon as the calculation is finished and ignores the command word and the context; the final comparison or interpretation is never written.
What to do instead
Underline the command word and any units before starting. Finish with a sentence that states the answer in context, includes units, and directly answers the question. Check the answer against the original problem.
Shares £84 in the ratio 3:4 by calculating £84 ÷ 3 and £84 ÷ 4, or treats the difference between two shares as the total number of parts.
The candidate confuses ratio parts with actual amounts and does not distinguish between a total, a difference and a single share.
What to do instead
Draw a bar model and label the total number of parts. For 3:4, total parts = 7, so one part = £84 ÷ 7 = £12. If the difference is given, use the difference in parts instead. Always identify whether the question gives the total, one share or the difference.