The GCSE Maths Higher mistakes examiners flag every series

Mixing up m and c. The most common GCSE Higher Algebra mistake, costing two to three marks per paper.

Computing Δy instead of Δy ÷ Δx, confusing total vertical change with the rate of change per unit.

Dropping the minus sign on descending lines, so the magnitude is right but the direction is lost.

Not recognising that y = 4 + 2x and y = 2x + 4 are the same equation, even though examiners reorder deliberately.

Getting the maths right but the explanation wrong: “the gradient is 4” with no units or per-unit phrase.

Writing y = kx for a y ∝ 1/x relationship — the #1 proportion trap, appearing in 5 question-parts across all Higher series and worth up to 3 marks each.

Scaling y by the same factor as x even when y ∝ xⁿ — a top-band discriminator worth up to 4 marks (NOV24·3·17) that trips candidates who forget the power applies to the scale factor.

Computing k = y/x for an inverse law (instead of k = x·y) or expecting a reciprocal graph to be a straight line — tested across 4 question-parts in Higher series JUN23, JUN24 and NOV24.

Using the circumference angle straight as the central angle (or forgetting to halve): a grade 7–9 discriminator appearing in all 5 Higher series (count 9) worth multi-mark 'find the angle and give the reason' and 'show that' parts.

Failing to recognise the 90° at the tangent–radius junction, so Pythagoras and kite angle-chases stay locked — tested across NOV23, JUN24 and NOV24 for up to 3 marks each in the grade 7–9 band.

Adding adjacent instead of opposite angles in a cyclic quad, or accepting an alternate-segment step without checking which sides are equal — a 4-mark multi-step trap (NOV24·2·23b) and a reasoning-question surface (JUN23·2·20c) that separates grade 7–9 from the middle band.

Multiplying an area by the length scale factor k instead of k squared; tested across NOV24 and JUN22 in cost-per-area (phone screen £47.04 vs £117.60) and sector-area ratio contexts, a grade 7-9 discriminator worth up to 5 marks.

Applying the length scale factor k (or k squared) to a volume instead of k cubed; tested across JUN22, NOV23 and JUN24 in volume-ratio and price-proportional-to-volume contexts, a grade 7-9 discriminator worth up to 5 marks.

Dividing linearly to get a length from a volume (skipping the cube root) or treating surface-area and volume ratios as equal; anchored in JUN24 (150 cm edge total via cube root) and JUN23 (SA ratio 3:5, not 1:2), a grade 7-9 discriminator separating students who can set up the inverse scaling step.

Adding branch probabilities instead of multiplying them; a grade 7-9 discriminator in two-event and repeated-event tree questions worth up to 3 marks per question-part.

Summing individual probabilities for 'at least one' instead of using 1 minus P(none); the complement route is the standard Higher method and avoids double-counting, tested across multi-event tree and listing questions.

Using the whole-sample-space denominator for a conditional probability or a without-replacement draw instead of shrinking it to the given or remaining set; a key discriminator in tree-diagram and two-way-table questions at grade 7-9.

Finding the upper bound of A minus B (or A over B) by pushing every quantity up, instead of taking the second quantity to its lower bound because subtracting or dividing by it works against you.

Testing an at-least or safely-under-the-limit claim with the rounded values, instead of the single worst case: all lower bounds to prove at least, all upper bounds to prove it stays under a limit.

Giving a perpendicular line the same gradient, or the reciprocal without the sign change, instead of the negative reciprocal, so the two gradients fail to multiply to minus one.

Treating the point that divides a line in a given ratio as the midpoint, or stepping the right fraction in the wrong direction, instead of counting the parts from the named end.

Finding the average speed of a there-and-back or multi-stage journey by taking the mean of the speeds, instead of total distance divided by total time, which is always closer to the slower speed.

Multiplying when you should divide to find the subject of a density, pressure or rate formula, and using mismatched units, instead of rearranging for the quantity asked and converting first.

Reading a rate off a graph as one coordinate divided by another, instead of as the gradient, change over change, and on a curve as the gradient of the tangent.

Reading a⁻ⁿ as a negative number (minus aⁿ) instead of a reciprocal (1/aⁿ), so 8⁻⁵ is wrongly taken as minus 8⁵ rather than the small positive value 1/8⁵.

Treating a fractional index as dividing (9^(1/2) = 4.5) rather than as a root (9^(1/2) = 3), and mishandling a^(m/n) by ignoring the numerator power or denominator root.

Adding indices across different bases without rewriting to a common prime base first, and applying a bracket power only to the power of ten in standard form, leaving the coefficient unchanged.

Forming the perfect-square bracket but keeping the original constant unchanged, so x²+8x−5 is incorrectly written as (x+4)²−5 instead of (x+4)²−21, missing the −16 adjustment.

Copying the printed sign from (x−7)²+8 to get x=−7, instead of solving (x−7)=0 to get x=7, because the minimum is where the squared bracket is zero.

Taking one root as the x-coordinate of the turning point instead of calculating the midpoint (a+b)/2, so for roots 1 and 5 the axis is wrongly given as x=1 or x=5 rather than x=3.

Dividing both sides by x (or setting each factor equal to the right-hand expression) instead of collecting everything to one side = 0 and factorising, so one root is silently lost.

Reporting the y-intercept or turning-point coordinates as the roots of f(x) = 0, instead of the x-values where the parabola crosses the x-axis.

Moving y=(x+3)² to the right (or up) instead of 3 to the LEFT, missing that a change inside the bracket shifts the graph horizontally and the opposite way to the sign, so the vertex sits at x=−3.

Writing y=(−x)² for an x-axis reflection of y=x² (which equals x² and changes nothing) instead of y=−x², by negating the input rather than the output.

Treating the +2 in y=x²+2 as a sideways shift, giving a minimum of (−2,0) or (2,0), instead of an upward shift with minimum (0,2).