HKDSE Maths (Core) common mistakes
HKDSE Maths (Core) · Understand the traps and how to avoid them.
In Paper 1, writing a final answer without showing the intermediate equation or formula substitution, e.g. jumping straight to x = 4 after a quadratic word problem.
Candidates practise MC-style mental arithmetic and treat Paper 1 like a short-answer test; they do not realise method marks are awarded separately from the answer mark, so an unsupported answer can earn zero even when correct.
What to do instead
Adopt a fixed four-line habit for every Paper 1 part: state the formula, substitute the numbers, show the simplified equation, then box the answer with units. Practise by re-marking past Paper 1 scripts against the marking scheme and highlighting which line earned each M and A mark.
Treating a change of 20% up followed by 20% down as returning to the original value, and writing 'no change' or the original amount.
Percentages are processed as additive quantities rather than as multipliers; the candidate computes 1 + 0.2 - 0.2 = 1 without converting each change into a multiplying factor.
What to do instead
Force every percentage change into a multiplier before calculating: increase 20% becomes x1.2, decrease 20% becomes x0.8, and the combined factor is 0.96, i.e. a 4% net decrease. Drill ten mixed chains (successive discounts, marked-up then discounted prices, percentage profit on cost) writing only multipliers, then convert the final factor back to a percentage.
Solving a linear inequality such as -3x > 12 and giving x > -4, forgetting to reverse the sign when dividing by a negative number.
The procedure is memorised as 'do the same to both sides', identical to solving equations, and the reversal rule is a small exception that is easily dropped under time pressure.
What to do instead
After isolating x, always test one number from the claimed solution set in the original inequality; for x > -4 pick x = 0, which gives 0 > 12, false, exposing the error. Alternatively, move the x-term to the side that keeps its coefficient positive before dividing, so no reversal is ever needed.
Changing the subject of a formula containing the subject twice, e.g. making x the subject of y = (ax + b)/(x - c), and giving up or producing y = ax/x type cancellation.
Candidates cancel terms across a fraction or treat x as if it appeared once; they lack the routine of collecting all x-terms on one side and factorising.
What to do instead
Follow a fixed sequence: multiply out the denominator, expand all brackets, gather every term containing x on one side and everything else on the other, factorise x out, then divide. Check by substituting numerical values for the other letters into both the original and the rearranged formula.
Expanding (a + b)^2 as a^2 + b^2, and similarly mishandling (a - b)^2 and (a + b)(a - b).
The notation is read as 'square each thing inside', a natural but false generalisation from the distributive law for multiplication; the middle cross-term is invisible in the compact notation.
What to do instead
Write the bracket twice explicitly, (a + b)(a + b), and expand all four products before collecting, doing this for at least twenty mixed examples until the cross-term appears automatically. Then memorise the three identities and verify each by substituting a = 3, b = 2 numerically.
Applying a transformation to a graph in the wrong direction, e.g. saying y = f(x + 2) shifts the graph 2 units to the right, or y = f(x) + 2 shifts it right.
Horizontal transformations act 'inside' the function and therefore behave counter-intuitively; candidates transfer the intuition from vertical shifts, where the sign matches the direction.
What to do instead
Anchor each rule to a single test point: for y = f(x + 2), the value f(0) now occurs at x = -2, so the graph moves left. Sketch y = x^2, y = (x + 2)^2 and y = x^2 + 2 on the same axes and label the vertex of each, then repeat for reflections and stretches.
Using the wrong ratio in a similarity or area-and-volume problem, e.g. applying a length ratio of 1:3 directly to volumes instead of cubing it.
Candidates remember 'ratio' but not which power applies, and the question often supplies the ratio in one dimension while asking about capacity or surface area.
What to do instead
Write the ratio chain explicitly before calculating: length a:b, area a^2:b^2, volume a^3:b^3. For every problem, state which quantity the given ratio refers to and convert it to the length ratio first, then raise it to the required power. Include one reverse problem where the volume ratio is given and the length ratio is required.
In coordinate geometry, computing the slope as (x2 - x1)/(y2 - y1) or forgetting that perpendicular slopes multiply to -1, and then mis-writing the equation of the line.
The formula is recalled as a vague 'difference over difference' and the vertical change is not firmly attached to the numerator; the perpendicular condition is memorised as 'negative' without the reciprocal.
What to do instead
Always label the two points (x1, y1) and (x2, y2) on the diagram before substituting, and say aloud 'change in y over change in x'. For perpendicularity, write m1 x m2 = -1 and solve for the unknown slope rather than guessing. Verify by substituting both given points back into the final equation.
In trigonometry, pressing the calculator into degree mode for a radian question (or the reverse), and misapplying the sine or cosine rule by choosing the wrong side-angle pairing.
The calculator mode is invisible on screen and the rules look interchangeable; candidates match letters superficially instead of checking that the angle is included between the two sides (cosine rule) or opposite a known side (sine rule).
What to do instead
Write 'DEG' or 'RAD' at the top of the working whenever the question involves pi or a radian measure, and set the calculator mode before starting the question. For triangle problems, mark the included angle and the opposite side on a sketch, then choose the rule from that sketch rather than from memory. Check the answer against the triangle inequality and the expected size of the angle.
In probability and statistics, adding probabilities of non-mutually-exclusive events without subtracting the overlap, and confusing 'at least one' with 'exactly one'.
The addition rule is memorised as P(A) + P(B) without the condition, and the phrasing 'at least one' is read as a single occurrence; candidates also fail to use the complement for 'at least one' problems.
What to do instead
Before any calculation, write whether the events can occur together and draw a two-circle Venn diagram with the overlap labelled. For 'at least one', compute 1 minus P(none) and state that choice explicitly. For grouped data, separate the classes involved and sum the relevant frequencies rather than reading a single cell.