JCE Mathematics (Syllabus 13) common mistakes
JCE Mathematics (Syllabus 13) · Understand the traps and how to avoid them.
Evaluates -3² as 9, and works chains such as 5 - 2 × 3² straight across the page left to right, arriving at 81 rather than -13.
The leading minus is read as part of the number rather than as an operation applied after the power, and all four operations are assumed to carry equal priority, so a left-to-right scanning habit takes over.
What to do instead
Drill a fixed order (brackets, indices, × and ÷, then + and -). Make students rewrite -3² as -(3 × 3) and insert brackets on every line before evaluating, then confirm one answer on a calculator that respects precedence.
Answers 'after a 15% rise a price is $92, find the original' by taking 15% of 92 and subtracting it, or by multiplying 92 by 1.15 instead of dividing.
The base of the percentage is misidentified: the percentage is attached to whichever number is visible rather than to the original amount, and 'increase means multiply' is memorised without tracking the direction of the change.
What to do instead
Require the base to be written explicitly, as original × 1.15 = 92, then solved by dividing. Set paired questions (find the new price, then find the old price) and insist on a back-substitution check: does 1.15 × the answer give 92?
Solves 3x + 5 = 20 by writing 3x = 20 + 5, and turns 5 - 2x = 11 into 2x = 11 - 5.
The shortcut 'change the side, change the sign' is memorised without the balance model behind it, so it is applied to the wrong term, and students forget that an operation acts on a whole side rather than on one term within it.
What to do instead
Demand one line per operation with the operation shown on both sides (subtract 5 from both sides, then divide both sides by 3). End every equation with a substitution check, which exposes the sign error immediately.
Expands (x + 3)² as x² + 9, and cancels across a sum by simplifying (x + 2)/2 to x + 1.
The index is distributed over each term inside the bracket, a move that is valid for multiplication but not for addition, and cancelling is over-generalised from fractions whose numerators are single products.
What to do instead
Always rewrite (x + 3)² as (x + 3)(x + 3) and expand fully before collecting. Test any proposed simplification numerically: at x = 2, (2 + 2)/2 = 2 while 2 + 1 = 3, so the cancellation is false. Factorise the numerator completely before cancelling.
Converts 1 m² to 100 cm², and gives a perimeter value when asked for the area of a composite shape, or the reverse.
The linear conversion factor is applied once even though area scales with the square of the length, and area and perimeter are treated as interchangeable labels rather than as distinct measurements with different units.
What to do instead
Derive the conversion from a sketch of a 1 m by 1 m square redrawn in centimetres, giving 100 × 100 = 10 000 cm². Require the unit to be written against every intermediate value and check the dimension: squared units for area, single units for perimeter.
Applies Pythagoras or a sine/cosine/tangent ratio to a triangle that is not stated to be right-angled, or treats the hypotenuse as the adjacent side because the sketch looks that way.
The diagram is read as literal evidence, and the ratio labels are recalled as a string of letters rather than tied to a marked reference angle; right-triangle methods are assumed because they are the only ones the candidate knows.
What to do instead
Mark the right angle and the reference angle on the diagram before choosing a method, and quote the condition first ('Pythagoras needs a right angle'). If it is absent, state that the rule does not apply and use another route, such as the angle sum, an isosceles property, or dropping a perpendicular to create a right angle.
Finds the median of 4, 11, 7, 9 by taking the middle value as listed, and estimates the mean from a grouped frequency table by averaging class labels instead of using frequency-weighted midpoints.
Median is associated with 'middle of the list' rather than 'middle of the ordered data', and grouped data are handled as if they were raw values, with the frequency column read as extra data rather than as weights.
What to do instead
Make ordering a written step before any median or range work, crossing off pairs from the ends. For grouped data, build a table with a midpoint column and an f × x column, then divide the total of f × x by the total frequency.
Gives the probability that two dice total 7 as 6/12, and adds P(A) + P(B) for events that can happen together, producing a total above 1.
The sample space is imagined rather than listed, so the number of outcomes is guessed, and the word 'or' is translated directly into addition without checking whether the events overlap.
What to do instead
Require a full sample-space table or list for any two-stage experiment before a probability is written, and count favourable cells against total cells. When combining events, check whether the sum exceeds 1; if it does, subtract the overlap or use a two-way table as a check.
Reads a gradient as horizontal change over vertical change, or computes it from coordinates while ignoring that the axes are scaled in twos or fives, and confuses the gradient with the y-intercept when stating the equation of a line.
Rise over run is recalled imprecisely, a scale of one unit per square is assumed, and y = mx + c is memorised as a string of symbols without m and c being tied to visible features of the line.
What to do instead
Have students write Δy/Δx with both coordinate pairs substituted, after reading each axis scale aloud. Once an equation is found, test two points taken from the graph in it, and label m as the steepness and c as the point where the line cuts the y-axis.
Evaluates f(-2) for f(x) = x² - 3x by taking the negative of f(2), and finds an inverse by swapping x and y but stopping there, leaving the answer as x = y² - 3.
The bracket is read as a label rather than as a substitution instruction, so a negative input is handled as a minus sign in front of the function, and the inverse is seen as a swapping procedure rather than as solving for the input.
What to do instead
Write the substitution out with brackets, f(-2) = (-2)² - 3(-2), and evaluate indices before multiplication. For inverses, always finish by making y the subject, then check one pair: if f(2) = 5, then f⁻¹(5) must equal 2.