AFM Enlistment (Maths) common mistakes
AFM Enlistment (Maths) · Understand the traps and how to avoid them.
Evaluating a mixed-operation expression strictly left to right, e.g. computing 3 + 4 × 5 as 35 instead of 23.
The left-to-right reading habit from ordinary text overrides the precedence hierarchy (brackets, indices, division/multiplication, addition/subtraction), and candidates have often never had the hierarchy drilled to automaticity.
What to do instead
Before touching the numbers, underline the operation that must be done first and rewrite the expression one step at a time on a fresh line, carrying everything else down unchanged. Practise 20 mixed strings of the form a + b × c, a × b − c, and a + (b + c) × d until the underlining is automatic.
Getting the wrong sign or wrong magnitude when subtracting and when multiplying/dividing with negative numbers, e.g. writing 7 − (−3) = 4 or (−2) × (−5) = −10.
Minus signs are treated as decorations on the digit rather than as operations, and the two negative signs in a row are collapsed into one instead of being resolved as 'subtracting a negative adds'.
What to do instead
Rewrite every subtraction as addition of a negative first: 7 − (−3) becomes 7 + 3. For multiplication and division, decide the sign separately from the size and state the rule aloud ('same signs, positive result'). Check the answer's sign against the context (a debt times a debt is a credit).
Adding fractions by adding numerators and denominators, e.g. 1/2 + 1/3 = 2/5.
The rule for adding whole numbers is over-generalised to a notation where the denominator is a label for the size of the piece, not a quantity to be combined. The candidate has not internalised that only like-sized pieces can be counted.
What to do instead
Force a common denominator before any addition or subtraction, and sanity-check with a rough estimate: 1/2 + 1/3 must be close to 1, so 2/5 is immediately wrong. Build the habit of converting to a common denominator even when the numbers look friendly.
Inverting the wrong fraction when dividing, e.g. computing 3/4 ÷ 2/5 as (4/3) × (2/5) or as (3/4) × (2/5).
The 'flip and multiply' rule is memorised without the attachment that only the divisor is inverted, and the divisor is not clearly identified when both fractions look similar.
What to do instead
Mark the division sign and label the fraction after it 'divisor' before doing anything. Rewrite as 'first fraction × reciprocal of the divisor' in words, then substitute. Verify with an estimate: dividing by 2/5 (less than 1) must give a larger answer than 3/4.
Misaligning decimal points when adding or subtracting decimals, or miscounting decimal places when multiplying, e.g. 0.3 × 0.4 = 1.2.
Decimals are handled as strings of digits rather than as quantities, so place value is not tracked. In multiplication, the total number of decimal places in the factors is not counted.
What to do instead
Write decimals in a column with points vertically aligned and pad with zeros so every number has the same number of places. For multiplication, multiply as whole numbers first, then count the total decimal places across both factors and place the point accordingly; confirm with a magnitude estimate (0.3 × 0.4 is about a tenth, so 0.12, not 1.2).
Computing a percentage change against the wrong base, e.g. treating a 20% increase followed by a 20% decrease as returning to the original value, or taking a discount off the already-discounted price.
Percentages are applied to whichever number is nearest rather than to the stated base, and the candidate assumes percentage changes are additive and reversible.
What to do instead
Write the base explicitly before each calculation ('this 20% is of the new price, which is 1.2 × original'). Use multipliers (×1.2, ×0.8) and multiply them to see that 1.2 × 0.8 = 0.96, a 4% net fall. Always restate what the percentage is 'of'.
Solving a linear equation by moving terms without changing sign, e.g. going from 3x + 5 = 20 to 3x = 20 + 5.
The operation is seen as 'moving' a term across the equals sign rather than as applying the same operation to both sides, so the inverse operation is not applied.
What to do instead
Annotate each step with the operation performed on both sides ('subtract 5 from both sides'). Substitute the answer back into the original equation as a mandatory final check, and never skip that substitution.
Applying a formula with the wrong quantity substituted, e.g. using the diameter in place of the radius in area = πr², or using the slant height where perpendicular height is required.
The formula is recalled as a shape of symbols without the meaning of each symbol, and diagrams are read by eye rather than by labelled dimension.
What to do instead
Before substituting, write the formula and beneath it list each symbol with its value and unit, marking clearly which given dimension is the radius and which is the diameter. Halve the diameter explicitly as a written step rather than mentally.
Mixing units within one calculation, e.g. multiplying a length in centimetres by a width in metres, or reporting an area in centimetres when the question asks for square metres.
Units are treated as labels to be dropped rather than as quantities that must be consistent, and area/volume unit conversions (×100, ×10 000) are confused with linear ones (×100).
What to do instead
Convert every measurement to one unit in a written first line before any arithmetic, and carry units through the working. Remember that converting a linear unit squares or cubes the factor: 1 m² = 10 000 cm², not 100 cm².
Reading a value from a table or chart at the wrong scale, e.g. taking a bar height against the wrong gridline, or misreading which column a row label refers to.
The axis interval and the row/column headers are skimmed rather than checked, and candidates assume each gridline is one unit when the axis may step by 5, 20, or 0.5.
What to do instead
State the axis interval and the column headings in writing before extracting any number, and trace from the label to the value with a finger or ruler. For grouped data, confirm whether the question asks for a total, a difference, or a rate before choosing which numbers to combine.