ICAS Mathematics common mistakes
ICAS Mathematics · Understand the traps and how to avoid them.
When adding fractions such as 1/2 + 1/3, writes 2/5 by adding the numerators and the denominators.
Whole-number addition is over-generalised; the fraction bar is not treated as a division that requires a common unit before quantities can be combined.
What to do instead
Model the addition with fraction strips or a number line so the need for equal-sized parts is visible, then practise converting to a common denominator before adding. Check that the answer is at least as large as the larger fraction.
Evaluates 3 + 4 × 5 as 35 by working strictly from left to right.
The expression is read the way English text is read; there is no established habit of ranking operations before calculating.
What to do instead
Before calculating, circle the multiplication and division parts, replace each with its value, and rewrite the expression. Estimate first (about 3 + 20) so an answer of 35 is rejected as implausible.
Finds a 20% discount on $80 by calculating 20% of 80 and adding it on, giving $96.
Keyword matching ('discount' triggers 'percentage') without identifying the direction of the change or which amount is the base.
What to do instead
Write a number sentence with the base labelled: discounted price = original × (1 − rate). Test with an easy case (50% off $80 must be $40) to confirm the operation chosen.
Substitutes x = −3 into x² and obtains −9, or into 2x² and obtains −18.
The minus sign is treated as an operation performed after squaring rather than as part of the number, so brackets are omitted when substituting.
What to do instead
Substitute with brackets every time: write (−3)², evaluate the bracket, then apply the index. Drill a short mixed set of x², −x² and (−x)² so the difference becomes automatic.
Solves 3x + 5 = 20 by subtracting 5 from the left-hand side only, producing 3x = 20.
Equation solving is treated as a sequence of tidy-up steps on one expression rather than as maintaining equality between two quantities.
What to do instead
Record each operation on both sides as a written line: 3x + 5 − 5 = 20 − 5. Finish every equation by substituting the solution back into the original equation to verify it.
Given the sequence 2, 6, 12, 20, ..., predicts the next term by repeating the last difference, or writes a rule from only two terms.
Additive reasoning dominates, and students do not check whether a proposed rule reproduces every term already given.
What to do instead
Build a difference table and inspect second differences before deciding the type of rule. Write the candidate rule and test it against all given terms, not just the final pair.
Converts 3 m² to square centimetres by multiplying by 100, giving 300 cm².
A linear conversion factor is applied to a two- or three-dimensional measure; the exponent is not connected to the number of dimensions involved.
What to do instead
Derive the factor from the definition: 1 m = 100 cm, so 1 m² = 100 cm × 100 cm = 10 000 cm². Convert by substituting the units into the area or volume formula rather than recalling a memorised factor.
Assumes a geometry diagram is drawn to scale and estimates an angle or side length by eye, or treats two lines as parallel because they look parallel.
The picture is treated as a source of data, when diagrams in this exam are conventionally not drawn to scale.
What to do instead
List the given information first and mark only those facts on the diagram. Write a reason (angle sum, alternate angles, given parallel) beside every value used, and treat 'not to scale' as the default assumption.
Reads a value from a graph or table using the wrong scale interval (treating each gridline as 1 when it represents 5), or uses the grand total instead of the row total in a two-way table.
Axis labels and table totals are skimmed, and the condition in the question ('of the students who ...') is not matched to the correct denominator.
What to do instead
Annotate the axis scale before reading any value. Underline the row or column named in the question, write the fraction with its denominator explicitly, then calculate.
For two independent events, adds the probabilities (1/6 + 1/6 = 1/3) instead of multiplying, or assumes every listed outcome is equally likely.
The addition rule for mutually exclusive events is over-applied, 'and' versus 'or' is not distinguished, and outcome lists are trusted without checking symmetry.
What to do instead
Classify the event before computing: 'and' with independence means multiply; 'or' with mutually exclusive events means add; 'at least one' means 1 − P(none). Check equal likelihood by asking whether each outcome has the same physical chance of occurring.