ICAS Mathematics study guide
ICAS Mathematics · Work through your exam, one topic at a time.
ICAS Mathematics is one of the six subjects in the ICAS academic competition - a school-based challenge run by Janison and supported by The University of Sydney, taken by students from Years 2 to 12 in Australia, New Zealand, Asia and further afield. It is a competition rather than a curriculum test: candidates sit a Mathematics paper pitched at their own year level, and outcomes are reported against clearly defined, nationally standardised achievement levels, so a result carries the same meaning wherever the paper was sat. The ICAS Mathematics study guide has 4 sections and about 1,148 words.
01Number and Arithmetic
Number questions reward fluency with the four operations applied to integers, fractions, decimals and percentages, plus confident movement between those forms. You need place value and rounding (including significant figures), order of operations, factors and multiples, prime factorisation, HCF and LCM, ratio and proportion, powers and roots, and standard form.
293 words, about 1 min02Algebra and Patterns
Algebra expresses relationships generally and then manipulates them accurately. Candidates must substitute into expressions and formulas, collect like terms, expand and factorise, solve linear equations and inequalities, solve simultaneous equations, rearrange formulas to change the subject, use function notation, and describe sequences with an nth-term rule.
302 words, about 2 min03Measurement and Geometry
Geometry questions combine formula recall with careful diagram reading. You must know perimeter and area of rectangles, triangles, parallelograms, trapezia and circles; volume and surface area of prisms and cylinders; angle facts for straight lines, triangles, parallel lines and polygons; Pythagoras' theorem; the trigonometric ratios; similarity and congruence; and unit conversion, including scale drawings and bearings.
285 words, about 1 min04Statistics and Probability
This domain covers summarising data and quantifying chance. You need mean, median, mode and range from raw data and from frequency tables; reading and interpreting graphs; the probability scale from 0 to 1; theoretical versus experimental probability; complementary events; combined events using lists, tables and tree diagrams; and the difference between independent and mutually exclusive events.
268 words, about 1 min