Mathematical skills in a range of contexts from the following areas

### Algebra & patterns

#### Change & data

#### Measures & units

#### Number & arithmetic

#### Space & geometry

**Assess school studentsâ€™ numeracy skills with ICAS Mathematics**As the foundation of STEM and a fundamental part of human thought and logic, Mathematics is a crucial building block for academic success.

In recognition of the subjectâ€™s educational importance, ICAS Mathematics assessments are designed to provide an objective ranking of studentsâ€™ performance based on the curricula for the relevant year. Maths skills such as logical reasoning, problem solving and critical thinking not only help students perform well in STEM subjects â€” they also underpin key areas of our daily lives as consumers of money and media.

From simple everyday connections to baking, banking and budgeting, to the complex mathematics behind technology used in programming, engineering and machine learning, mathematics is all around us. Thereâ€™s even fractions and ratios in music, geometry and data analysis in sports, and measurements and financial maths in fashion. Clearly, mathematics is integral to doing well in school and understanding the world, and there is no better opportunity to test your mathematical mettle than with ICAS assessments.

More than simply a maths competition, ICAS Mathematics assessments consist of questions written and reviewed every year by expert educators. Papers are carefully graded to stimulate interest and learning across a wide range of abilities, including gifted and talented students. Students encounter questions related to key mathematical learning areas including:

- number and arithmetic
- algebra and patterns
- comprehension
- measures and units
- space and geometry
- chance and data.

In turn, students receive a unique academic experience designed to challenge their abilities beyond the classroom, a greater understanding of where their strengths and areas of improvement lie, and recognition and encouragement of academic success.

**Year 3 to Year 7 ICAS Mathematics Assessments**The primary school level papers of ICAS maths exams challenge and extend high-achieving school students while reinforcing key numeracy skills in these crucial foundational years, providing a strong building block for future learning. Students answer a variety of questions on topics such as arithmetic, patterns, geometry, data and pre-algebra, which increase in complexity throughout the paper and encourage the use of higher-order thinking skills.

The Introductory paper, for students in the equivalent of Year 3, assesses concepts such as skip counting, place value, time and probability. Questions may require students to solve number problems involving whole numbers up to 100, continue simple linear patterns with numbers and shapes, or read a basic table with frequencies and tallies.

ICAS Mathematics tests more sophisticated skills as school students progress through the years. For example, in Paper A (Year 4), students may be asked to order and compare halves, quarters and eighths, multiply and divide by single digits using different techniques, describe 2D and 3D shapes or read and interpret common graphs. Papers B and C (Years 5 and 6) assess knowledge of number sentences, areas and perimeters, metrics units, symmetry, angles and many other topics.

Finally, in Paper D (Year 7), in addition to more advanced questions on decimals and fractions, metric units and probabilities, questions may require students to complete number sentences involving all four equations, solve problems involving parallel and perpendicular lines, or interpret and compare column graphs, dot plots and tables.

**Year 8 to Year 12 ICAS Mathematics assessments**The high school level papers of ICAS maths exams challenge and extend high-achieving students while preparing them for the advanced level of mathematics involved in various STEM subjects. Students answer a variety of questions on topics such as algebra, measurement, geometry, chance and data, which increase in complexity throughout the paper and encourage the use of higher-order thinking skills.

Papers E and F, for students in the equivalent of Year 8 and Year 9, assess advanced content such as order of operations, angle properties and numerical probabilities, as well as new areas such as algebra, index notation, prime numbers, the cartesian plane and descriptive statistics. For example, questions may require students to solve percentage and ratio problems, interpret authentic graphs to solve linear equations, solve problems using angle sum of triangles and quadrilaterals, or calculate mean, median, mode and range.

Papers G and H (Year 10 and Year 11) set the foundation for the final years of schooling by challenging and extending students on a range of mathematical topics. Students may be asked to convert terminating and recurring decimals to fractions, factorise linear expressions, solve linear equations graphically and algebraically, calculate various geometrical measurements, solve problems using congruence conditions for triangles, find probabilities of events involving â€˜andâ€™, â€˜orâ€™ and â€˜at leastâ€™, and recognise the effect of outliers on measures of location and spread.

Papers IÂ (Years 12) also help students to prepare for their critical final years of schooling. Questions may require students to apply index laws involving integer and fractional indices, solve financial problems using simple and compound interest, solve and graph advanced algebraic equations and transformations, use trigonometry in 3D problems, calculate conditional probabilities or interpret histograms, box plots and scatterplots. While senior high school students often set aside some of their previous extracurricular activities, ICAS tests provide valuable assessment experience and performance insights in such a key subject as Mathematics.