#### ICAS - Mathematics - 2024

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 subject’s educational importance, ICAS Mathematics assessments are designed to provide an objective ranking of students’ 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 — 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. There’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.

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- The Assessments consist of a range of multiple-choice and free-response questions.
- For the multiple-choice questions, students will have to choose the correct answer from the four possible options.
- Each question is worth one mark.
- The total score is the number of correct answers.
- Marks are NOT deducted for incorrect answers.
- Papers are ordered from the easiest items to the most difficult items.
- The items towards the end of the paper are designed to provide an opportunity for the most able students to demonstrate a high level of skill.
- The questions are carefully graded to cater to a wide range of student abilities using contexts that stimulate students' interest and engage their attention. Students at all levels of competency stand to benefit from participation in the diagnostic assessments.

**Note:**For Classes 2 to 7

- Calculators are not permitted.
- Formal algebra is tested. Students are expected to be familiar with some conventions of algebra.
- Formal geometry is tested. Students are expected to be familiar with some conventions of geometry.

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
- measures and units
- space and geometry
- chance and data

- For Pacific & International - 26 – 30 August 2024
- For Australia - 26 – 30 August 2024
- For New Zealand - 26 – 30 August 2024

**Class 2 syllabus for ICAS Assessments - Mathematics:****Number & Arithmetic:****Number:**count, order and compare whole numbers to 100, skip by 2s, 5s, and 10s, understand place value of whole, numbers to 100 and position numbers, on the number line, recognise halves and wholes**Arithmetic:**use the four operations with single, digits using stimulus for multiplication and division, add and subtract by counting on; partitioning and rearranging, solve number problems involving whole numbers to 100

**Algebra & Patterns:****patterns:**continue simple linear patterns with numbers and shapes**Pre-Algebra:**solve simple number puzzles expressed in words or symbols**Algebra:**not tested at this level

**Measures & Units:****Measures:**informally measure and compare mass; length; area; volume and capacity, measure and compare time in hours; days; weeks; months and years**Measurement:**read analog and digital clocks to the half hour

**Space & Geometry:****Space:**give and follow directions, identify relative position on a picture or map**Shape:**recognise and classify basic shapes and solids using obvious features, identify shapes that are the same; similar or different

**Chance & Data:****Chance:**give simple estimates of probability in terms of what will happen; might happen and won’t happen**Data:**complete a basic table, read a basic table with frequencies and tallies, read a picture graph

**Class 3 syllabus for ICAS Assessments - Mathematics:****Number & Arithmetic:****Number:**count; order and compare whole numbers to 1000, place value of whole numbers to 1000, skip by 2s; 3s; 5s and 10s, order and compare halves; quarters and eighths-
**Arithmetic:**multiply and divide by single digits using repeated addition; arrays or groups, solve simple addition and subtraction problems

**Algebra & Patterns:****Patterns:**continue simple linear patterns with numbers and shapes, identify missing elements in a pattern**Pre-Algebra:**solve simple number puzzles expressed in words or symbols, complete number sentence

**Measures & Units:****Measures:**informally measure and compare mass; length; area; volume and capacity, order months and seasons, read a calendar**Measurement:**read analog and digital clocks to the quarter hour

**Space & Geometry:****Space:**give and follow directions, identify relative position on a picture or map, identify image after one-step flip; slide and half or quarter turns-
**Shape:**describe 2-D and 3-D shapes, identify shapes or solids that are the same or different

**Chance & Data:****Chance:**give simple estimates of probability in terms of likelihood-
**Data:**classify data, interpret lists; tables and picture graphs, complete a basic table

**Class 4 syllabus for ICAS Assessments - Mathematics:****Number & Arithmetic:****Number:**count; order and compare whole numbers to 10 000, understand place value of whole, numbers to 10 000, recognise odd and even numbers-
**Arithmetic:**solve problems involving unit fraction with denominators of 2; 3; 5 and 10, multiply and divide by 2; 3; 5 and 10, use informal factors and multiples of whole numbers to solve problems, add and subtract to 100

**Algebra & Patterns:****Pre-Algebra:**complete number sentences involving the four operations

**Measures & Units:****Measures:**estimate; order; measure and compare mass; length; and capacity**Units:**use familiar metric units such as cm; m; km; g; kg; L and mL**Measurement:**read analog and digital clocks, calculate areas and perimeters using a grid

**Space & Geometry:****Space:**identify pathways and interpret grid maps for relative position, identify axes of symmetry**Shape:**identify nets and elevations of 3-D shapes**Geometry:**recognise angles as measures of turn, order and compare angles

**Chance & Data:****Chance:**count the number of arrangements of sets of objects and events**Data:**read and interpret bar charts; a range of common graphs and two-way tables

**Class 5 syllabus for ICAS Assessments - Mathematics:****Number & Arithmetic:****Number:**count; order and compare numbers from 0.01 to 100000, understand place value of numbers from 0.01 to 100000, count by halves; thirds; quarters; tenths and hundredths**Arithmetic:**solve problems involving equivalent fractions, convert decimals to fractions, use all number facts to 100

**Algebra & Patterns:****Patterns:**sequence numbers in multiples of 2 to 10**Pre-Algebra:**solve complex number puzzles expressed in words

**Measures & Units:****Measures:**use scaled instruments to measure and compare quantities; temperatures and lengths**Units:**select appropriate metric units, choose appropriate order of magnitude, convert time**Measurement:**compare areas and perimeters using a grid, solve time problems involving am and pm

**Space & Geometry:****Space:**use scales; legends and directions to interpret maps, complete symmetrical patterns**Shape:**informally compare areas of composite or irregular shapes**Geometry:**compare angles less than 180°

**Chance & Data:****Chance:**order likelihood of events, recognise complementary and independent events**Data:**select and interpret data appropriate display, interpret line graphs

**Class 6 syllabus for ICAS Assessments - Mathematics:****Number & Arithmetic:****Number:**round numbers, compare and order fractions and decimals and locate them on the number line**Arithmetic:**use factors and multiples to solve problems, solve problems involving long multiplication and division with remainders, solve problems involving fractions; mixed numerals and whole numbers, estimate products

**Algebra & Patterns:****Patterns:**continue and describe patterns involving fractions; decimals and whole numbers**Pre-Algebra:**complete equivalent number sentences involving all four operations

**Measures & Units:****Measures:**convert metric units of length**Units:**choose and use appropriate metric units**Measurement:**calculate areas and perimeters of rectangles, convert 24-hour time

**Space & Geometry:****Space:**connect 3-D objects with 2-D views and nets, use grid reference and directional language, identify line and rotational symmetry**Geometry:**measure and compare angles, solve problems involving parallel and perpendicular lines

**Chance & Data:****Chance:**list sample space, represent probabilities as fractions, recognise probabilities lie from 0 to 1**Data:**interpret and compare column graphs; dot plots and tables

**Class 7 syllabus for ICAS Assessments - Mathematics:****Number & Arithmetic:****Number:**identify and apply properties of prime; composite; square and triangular numbers, convert between fractions; decimals and percentages**Arithmetic:**order integers, solve problems involving order of operations including decimals and fractions, add and subtract related fractions, find fractions of whole numbers, solve percentage problems such as discounts

**Algebra & Patterns:****Patterns:**continue a pattern of related fractions**Pre-Algebra:**complete equivalent number sentences involving order of operations

**Measures & Units:****Measures:**convert metric units of area and volume**Measurement:**calculate areas and perimeters of composite shapes including triangles, interpret timetables

**Space & Geometry:****Space:**apply combinations of transformations to an image, use the cartesian plane to represent points**Geometry:**apply angle properties including complementary; supplementary; vertically opposite angles and angles at a point, solve problems involving the angle sum of a triangle

**Chance & Data:****Chance:**represent probabilities as decimals and percentages, compare experimental and expected frequencies**Data:**interpret and compare double column graphs, interpret sector graphs

**Class 8 syllabus for ICAS Assessments - Mathematics:****Number & Arithmetic:****Number:**use index notation, represent numbers as product of primes, find squares and square roots, compare and order integers and unrelated fractions, round decimals**Arithmetic:**use order of operations with integers and unrelated fractions, solve ratio problems, express one quantity as a percentage or fraction of another

**Algebra & Patterns:****Patterns:**continue patterns involving powers; integers and unrelated fractions**Algebra:**create and evaluate algebraic equations using substitution, interpret authentic graphs and solve linear equations, simplify expressions

**Measures & Units:****Measurement:**use formulae to calculate areas of triangles and parallelograms, calculate volumes of rectangular prisms

**Space & Geometry:****Space:**use simple bearings, plot and identify co-ordinates in all four quadrants**Shape:**classify and use properties of triangles and quadrilaterals**Geometry:**calculate angles between transversals and parallel lines, use angle sum of quadrilaterals to solve problems

**Chance & Data:****Data:**interpret and compare stem and leaf plots; and dot plots, calculate mean; median; mode and range

**Class 9 syllabus for ICAS Assessments - Mathematics:****Number & Arithmetic:****Number:**apply index laws involving positive and zero indices, convert terminating and recurring decimals to fractions**Arithmetic:**use order of operations with integers and rational numbers, solve ratio and rates problems

**Algebra & Patterns:****Patterns:**continue patterns involving recurring decimals**Algebra:**expand and simplify expressions, factorise linear expressions, solve linear equations graphically and algebraically, change the subject of a formula

**Measures & Units:****Measurement:**calculate areas and perimeters of a kite; rhombus and trapezium, calculate area of composite shapes, calculate circumference and areas of circles, calculate volumes and surface areas of right prisms, apply Pythagoras’ Theorem to solve right-triangle problems

**Space & Geometry:****Shape:**use angle properties of shapes**Geometry:**apply congruence conditions for triangles to solve problems, use ratio and scale factor of similar figures, apply angle sum of polygons to solve problems

**Chance & Data:****Chance:**calculate probabilities of events involving ‘and’; ‘or’ and ‘at least’**Data:**interpret two-way tables; Venn diagrams and frequency histograms, recognise effect of outliers on measures of location and spread

**Class 10 syllabus for ICAS Assessments - Mathematics:****Number & Arithmetic:****Number:**apply index laws involving integer indices, convert numbers to scientific notation**Arithmetic:**solve problems involving simple interest, operate on surds

**Algebra & Patterns:****Algebra:**apply index laws to simplify expressions, expand and simplify binomials, factorise quadratics, calculate midpoints; distance; gradient and find the equation of a line, solve linear simultaneous equations, solve problems involving parallel and perpendicular lines, graph parabolas; hyperbolae; polynomials; exponentials and circles, solve quadratic equations

**Measures & Units:****Measures:**solve problems with very small time scales and intervals**Measurement:**calculate surface area and volume of cylinders; cones; spheres and right pyramids

**Space & Geometry:****Space:**solve problems involving bearings; depression; elevation and area in right angled triangles**Geometry:**find unknown sides and angles in right angled triangles using the sine; cosine and tangent ratios

**Chance & Data:****Chance:**use two-step probability with and without replacement, calculate relative frequencies**Data:**interpret and compare back-to-back stem and leaf plots; and cumulative frequency histograms, compare displays using measures of location and spread, interpret box plots and scatterplots, identify quartiles, describe distributions

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