Free ICAS Mathematics Exam Flashcards
Memorize 50 essential terms and definitions for the International Competitions and Assessments for Schools (ICAS) Mathematics — Introductory and Papers A–J. See the term, recall the definition, then flip to check yourself.
[Intro–A] What does a digit's place value tell you?
It tells how much the digit is worth because of its position. In 472, the 7 is in the tens place, so its value is 70.
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About These ICAS Mathematics Flashcards
These 50 flashcards are designed to help you memorize key terms and definitions for the International Competitions and Assessments for Schools (ICAS) Mathematics — Introductory and Papers A–J. Each card shows a term on the front and its definition on the back—the classic flashcard format for vocabulary memorization. Use these alongside our practice questions to build both recall and comprehension.
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Review every term in this set. Open any term to reveal its definition.
[Intro–A] What does a digit's place value tell you?
It tells how much the digit is worth because of its position. In 472, the 7 is in the tens place, so its value is 70.
[B–D] How are factors different from multiples?
A factor divides a number exactly; a multiple is produced by multiplying that number by an integer. For 12, 3 is a factor and 24 is a multiple.
[C–D] What is a reliable way to compare a fraction with a decimal?
Express both in the same form. Divide the fraction's numerator by its denominator to make a decimal, or write the decimal as a fraction with a power-of-ten denominator.
[D–E] What does it mean for two fractions to be equivalent?
They name the same value. Multiplying or dividing both numerator and denominator by the same nonzero number preserves the fraction's value.
[E–F] How do you find a percentage of a quantity without a calculator?
Convert the percentage to a fraction or decimal, then multiply. Useful anchors include 10% = one tenth, 5% = half of 10%, and 25% = one quarter.
[E–G] What order should you use for mixed arithmetic operations?
Evaluate grouping symbols first, then powers, then multiplication and division left to right, then addition and subtraction left to right.
[H–J] What does a negative index mean?
For nonzero a, a^(-n) is the reciprocal of a^n: a^(-n) = 1/a^n.
[G–H] How can a recurring decimal be converted to a fraction?
Let a variable equal the decimal, multiply by a power of 10 that shifts one full repeating block, subtract the original equation, then solve for the variable.
[H–J] What does scientific notation require?
Write the number as a × 10^n where 1 ≤ |a| < 10 and n is an integer. Moving the decimal left gives a positive exponent; moving it right gives a negative exponent.
[I–J] How do simple and compound interest differ?
Simple interest is calculated only on the original principal. Compound interest is calculated on the principal plus interest already added, so the growth itself earns interest.
[Intro–A] How do you identify the rule in a simple linear pattern?
Compare consecutive terms or shapes and find the same change repeated each step, such as adding 3 or attaching two new tiles.
[B–D] How can inverse operations reveal a missing value in a number sentence?
Undo the known operation: addition is undone by subtraction, multiplication by division, and vice versa. Apply the inverse to both sides to preserve equality.
[C–D] What is the difference between a term and a term number in a sequence?
The term is the value in the sequence; the term number is its position. A rule may connect position n to the value of the nth term.
[D–E] What makes two number sentences equivalent?
They have the same value or the same solution even if written differently. Applying the same valid operation to both sides maintains equivalence.
[F] What does substituting into an algebraic expression mean?
Replace each variable with its given value, use parentheses when needed, and then evaluate using the order of operations.
[F–G] When may algebraic terms be combined?
Only like terms can be combined: they must have identical variable parts and exponents. Add or subtract their coefficients while keeping the variable part.
[G] What does factorising a linear expression do?
It rewrites a sum as a product by taking out a common factor. For example, 6x + 9 becomes 3(2x + 3).
[G–H] What is the goal when changing the subject of a formula?
Isolate the chosen variable on one side by applying inverse operations to both sides, while preserving the equation's equality.
[H–J] How does the zero-product rule help solve a factorised quadratic?
If a product equals zero, at least one factor must be zero. Set each factor equal to zero and solve each resulting equation.
[I–J] What does a solution to simultaneous equations represent?
It is a value or ordered pair that satisfies every equation at once; graphically, for two lines, it is their intersection point.
[Intro–A] What is the difference between measuring and comparing a quantity?
Measuring assigns a value using a unit; comparing decides which object has more, less or the same amount, sometimes without a formal unit.
[A–B] Why must a measurement include a unit?
The number alone does not identify the scale or kind of quantity. A unit such as centimetres, kilograms or litres gives the value meaning.
[B–C] Which metric relationships are most useful for length, mass and capacity?
1 km = 1000 m, 1 m = 100 cm, 1 kg = 1000 g, and 1 L = 1000 mL.
[C–D] How do perimeter and area differ?
Perimeter measures distance around a boundary in linear units; area measures the surface enclosed in square units.
[D–E] Why is converting square units different from converting length units?
Area has two dimensions, so the length conversion factor is squared. Since 1 m = 100 cm, 1 m² = 100² = 10,000 cm².
[E–F] How can you find the area of a composite shape?
Split it into familiar non-overlapping shapes, calculate each area, and add them; or subtract a missing piece from a larger familiar shape.
[F] What is the volume formula for a right prism?
Volume = area of the constant cross-section × perpendicular length of the prism. The result is expressed in cubic units.
[G] How are a circle's circumference and area calculated?
Circumference C = 2πr (or πd); area A = πr², where r is radius and d is diameter.
[H] How do surface area and volume describe a three-dimensional object differently?
Surface area totals the areas of all outside faces in square units; volume measures enclosed space in cubic units.
[I–J] What is the volume relationship among a cylinder, cone and sphere?
A cylinder has V = πr²h; a cone with the same base and height has one third of that volume; a sphere has V = (4/3)πr³.
[Intro–A] What do relative-position words describe?
They locate one object in relation to another, using ideas such as above, below, beside, between, left, right, near and far.
[Intro–B] How do two-dimensional and three-dimensional shapes differ?
A 2-D shape has length and width; a 3-D solid also has depth and occupies volume. Faces of a 3-D solid are 2-D shapes.
[B–D] What is a line of symmetry?
It is a line that divides a figure into mirror-image halves that would match if folded along the line.
[C–D] How are acute, right, obtuse and straight angles classified?
Acute is less than 90°, right is 90°, obtuse is between 90° and 180°, and straight is 180°.
[D] How do parallel and perpendicular lines differ?
Parallel lines in a plane remain the same distance apart and never meet; perpendicular lines intersect at a right angle.
[E] Which angle relationships help when two lines intersect?
Vertically opposite angles are equal; adjacent angles on a straight line sum to 180°; angles around a point sum to 360°.
[F] What angle sums should be recalled for triangles and quadrilaterals?
Interior angles total 180° in a triangle and 360° in a quadrilateral.
[G] How do congruent and similar figures differ?
Congruent figures have the same shape and size. Similar figures have the same shape with proportional corresponding lengths, so their sizes may differ.
[G–H] When does Pythagoras' theorem apply?
Only in a right triangle: a² + b² = c², where c is the hypotenuse opposite the right angle.
[H–J] How do sine, cosine and tangent relate the sides of a right triangle?
For angle θ: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, and tan θ = opposite/adjacent.
[Intro–A] What do impossible, possible and certain mean in probability?
An impossible event cannot happen, a possible event may happen, and a certain event must happen under the stated conditions.
[A–B] Why are titles and labels essential when reading a table or graph?
They identify what is counted or measured, the categories, and any scale or units; without them, a displayed number can be misinterpreted.
[B–C] What does a frequency tell you?
It tells how many times a value, category or event occurs in the data set.
[C–D] What is the complement of an event?
It is the event not occurring. Their probabilities sum to 1, so P(not A) = 1 − P(A).
[D] How is theoretical probability calculated for equally likely outcomes?
Divide the number of favourable outcomes by the total number of outcomes in the sample space.
[E] How do experimental probability and expected frequency differ?
Experimental probability is observed successes divided by trials. Expected frequency predicts a count: probability × number of trials.
[F] What do mean, median, mode and range measure?
Mean is the arithmetic average, median the middle ordered value, mode the most frequent value, and range the maximum minus the minimum.
[G] In probability, when do you add and when do you multiply?
For mutually exclusive alternatives ('A or B'), add their probabilities. For independent successive events ('A and B'), multiply their probabilities.
[H] How does sampling without replacement affect a second probability?
The first selection changes both the remaining favourable outcomes and the total remaining outcomes, so the second probability must be recalculated.
[I–J] What is conditional probability?
It is the probability of an event given that another event has occurred: P(A|B) = P(A ∩ B) / P(B), provided P(B) is not zero.
Frequently Asked Questions
Does every student sit the same ICAS Mathematics paper?
No. ICAS Mathematics is a family of Introductory and Papers A–J. The paper-to-year mapping and the papers available differ by country, so students should check the current official table before choosing revision content.
Why are there ten cards in each topic?
ICAS names five Mathematics learning areas but does not publish one domain weighting for the whole Intro-to-J family. This deck therefore gives each area ten cards as an editorial navigation aid; the split is not an official blueprint or a prediction of any paper's question mix.
How many questions and how much time does ICAS Mathematics allow?
The current official table lists 30 questions in 35 minutes for Introductory, 40 questions in 45 minutes for Papers A–C, and 40 questions in 60 minutes for Papers D–J.
Are all five learning areas tested at every level?
No. Coverage and depth change by paper. For example, the official framework says formal Algebra and formal Geometry are not tested on Introductory, while later papers add progressively more advanced algebra, geometry, probability and statistics.
Is there a passing mark for ICAS Mathematics?
ICAS Assessments does not publish a fixed pass mark. Students receive cohort-benchmarked results such as a percentile and an achievement level rather than a pass/fail decision.
Do these flashcards reproduce official ICAS questions?
No. The cards are original active-recall prompts about mathematical concepts named in the public framework. They do not copy ICAS test questions, past papers or proprietary item wording.
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