Year 9 Mathematics Foundations

Vocabulary flashcards defining the foundational topics and core mathematical concepts outlined in the Year 9 curriculum checklist.

Fractions, decimals and percentages

Methods of representing parts of a whole, where fractions express ratios of integers, decimals use base-10 positional notation, and percentages represent parts per hundred ($100$).

Ratios and rates

Mathematical comparisons between quantities, where a ratio compares two quantities measured in the same unit and a rate compares quantities measured in different units (such as distance over time).

Percentages: increase and decrease

Calculations used to determine the final amount after adding or subtracting a specified percentage of the original quantity.

Algebraic expressions and simplification

Combinations of variables, numbers, and arithmetic operations that are simplified by collecting like terms and applying algebraic rules.

Expanding brackets

The algebraic procedure of removing brackets by multiplying every term inside by the factor outside using the distributive law, represented as $a(b + c) = ab + ac$.

Factorising simple expressions

The inverse process of expanding brackets, involving the identification and extraction of the highest common factor from each term into factored form.

Solving linear equations

Finding the specific value of an unknown variable in a degree-$1$ equation by applying inverse operations symmetrically to both sides.

Rearranging formulas

The algebraic manipulation of a given formula using inverse operations to isolate a different variable as the subject.

Simultaneous equations

A system of two or more equations containing common variables that are solved together to find values that satisfy all equations at the same time.

Linear graphs and gradients

Graphical representations of straight lines typically given in the form $y = mx + c$, where the gradient ($m$) describes steepness and is calculated as $\frac{\text{rise}}{\text{run}}$.

Coordinates and graph interpretation

Using pairs of values $(x, y)$ to pinpoint positions on a Cartesian coordinate plane and analyzing patterns, intercepts, or trends shown by graphical data.

Pythagoras' theorem

A fundamental geometric theorem for right-angled triangles stating that the square of the hypotenuse is equal to the sum of the squares of the two shorter sides: $a^2 + b^2 = c^2$.

Area, perimeter and volume

Key spatial metrics: perimeter measures total outer boundary length, area measures total two-dimensional surface space, and volume measures total three-dimensional space enclosed.

Angles and geometric reasoning

The application of deductive geometric properties and rules (such as angles at a point, in triangles, and between parallel lines) to deduce unknown angles.

Probability

The quantitative measure of the likelihood that an event will occur, ranging from $0$ (impossible) to $1$ (certain).

Statistics: mean, median, mode and range

Summary statistics where mean is the arithmetic average, median is the central value of an ordered set, mode is the most frequent value, and range is the difference between maximum and minimum values.

Worded mathematical problems

Mathematical scenarios presented in descriptive language that require identifying relevant information and formulating mathematical operations to find a solution.

Patterns and sequences

Ordered progressions of numbers or figures governed by a defined mathematical rule connecting consecutive terms.

Indices and square roots

Exponents representing repeated multiplication of a number by itself, and roots (\root{2}\relax or $\text{square root}$) indicating the value that produces a specified number when squared.

Speed, distance and time

The kinematic relationship defined by the formula $\text{Speed} = \frac{\text{Distance}}{\text{Time}}$, alongside its rearranged forms for distance and time.