Fiji Year 10 Mathematics: Key Vocabulary

Vocabulary practice flashcards covering definitions, formulas, and concepts from the Fiji Year 10 Mathematics curriculum.

Function

A set of ordered pairs in which each $x$-element has only one $y$-element associated with it, providing a single distinct output for each input.

Relation

Any set of ordered pairs.

Linear Function

A function in which the degree or index on the input variable is $1$ (for example, $y = x + 2$).

Quadratic Function

A function in which the degree, power, or index on the input variable $x$ is equal to $2$ (for example, $y = x^2$).

Domain ($D_x$)

The complete set of input values or $x$-values that can be substituted into an equation or function.

Range ($R_y$)

The set of all resultant output values or possible $y$-values generated by a function.

Gradient

The measure of steepness or slope of a straight line, calculated as the vertical change divided by the horizontal change ($\text{Gradient} = \frac{\text{Rise}}{\text{Run}} = \frac{y_2 - y_1}{x_2 - x_1}$).

Factorisation

The process of rewriting an algebraic expression or polynomial as a product of its simpler factors.

Null Factor Law

A principle stating that if the product of two or more numbers or expressions is zero ($ab = 0$), then at least one of the factors must equal zero ($a = 0$ or $b = 0$).

Subject of a Formula

The single variable isolated entirely on the left-hand side of an equation, expressed in terms of the remaining variables on the right-hand side.

Exponent

A number or symbol placed above and to the right of a base number indicating how many times the base is multiplied by itself.

Exponential Growth

A pattern of data increase that grows at a consistent percentage rate over time, beginning slowly and accelerating rapidly.

Exponential Decay

A process occurring when a quantity decreases proportionally over time, dropping rapidly at first and progressively slowing down.

Half-Life

The period of time required for half the quantity of an unstable or decaying substance to disintegrate.

Pythagoras' Theorem

A fundamental theorem stating that in a right-angled triangle, the area of the square on the hypotenuse equals the sum of the areas of the squares on the other two sides ($a^2 + b^2 = c^2$).

Hypotenuse

The longest side of a right-angled triangle, located directly opposite the $90^\circ$ right angle.

Clinometer

An instrument designed for measuring angles of elevation, depression, or inclination.

Angle of Elevation

The angle formed between the horizontal line of sight and the upward line of sight to an elevated object.

Angle of Depression

The angle formed between the horizontal line of sight and the downward line of sight to an object below.

Incenter

The point of concurrency where the three internal angle bisectors of a triangle intersect, serving as the center of the incircle.

Circumcenter

The point of concurrency where the perpendicular bisectors of the three sides of a triangle meet, forming the center of the circumscribed circle.

Centroid

The point of concurrency where the three medians of a triangle intersect, corresponding to the triangle's center of gravity.

Orthocenter

The point of concurrency where the three altitudes of a triangle intersect.

Intersecting Chord Theorem

A geometric theorem stating that if two chords intersect inside a circle, the product of the segments of one chord equals the product of the segments of the other ($a \cdot b = c \cdot d$).

Hire Purchase

A credit purchasing agreement where a customer pays a deposit, takes possession of the goods, and completes the purchase via regular installments with interest added.

Lay-by

A purchase method in which a retailer reserves an item while the customer makes regular payments, receiving the item only after paying the full ticketed price without interest charges.

Chargeable Income

An individual's total income minus allowable deductions and personal exemptions, forming the basis on which normal tax is calculated.

Compound Interest

Interest calculated on both the original principal balance and the accumulated interest earned during prior periods.

Simple Interest

Interest computed exclusively on the original principal amount throughout the entire investment or loan term.

Histogram

A graphical display of a frequency distribution using contiguous rectangles whose widths represent continuous class intervals and whose heights reflect class frequencies.

Interquartile Range

A measure of statistical dispersion representing the difference between the upper quartile ($Q_3$) and the lower quartile ($Q_1$).

Sample Space

The set containing all possible outcomes of a specific probability experiment.