GCSE Mathematics Higher Tier Paper 3 Review

Vocabulary flashcards covering core mathematical concepts, terms, and formulas from the GCSE Mathematics Higher Tier Paper 3 examination.

Identity

A mathematical statement equating two algebraic expressions that is true for all values of the variable $x$, denoted by the symbol $\equiv$ (for example, $3(x - 1) \equiv 3x - 3$).

Population Density

A measure of population per unit area, calculated using the formula $\text{Population density} = \frac{\text{population}}{\text{area}}$.

Relative Frequency

The experimental proportion of times an event occurs during a set number of trials, calculated by dividing the event's observed frequency by the total number of trials.

Theoretical Probability

The calculated likelihood of an outcome occurring based on equally likely mathematical possibilities under ideal conditions, such as $\frac{1}{6}$ for rolling a specific number on a fair six-sided dice.

Roots of an Equation

The values of $x$ that satisfy the equation $f(x) = 0$, representing the $x$-intercepts on the graph of $y = f(x)$.

Direct Proportion

A relationship between two variables, such as $P$ and $Q$, where one is a constant multiple of the other ($P = kQ$), meaning as one increases, the other increases at a constant rate.

Inverse Proportion

A relationship between two variables where one increases as the other decreases proportionally, such as $R$ being inversely proportional to $Q^2$ ($R = \frac{k}{Q^2}$).

Invariant Point

A point or vertex on a geometric figure that does not change its position after a transformation, such as points located directly along the line of reflection.

Probability Tree Diagram

A diagram with branching lines used to map out all possible sequential outcomes of multiple events and calculate their combined probabilities.

Composite Function

A function created by applying one function to the output of another function, denoted as $fg(x)$ where $g(x)$ is evaluated first and then substituted into $f(x)$.

Sine Rule

A trigonometric relationship used in non-right-angled triangles that equates the ratios of the lengths of sides to the sines of their opposite angles.

Pythagoras' Theorem

A geometric theorem used in right-angled triangles to determine an unknown side length by relating the hypotenuse to the two shorter perpendicular sides.