Year 10 Mathematics Mock Test Review: Area, Volume, Linear Relationships, and Trigonometry

This set of vocabulary flashcards covers essential terms and formulas from the Year 10 Mathematics Mock Test, focusing on geometry, coordinate geometry, and trigonometry.

Perpendicular height (Pyramid)

The vertical distance from the apex of a pyramid to the center of its base.

Slant height (Pyramid)

The distance measured from the apex of a pyramid along the face to the midpoint of an edge of the base.

Surface Area of a closed cone

The total area of the circular base and the curved lateral surface, calculated as SA = \text{\pi} r^2 + \text{\pi} rs, where $s$ is the slant height.

Radius of the Earth

According to the test, this value is approximately $6378\,km$.

Volume of a sphere

The total capacity of a sphere, calculated using the formula $V = \frac{4}{3} \pi r^3$.

Composite solid

A three-dimensional object made up of two or more simpler shapes, such as a cone with a hemisphere attached at the top.

Cartesian plane

A two-dimensional coordinate system formed by the intersection of a horizontal x-axis and a vertical y-axis.

Midpoint

The exact middle point between two coordinates $M(x_1, y_1)$ and $N(x_2, y_2)$, found using the formula $(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})$.

Gradient ($m$)

A measure of the steepness of a line, defined as the ratio of the vertical change to the horizontal change ($\frac{y_2 - y_1}{x_2 - x_1}$).

y-intercept

The point where a straight line crosses the vertical y-axis on a Cartesian plane.

Gradient-intercept form

The equation of a straight line written as $y = mx + b$, where $m$ is the gradient and $b$ is the y-intercept.

General form (Linear Equation)

A linear equation written in the format $ax + by + c = 0$.

Parallel lines

Lines in the same plane that never intersect and have identical gradients ($m_1 = m_2$).

Perpendicular lines

Lines that intersect at a right angle ($90^\circ$), where the product of their gradients is $-1$ ($m_1 \times m_2 = -1$).

Sine ratio ($\sin(\theta)$)

The trigonometric ratio in a right-angled triangle defined as $\frac{\text{opposite}}{\text{hypotenuse}}$.

Cosine ratio ($\cos(\theta)$)

The trigonometric ratio in a right-angled triangle defined as $\frac{\text{adjacent}}{\text{hypotenuse}}$.

Tangent ratio ($\tan(\theta)$)

The trigonometric ratio in a right-angled triangle defined as $\frac{\text{opposite}}{\text{adjacent}}$.