Year 10 Mathematics: Trigonometry, Area, Volume, and Non-Linear Relationships Vocabulary

Flashcards covering key terms, definitions, formulas, and graph transformations from Trigonometry C through Non-Linear Relationships C.

Space Diagonal Formula

The formula $D = \sqrt{a^2 + b^2 + c^2}$ used to calculate the space diagonal of a rectangular prism with dimensions $a$, $b$, and $c$.

Sine Rule

The rule stating $\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}$, where each side of a triangle is paired with its opposite angle.

Cosine Rule

The rule stating $a^2 = b^2 + c^2 - 2bc \cos(A)$, used for non-right-angled triangles given two sides and the included angle.

Cosine Rule for an Angle

The rearranged cosine formula $A = \cos^{-1}\left(\frac{b^2 + c^2 - a^2}{2bc}\right)$ used to calculate an unknown angle when three side lengths are given.

Area Rule for Triangles

The formula $\text{Area} = \frac{1}{2}bc \sin(A)$ used to find the area of any triangle given two sides and the included angle $A$.

Surface Area

The total area of the outside surfaces of a three-dimensional object.

Surface Area of a Rectangular Prism

Calculated using $SA = 2lw + 2lh + 2wh$, which sums the areas of the three pairs of equal rectangular faces.

Surface Area of a Cylinder

Calculated using $SA = 2\pi r^2 + 2\pi rh = 2\pi r(r + h)$, combining two circular ends and the curved surface.

Volume

The amount of three-dimensional space inside an object, measured in cubic units such as $\text{cm}^3$, $\text{m}^3$, or $\text{mm}^3$.

Volume of a Prism

Calculated using $V = Bh$, where $B$ is the area of the cross-section or base and $h$ is the perpendicular length.

Volume of a Pyramid

Calculated using $V = \frac{1}{3}Bh$, where $B$ is the base area and $h$ is the perpendicular height.

Volume of a Cone

Calculated using $V = \frac{1}{3}\pi r^2 h$, where $r$ is the radius and $h$ is the perpendicular height.

Volume of a Sphere

Calculated using $V = \frac{4}{3}\pi r^3$, where $r$ is the radius.

Volume of a Hemisphere

Calculated using $V = \frac{2}{3}\pi r^3$, representing half the volume of a sphere.

Parabola Vertex Form

The equation $y = a(x - h)^2 + k$, where $(h, k)$ is the vertex of the parabola.

Exponential Growth

Represented by $y = a^x$ when $a > 1$, where the graph rises rapidly as $x$ increases.

Exponential Decay

Represented by $y = a^x$ when $0 < a < 1$, where the graph falls towards zero as $x$ increases.

Hyperbola Transformed Form

The equation $y = \frac{a}{x - h} + k$, having a vertical asymptote at $x = h$ and a horizontal asymptote at $y = k$.

Asymptote

A line that a graph continuously approaches.

Circle Graph Equation

The equation $(x - h)^2 + (y - k)^2 = r^2$, representing a circle centered at $(h, k)$ with radius $r$.

Polynomial

An algebraic expression containing powers of $x$ with non-negative integer exponents.

Degree of a Polynomial

The highest power of $x$ in a polynomial expression.

Horizontal Translation $f(x - h)$

A transformation that shifts the graph of $y = f(x)$ to the right by $h$ units.

Horizontal Translation $f(x + h)$

A transformation that shifts the graph of $y = f(x)$ to the left by $h$ units.