Mathematics
Form 3 · 24 topics available
Chapter 1 · Indices
Zero, Negative and Fractional Indices
Extend the laws of indices to zero (a⁰ = 1), negative (a⁻ⁿ = 1/aⁿ) and fractional (a^(1/n) = ⁿ√a) powers.
OpenIndex Notation
Learn how aⁿ records repeated multiplication: the base, the index, and how to read and evaluate simple powers.
OpenLaw of Indices
Master the laws of indices: add indices to multiply, subtract to divide, multiply for a power of a power, plus zero and negative indices.
OpenChapter 2 · Standard Form
Chapter 3 · Consumer Mathematics: Savings, Investments, Credit and Debt
Chapter 4 · Scale Drawings
Using Scale to Find Actual Measurements
A scale 1:n means 1 unit on the drawing represents n units in real life. Actual length = drawing length × n.
OpenConstructing Scale Drawings
To draw an object to scale 1:n, divide each actual length by n: drawing length = actual length ÷ n.
OpenScale Drawings
See how scale drawings shrink or enlarge real objects, and convert between drawing lengths and actual lengths using the scale.
OpenChapter 5 · Trigonometric Ratios
Finding Unknown Sides Using Trigonometric Ratios
In a right-angled triangle: sin θ = opp/hyp, cos θ = adj/hyp, tan θ = opp/adj. Rearrange to find an unknown side.
OpenFinding Unknown Angles and Applications
Use sin⁻¹, cos⁻¹ or tan⁻¹ to find an angle from two known sides, including angles of elevation and depression.
OpenSine, Cosine and Tangent of Acute Angles in Right-angled Triangles
Define sin, cos and tan of an acute angle as ratios of sides in a right-angled triangle, and use them to find sides.
OpenChapter 6 · Angles and Tangents of Circles
Angles at the Circumference and Central Angle Subtended by an Arc
Learn that the central angle on an arc is twice the angle at the circumference, and that same-arc circumference angles are equal.
OpenCyclic Quadrilaterals
A cyclic quadrilateral has all four vertices on a circle; its opposite angles add to 180° and its exterior angle equals the interior opposite angle.
OpenTangents to Circles
A tangent touches a circle at one point and is perpendicular to the radius there; two tangents from one external point are equal.
OpenAngles and Tangents of Circles
Combine circumference and central angles, cyclic quadrilaterals and tangent properties to solve mixed circle problems.
OpenChapter 7 · Plans and Elevations
Chapter 8 · Loci in Two Dimensions
Chapter 9 · Straight Lines
Gradient of a Straight Line
The gradient measures steepness: m = (y₂ − y₁)/(x₂ − x₁). Positive rises, negative falls, horizontal lines have gradient 0.
OpenThe Equation of a Straight Line
Every straight line can be written y = mx + c, where m is the gradient and c is the y-intercept.
OpenStraight Lines
Gradient m = change in y over change in x, and every line is y = mx + c with y-intercept c.
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