Mathematics — A-Level
Ten foundational chapters — from coordinate geometry through trigonometry.
Chapter 1
Introduction to Coordinate Geometry
Locate points precisely with coordinates, measure the distance and midpoint between them, and describe straight lines with slope and the equation y = mx + c.
Chapter 2
Exponents and Radicals
The laws that govern powers and roots, from zero and negative exponents to simplifying, combining, and rationalizing radicals, and solving exponential equations.
Chapter 3
Logarithms
Scientific notation, what a logarithm means and how it connects to exponents, the product, quotient, and power rules, changing base, and the common and natural logarithms.
Chapter 4
Functions
Product sets and their cardinality, relations and how to represent them, and what makes a relation a function — domain, range, the vertical line test, and function notation.
Chapter 5
Quadratic Functions
Graphing parabolas — upward, downward, narrow, and wide — the vertex formula, the discriminant, the quadratic formula, and solving quadratic inequalities.
Chapter 6
Absolute Value Functions
Graphing V-shaped functions — upward, downward, narrow, and wide — the general vertex form, and solving absolute value equations and inequalities.
Chapter 7
Probability
Sample spaces and the probability formula, the complement rule, the addition and multiplication rules for combined events, conditional probability, and expected frequency.
Chapter 8
Similarity
Similar figures and triangles, the basic proportionality theorem, tests for similar triangles, the angle bisector theorem, the Pythagoras theorem, and special right triangles.
Chapter 9
Circles
Central and inscribed angles, the angle in a semicircle, cyclic quadrilaterals, and the properties of chords — equal chords, the perpendicular bisector, and intersecting chords.
Chapter 10
Trigonometry
Angles in standard position, degree-radian conversion, arc length and sector area, the six trigonometric ratios and their relations, special angles, solving right triangles, and angles of elevation and depression.