Additional Mathematics study guides

An O-Level Additional Mathematics (4049) overview of the binomial theorem and partial fractions in the Algebra strand. How to expand a plus b to a positive integer power, use the general term to find a specified coefficient or the constant term, and split a proper rational fraction into partial fractions, with links to every dot point.

An O-Level Additional Mathematics (4049) overview of coordinate geometry and circles in the Geometry and Trigonometry strand. How gradients, distances, midpoints and line equations, the shoelace area method, the equation of a circle, and combined line-and-circle problems fit together, with links to every dot point.

An O-Level Additional Mathematics (4049) overview of differentiation and its applications in the Calculus strand. How the derivative as a gradient leads to the power, product, quotient and chain rules, then to tangents and normals, stationary points and their nature, and connected rates of change, with links to every dot point.

An O-Level Additional Mathematics (4049) overview of integration and its applications in the Calculus strand. How integration reverses differentiation, the integrals of powers and standard functions including linear composites, definite integrals and the area under a curve, and the area between two curves, with links to every dot point.

An O-Level Additional Mathematics (4049) overview of kinematics in the Calculus strand. How displacement, velocity and acceleration relate for motion in a straight line, how differentiation and integration move between them, and how to solve applied problems on maximum displacement, total distance and changes of direction, with links to every dot point.

An O-Level Additional Mathematics (4049) overview of logarithmic and exponential functions in the Algebra strand. How the laws of logarithms, the shapes of exponential and logarithmic graphs, solving equations with the unknown in an exponent or a logarithm, and the linear law for transforming non-linear relationships fit together, with links to every dot point.

An O-Level Additional Mathematics (4049) overview of quadratic functions and equations in the Algebra strand. How completing the square reveals the vertex, the discriminant decides the nature of the roots, quadratic inequalities give a solution range, and a substitution reduces other equations to quadratic form, with links to every dot point.

An O-Level Additional Mathematics (4049) overview of the surds, indices and polynomials foundations in the Algebra strand. How the laws of indices, surd manipulation, the remainder and factor theorems, and full factorisation work together to solve cubic and higher polynomial equations, with links to every dot point.

An O-Level Additional Mathematics (4049) overview of trigonometry and identities in the Geometry and Trigonometry strand. How the unit circle extends the ratios to any angle, the standard identities support proofs, equations are solved across an interval, and the addition, double angle and R-formulae expand and combine expressions, with links to every dot point.