CSEC Additional Mathematics study plan

Classify and evaluate functions using correct notation, including composite and inverse functions with restricted domains

Solve linear and quadratic equations and inequalities, expressing solution sets on a number line and in interval notation

Apply the factor and remainder theorems to factorise polynomials of degree up to four and find unknown coefficients

Sketch quadratic functions in completed-square form, stating vertex, axis of symmetry, intercepts and range

Solve simultaneous equations, one linear and one non-linear, by substitution and verify solutions graphically

Simplify rational and algebraic-fraction expressions and solve equations that reduce to quadratics

Use indices and log laws to solve exponential and logarithmic equations, including change of base

Apply the binomial theorem to expand positive-integer powers and find a specified term or coefficient

Compute gradient, midpoint, length and equation of a straight line, including parallel and perpendicular conditions

Find intersections of lines and circles algebraically and determine whether a line is tangent to a circle

Convert between degrees and radians and evaluate exact trigonometric ratios for standard angles

Prove and apply trigonometric identities, including the Pythagorean identities and double-angle forms

Solve trigonometric equations over a stated interval, finding all solutions using general solutions and periodicity

Apply the sine and cosine rules and the area formula to non-right triangles, including bearings and elevation problems

Draw and interpret graphs of sine, cosine and tangent, stating amplitude, period and transformations

Solve problems in three dimensions involving angles between lines and planes in simple solids

Differentiate polynomials and simple rational and surd powers from first principles and by rule

Apply the chain, product and quotient rules to composite and combined expressions

Find equations of tangents and normals, and locate stationary points, classifying them by second derivative or sign test

Solve rates-of-change and simple optimisation problems, stating the variable being maximised or minimised

Integrate powers of x and simple trigonometric and exponential expressions, including definite integrals

Evaluate definite integrals to find areas under curves and between a curve and a line

Apply the trapezium rule with a stated number of strips and estimate the error of the approximation

Solve simple differential equations by separating variables and apply an initial condition

Construct and solve linear programming problems, identifying feasible regions and optimal vertices

Apply vectors in two dimensions to displacement, velocity and relative position problems

Solve kinematics problems involving displacement, velocity and acceleration using differentiation and integration

Handle sequences and series, including arithmetic and geometric progressions and sums to n terms

Complete two full timed papers under exam conditions, allocating time by domain weighting

Review every error and classify it as conceptual, procedural or careless, then rework it correctly

Rehearse a formula recall sheet from memory for all four domains

Target the two weakest topics identified across the mocks with focused drills