Cameroon GCE A-Level Pure Math with Mechanics study plan

Factorise and simplify polynomial, rational and surd expressions, including completing the square, until you can do ten mixed simplifications in 25 minutes with no errors.

Solve quadratic, simultaneous and inequality problems (including modulus and rational inequalities) and sketch the solution sets on a number line.

Sketch graphs of polynomials, rational functions and modulus functions, marking intercepts, asymptotes and turning points without a calculator.

Apply the factor and remainder theorems to find unknown coefficients and fully factorise cubics.

Solve equations involving indices and surds, and rationalise denominators of the form a + sqrt(b).

Work with functions: find domains and ranges, form composite functions and invert one-to-one functions algebraically.

Find equations of lines, perpendicular bisectors, circles and tangents, and convert circle equations between expanded and centre-radius form.

Solve intersection problems between lines and circles, interpreting the discriminant as a tangency condition.

Differentiate powers, products, quotients and composite functions fluently, including trigonometric, exponential and logarithmic forms.

Use differentiation to find gradients, tangents, normals, stationary points and to classify them with the second derivative.

Integrate standard forms and use substitution and integration by parts on recognisable patterns.

Evaluate definite integrals and use them to find areas under curves and between two curves, including where the curve crosses the axis.

Set up and solve rates-of-change and optimisation word problems, defining variables and stating the constraint before differentiating.

Apply calculus to kinematics: differentiate displacement to get velocity and acceleration, and integrate in reverse with initial conditions.

Compute volumes of revolution about the x-axis and handle improper or bounded-area cases carefully.

Write out full solutions in exam style, showing substitution limits and justification for maxima or minima.

Use arithmetic and geometric progressions: nth term, sum formulas, sum to infinity and convergence conditions.

Solve binomial expansion problems for positive integer and rational indices, including finding a particular coefficient.

Prove and apply trigonometric identities, solve trigonometric equations over a given interval, and use the compound and double-angle formulas.

Convert freely between exponential and logarithmic form, apply log laws, and solve exponential equations including disguised quadratics.

Solve one-dimensional kinematics problems with constant acceleration using the standard equations, choosing a positive direction explicitly each time.

Resolve velocity and acceleration into components and solve projectile problems, finding time of flight, range and maximum height.

Draw correct force diagrams for connected particles, inclines, pulleys and lifts, then apply Newton's second law to each body.

Handle friction using the coefficient of friction and the normal reaction, including limiting equilibrium cases.

Perform vector arithmetic in two and three dimensions, find magnitudes, unit vectors and scalar products, and use the scalar product to find angles.

Apply vectors to relative position and velocity problems, and to forces expressed in component form.

Take moments about a point, resolve forces in two perpendicular directions, and solve equilibrium problems for rods, ladders and hinged beams.

Identify and exclude extraneous forces or reactions when a system is on the point of slipping or toppling.

Complete two full past-paper-style mocks under timed conditions, allocating time per mark and leaving the last five minutes for checking.

Diagnose recurring errors from both mocks and rework every lost mark on the error sheet until each is reproducible without notes.

Drill the highest-weight domains (Algebra, Differentiation, Integration, Kinematics) with short 20-minute mixed sets to build speed.

Rehearse calculator technique and formula recall so no marks are lost to presentation, units or premature rounding.