100+ Free Cameroon GCE A-Level Pure Math with Mechanics Practice Questions

Pure Mathematics — Algebra & Functions

Covers polynomial algebra, remainder and factor theorems, rational functions, partial fraction decomposition with linear and repeated quadratic factors, exponential and logarithmic equations and change of base rules, arithmetic progressions (AP) and geometric progressions (GP), summation of series using standard sigma formulas and method of differences, binomial theorem for rational indices $(1+x)^n$ and its range of validity, principle of mathematical induction, mappings and functions (domain, codomain, range, injection, surjection, bijection, composite and inverse functions), quadratic theory and discriminant conditions, rational and modulus inequalities, and systems of linear equations using matrix inversion and Gaussian elimination.

Pure Mathematics — Trigonometry & Vectors

Encompasses compound angle identities $\sin(A \pm B)$, $\cos(A \pm B)$, $\tan(A \pm B)$, double angle and half angle formulas, harmonic conversion form $R\cos(\theta \pm \alpha)$ and $R\sin(\theta \pm \alpha)$ with maximum/minimum determination, general and principal solutions of trigonometric equations, inverse trigonometric functions, two-dimensional and three-dimensional Cartesian vector algebra, unit vectors, scalar (dot) product and projection of vectors, angle between vectors, vector (cross) product and area of triangles/parallelograms, scalar triple product and coplanarity conditions, vector and Cartesian equations of straight lines in 3D, vector and scalar equations of planes, points of intersection of lines and planes, perpendicular distance from a point to a plane, and shortest distance between skew lines.

Pure Mathematics — Calculus

Covers differential and integral calculus: differentiation from first principles, standard derivatives of algebraic, exponential, logarithmic, trigonometric, and inverse trigonometric functions, differentiation rules (product, quotient, chain rule), implicit differentiation, parametric differentiation and second derivatives, tangent and normal equations, stationary points, points of inflexion, curve sketching, applied optimization and related rates of change, integration techniques (standard forms, substitution method, integration by parts, partial fractions, trigonometric integrals), definite integrals and fundamental theorem of calculus, area under curves and between intersecting curves, volumes of revolution about the x-axis and y-axis, Maclaurin and Taylor series expansions, numerical integration using the trapezium rule, and solving first-order separable and linear differential equations with integrating factors.

Mechanics — Kinematics & Dynamics

Encompasses kinematics of particles in one and two dimensions: equations of motion for constant acceleration in a straight line, variable acceleration using differentiation and integration ($v = ds/dt$, $a = dv/dt = v\,dv/ds$), projectile motion under gravity, time of flight, maximum height, horizontal range, equation of the parabolic trajectory, Newton's three laws of motion, resistive forces and friction (limiting friction $F_r = \mu R$), motion of bodies on smooth and rough horizontal and inclined planes, connected particles over smooth and rough pulleys, Atwood machines, linear momentum, impulse of a force, conservation of linear momentum, direct and oblique collisions between smooth spheres and fixed barriers, Newton's law of restitution ($e = (v_2 - v_1)/(u_1 - u_2)$), kinetic energy loss in impacts, uniform circular motion, conical pendulums, banked road tracks, vertical circular motion, simple harmonic motion (SHM), and relative velocity in 2D.

Mechanics — Statics & Energy

Treats statics of rigid bodies and energy mechanics: equilibrium of coplanar concurrent forces, triangle of forces and Lami's theorem, resolution of forces along perpendicular axes, moments of forces about points and axes, Varignon's theorem, couples and torque, equilibrium of non-concurrent forces, ladder leaning against smooth and rough vertical walls in limiting equilibrium, center of mass of systems of discrete coplanar particles, center of mass of standard uniform laminae (rectangles, triangles, circles, semicircles, composite T/L shapes, and laminae with cutouts), toppling versus sliding criteria on inclined planes, work done by constant and variable forces, gravitational potential energy and kinetic energy, Hooke's law for elastic springs and strings ($T = \lambda x / l_0$), elastic potential energy ($E_p = \lambda x^2 / (2l_0)$), work-energy theorem, mechanical power and tractive force of vehicles ($P = F v$), and stable, unstable, and neutral equilibrium.