100+ Free Cameroon GCE O-Level Additional Mathematics Practice Questions

Algebra & Functions

Quadratic equations, discriminant and nature of roots, completing the square, quadratic inequalities, polynomial division, remainder and factor theorems, non-linear simultaneous equations, laws of indices, surds rationalisation, logarithmic laws and equations, change of base, functional mapping, domain, range, composite functions, and inverse functions.

Coordinate Geometry & Vectors

Cartesian coordinate geometry of straight lines, gradient, length of a line segment, midpoint formula, parallel and perpendicular line conditions, perpendicular bisectors, circle equations $(x-a)^2+(y-b)^2=r^2$ and $x^2+y^2+2gx+2fy+c=0$, circle tangents and normals, 2D vector notation, vector magnitude, unit vectors, position vectors, and scalar (dot) products.

Trigonometry

Radian measure conversion ($180^\circ = \pi\text{ rad}$), arc length formula $s = r\theta$, area of circular sector $A = \frac{1}{2}r^2\theta$, segment area, trigonometric ratios for angles of any magnitude using the CAST rule, fundamental identities $\sin^2\theta + \cos^2\theta = 1$, $\tan\theta = \frac{\sin\theta}{\cos\theta}$, $\sec^2\theta = 1+\tan^2\theta$, and solving linear and quadratic trigonometric equations on bounded intervals.

Calculus: Differentiation & Integration

Differentiation from standard power rule $\frac{d}{dx}(ax^n) = anx^{n-1}$, product rule, quotient rule, chain rule for composite functions, derivatives of $\sin x$ and $\cos x$, equations of tangents and normals, stationary points and classification using the second derivative test, optimization word problems, connected rates of change, indefinite integration, boundary condition constants of integration, definite integrals, and area bounded by curves.

Mechanics & Statistics

Kinematics of a particle moving in a straight line with uniform acceleration (equations of motion $v=u+at$, $s=ut+\frac{1}{2}at^2$, $v^2=u^2+2as$) and variable acceleration using calculus ($v = \frac{ds}{dt}$, $a = \frac{dv}{dt} = \frac{d^2s}{dt^2}$, $s = \int v\, dt$), fundamental counting principle, permutations $_n P_r$, combinations $_n C_r$, sample spaces, and basic probability rules.