100+ Free Cameroon GCE A-Level Pure Mathematics with Statistics Practice Questions

Pure Mathematics: Algebra, Series & Functions

Polynomial algebra, remainder and factor theorems, rational functions, partial fractions with linear and quadratic factors, arithmetic and geometric progressions, infinite geometric series convergence ($|r| < 1$), binomial theorem for general index $n \in \mathbb{Q}$, domain and range of real functions, composition of functions $g \circ f$, and inverse functions $f^{-1}(x)$.

Pure Mathematics: Calculus & Coordinate Geometry

Differentiation fundamentals, derivatives of polynomial, trigonometric, logarithmic, and exponential functions, product, quotient, and chain rules, implicit differentiation, tangents and normals, stationary points, nature of extrema, rates of change, integration as reverse differentiation, standard integration rules, integration by substitution, integration by parts, definite integrals and areas under curves, first-order separable differential equations, and coordinate geometry of lines, gradients, parallel/perpendicular conditions, and circles $(x-a)^2 + (y-b)^2 = r^2$.

Pure Mathematics: Trigonometry & Vectors

Trigonometric identities including $\sin^2 \theta + \cos^2 \theta = 1$, $1 + \tan^2 \theta = \sec^2 \theta$, addition formulas $\sin(A \pm B)$ and $\cos(A \pm B)$, double angle formulas, conversion to $R\cos(\theta - \alpha)$ or $R\sin(\theta + \alpha)$, trigonometric equations on bounded domains, 2D and 3D vector representations, unit vectors, scalar product (dot product) $\vec{u} \cdot \vec{v} = |\vec{u}||\vec{v}|\cos \theta$, and perpendicularity condition $\vec{u} \cdot \vec{v} = 0$.

Statistics: Data Representation & Probability

Data summary statistics, calculation of mean $\bar{x}$, variance $\sigma^2$, and standard deviation $\sigma$ from raw and grouped frequency tables, linear transformation of data $y = ax + b$, measures of position (median, quartiles, percentiles, interquartile range), basic counting principles, permutations $_n P_r$, combinations $_n C_r$, sample spaces, axioms of probability, addition rule $P(A \cup B) = P(A) + P(B) - P(A \cap B)$, mutually exclusive events, conditional probability $P(A|B) = \frac{P(A \cap B)}{P(B)}$, independent events $P(A \cap B) = P(A)P(B)$, tree diagrams, and Bayes' theorem.

Statistics: Distributions & Inference

Discrete random variables, expectation $E(X) = \sum x P(X=x)$, variance $Var(X) = E(X^2) - [E(X)]^2$, linear properties $E(aX+b) = aE(X)+b$ and $Var(aX+b) = a^2 Var(X)$, Binomial distribution $X \sim B(n,p)$, Poisson distribution $X \sim Po(\lambda)$, continuous random variables, probability density functions $f(x)$, standard Normal distribution $Z \sim N(0,1)$, standardization $Z = \frac{X - \mu}{\sigma}$, normal approximation to Binomial and Poisson with continuity correction, sampling distribution of the sample mean $\bar{X} \sim N\left(\mu, \frac{\sigma^2}{n}\right)$, Central Limit Theorem, confidence intervals, null ($H_0$) and alternative ($H_1$) hypotheses, 1-tailed and 2-tailed tests, significance levels, critical values, and hypothesis testing for population means and proportions.