Zimbabwe Form 4 Curriculum - Additional Mathematics (Elective)

This course expands on the concepts learned in Form 1-4 Mathematics and provides a foundation for higher-level mathematics and related careers. It emphasizes problem-solving, logical reasoning, and application of mathematical concepts in practical contexts.

Pure Mathematics

• Indices and Irrational Numbers: Covers rational indices, rules of indices, algebraic applications, exponential equations, surds, and operations with surds.
• Polynomials: Includes definitions of polynomials, operations with polynomials, the factor theorem, the remainder theorem, and factorization.
• Algebraic Identities, Equations, and Inequalities: Focuses on distinguishing identities from equations, determining unknown coefficients using identities, solving linear, simultaneous, quadratic, and cubic equations, and solving linear and quadratic inequalities.
• Sequences and Series: Introduces notations for sequences and series, explores the behavior of sequences (periodic, oscillatory, convergent, divergent), and covers arithmetic and geometric progressions, including finding the nth term and sum of n terms, and sum to infinity.
• Coordinate Geometry in Two Dimensions: Includes calculating the distance between two points, gradient, equation of a straight line, parallel and perpendicular lines, and the equation of a normal.
• Functions: Covers definitions of functions, domain, range, one-to-one mapping, inverse functions, composite functions, and graphical representation of functions.
• Quadratic Functions: Includes quadratic expressions, equations, functions, maximum/minimum values, nature of roots, and graphical representation.
• Logarithmic and Exponential Functions: Covers definitions of logarithms, laws of logarithms, sketching graphs and their inverses, logarithmic and exponential equations, and expressing logarithms as exponential functions and vice versa.
• Trigonometrical Functions: Includes trigonometric ratios, simple identities, simple equations, trigonometric functions, sketching graphs, proving simple identities, and solving trigonometric equations using identities.
• Differentiation: Covers the gradient of a curve, derivative notation, rules of derivatives, derivatives of simple functions, stationary points (maximum and minimum), applications to tangents, normals, and rates of change.
• Integration: Introduces integration as the reverse process of differentiation, notation, integration of simple functions, and applications to finding area and volume under a curve.

Probability and Statistics

• Probability: Covers set language and notation (trial, sample spaces, outcomes, events, Venn diagrams), approaches to probability (objective, experimental, classical, subjective), addition and product rules (independent and mutually exclusive events, outcome tables, tree diagrams), and conditional probability.
• Data Collection and Presentation: Includes key statistical terms, sources and types of data, data collection methods, and forms of data presentation.
• Measures of Central Tendency and Dispersion: Covers mean, median, mode, variance, standard deviation, range, interquartile range, and coefficient of variation.
• Discrete and Continuous Probability Distributions: Includes discrete random variables and their probability distributions, binomial probability distribution, continuous random variables and their probability density functions, and mean and variance of random variables.
• Normal Distribution: Covers properties of the normal distribution curve, the standard normal variable, probabilities, using standard normal tables, and finding mean and variance.
• Sampling Methods: Includes sampling techniques (random and non-random), the central limit theorem, and the distribution of sample mean.
• Estimation: Covers point estimation (mean and variance), interval estimation (confidence intervals for population mean and normal population mean with known variance and large sample).

Mechanics

• Kinematics of Motion in a Straight Line: Covers distance, speed, x-t graphs, velocity, acceleration, v-t graphs, equations of motion, vector and scalar quantities.
• Forces and Equilibrium: Includes types of forces, representation of forces by vectors, resultants and components, composition and resolution, equilibrium of a particle, and friction.
• Newton's Laws of Motion: Covers Newton's laws of motion and their applications to linear motion.
• Energy, Work, and Power: Includes concepts of gravitational potential energy, kinetic energy, work, power, and the principle of energy conservation.