Subsidiary Mathematics

This syllabus covers Pure Mathematics, Probability, and Statistics, aiming to equip students with mathematical skills applicable to everyday situations and further learning. The focus is on skills acquisition, development, and application.

Senior Five Term 1

• Matrices and their Applications: This topic covers matrix operations, determinants, inverses, and their application in solving simultaneous equations. Students learn to formulate matrices, perform operations, and apply them to real-life problems.
• Linear Programming: Students learn to formulate constraints, graph inequalities, and optimize objective functions to maximize gains and minimize losses in real-life scenarios.
• Quadratics: This topic covers solving quadratic equations using various methods, identifying roots, forming equations from roots, and finding maximum/minimum values. Applications in physics and economics are also explored.
• Statistics: Students learn data collection, classification (discrete/continuous), presentation (frequency tables, histograms, ogives), and analysis using measures of central tendency (mean, median, mode) and dispersion (range, variance, standard deviation).

Senior Five Term 2

• Indices, Logarithms, and Surds: Students learn to simplify and evaluate expressions involving indices, logarithms, and surds, including solving equations and applying laws of logarithms.
• Series: This topic covers patterns, sequences, arithmetic progressions, and geometric progressions, including finding the nth term and sum of terms, and applying these concepts to real-life problems like compound interest.
• Permutations and Combinations: Students learn to determine the number of permutations and combinations of objects, applying formulas and notations to real-life situations.
• Moving Averages: Students learn to calculate and plot moving averages, identify trends, and use these to forecast events in business and other areas.
• Index Numbers: This topic covers calculating simple and weighted price index numbers, value indices, and cost of living indices, and using them to compare relative changes.

Senior Five Term 3

• Scatter Diagrams and Correlations: Students learn to draw and interpret scatter diagrams, determine correlation types, draw lines of best fit, and calculate correlation coefficients (Spearman's rank).
• Vectors: This topic covers vector notations, operations (addition, subtraction, scalar multiplication), displacement and position vectors, magnitude, direction, parallel and perpendicular vectors, dot products, and angles between vectors.
• Trigonometry: Students learn trigonometric ratios, special angles, graphs of sine and cosine, trigonometric identities, and solving quadratic trigonometric equations.
• Probability Theory: This topic covers probability terminologies, experimental probability, probability laws, contingency tables, Venn diagrams, tree diagrams, mutually exclusive and independent events, conditional probability, and problem-solving.

Senior Six Term 1

• Differentiation: This topic covers the first and second derivatives of functions (linear, quadratic, cubic, natural log), maximization and minimization, curve sketching (turning points, intercepts), and applications to displacement, velocity, and acceleration.
• Discrete Random Variables: Students learn about discrete random variables, probability mass functions, probability distribution tables, calculating expectation, variance, standard deviation, and the binomial distribution.

Senior Six Term 2

• Integration: This topic covers indefinite and definite integrals, calculating area under a curve, and applications to displacement, velocity, and acceleration.
• Continuous Random Variables: Students learn about continuous random variables, probability density functions, calculating probabilities, expectation, variance, and standard deviation.
• Normal Distribution: This topic covers properties of the normal distribution, standardization, using standard normal distribution tables and calculators to determine probabilities, and determining mean and standard deviation.

Senior Six Term 3

• Differential Equations: This topic covers the concept of differential equations, finding general and particular solutions, and solving problems related to natural occurrences using first-order differential equations with separable variables.