Uganda Senior Three Curriculum - Mathematics

This curriculum for Mathematics is designed to equip learners with essential mathematical skills for effective participation in various aspects of life. It emphasizes understanding through mathematical inquiry and rational thought, focusing on developing reasoning, logical thinking, problem-solving, and analytical skills. The curriculum is structured around four main themes: Numbers, Geometry and Measures, Data and Probability, and Patterns and Algebra.

Senior Three Curriculum Details:

Term 1:

• Equation of a Straight Line: Learners explore the relationship between linear equations (y = mx + c) and their graphs, determine x and y intercepts, calculate gradients, and apply the concepts of parallel and perpendicular lines.
• Trigonometry 1: This topic covers deriving sine, cosine, and tangent functions from the unit circle, using calculators for trigonometric calculations, applying these functions to right-angled triangles, and understanding angles of elevation and depression.
• Data Collection and Display: Learners delve into measures of central tendency (mode, mean, median) and dispersion (range), frequency tables for grouped and ungrouped data, estimating measures for grouped data, calculating the mean using an assumed mean, drawing histograms to estimate the mode, and drawing cumulative frequency curves (ogives) to estimate the median.
• Vectors: Building on prior knowledge, learners describe position vectors geometrically and as column vectors, find vectors of directed line segments, determine mid-point position vectors, use vector methods for proportional division, and demonstrate parallelism and collinearity using vectors.

Term 2:

• Ratios and Proportions: This topic encompasses equivalent ratios, direct and inverse proportional reasoning, and the application of ratio, proportion, and scale in various contexts. Learners also draw and interpret lines of best fit on scatter graphs.
• Business Mathematics: Learners apply business mathematics concepts, including percentage change using multipliers, compound interest, depreciation and appreciation, currency conversion, hire purchase, mortgages, and income tax calculations.
• Trigonometry 2: Extending Trigonometry 1, learners determine trigonometric ratios for angles greater than 90°, use graphs of trigonometric functions, and apply sine and cosine rules to real-life problems.
• Matrices: This topic introduces matrices, their order, addition and multiplication, determinants of 2x2 matrices, inverses, and their application in solving real-life problems.
• Matrix Transformations: Learners explore transformation matrices for reflection, rotation, and enlargement, determine images on coordinate grids, identify transformation matrices from objects and images, find inverse matrices, use inverse matrices to find objects from images, and understand the relationship between area scale factor and the determinant. They also determine single matrices for successive transformations.

Term 3:

• Simultaneous Equations: Learners solve simultaneous equations using substitution, elimination, graphical methods, and matrices.
• Probability: This topic covers probability terms (random, experiment, outcome, sample space, event, probability), constructing probability spaces, determining probabilities, differentiating between theoretical and experimental probabilities, understanding mutually exclusive and independent events, using probability trees and Venn diagrams.
• Quadratic Equations: Learners determine roots using factorization, completing the square, and the quadratic formula, form quadratic equations from roots, draw graphs of quadratic functions, link solutions to graphical representations, and solve simultaneous equations involving quadratic and linear equations.
• Circle Properties: Learners identify circle parts (arc, chord, sector, segment), relate angles at the circumference and center, determine tangent, chord, and angle properties, use properties of cyclic quadrilaterals, find common chord lengths, and calculate areas of sectors and segments.