Study and Master Mathematics Grade 12 Learner Book

Module 1. Numbers and Number Relationships; 1. Sequences and series*; Number patterns, Logarithms; Sequences; Arithmetic sequences; Sigma notation; Arithmetic series; Geometric sequences; Geometric series; Other sequences and recursive formulae; Applying geometric series to annuities and bond payments; 2. Comparing loan and investment options; Cost comparisons; Project 1. Micro-lending; Project 2. Pyramid schemes; Language skills; Check yourself; Review; Self-assessment rubric Module 2. Functions and Algebra 1. Relationships and functions; A function and its graph; The function machine and the function rule; Relations; Review of functions and relations 2. Inverse relations and functions; Inverse relations; Graphing the inverse relation; Increasing and decreasing functions; The inverse relation of an increasing or decreasing function 3. The remainder and factor theorems 4. The derivative; Functions and calculus; The derivative. a geometric definition; The derivative as a limit; A rule for differentiating powers of x; The notation dy/dx for the derivative; The chain rule; Shapes of curves; Stationary points and turning points; Second derivatives; Concavity and points of inflection; Sketching cubic functions showing their x-intercepts; global maxima and minima; Calculus in real life; Rates of change; 5. Linear programming; Finding optimum solutions; Linear programming in action; More complex problems; Project 3. Optimum order supply; Language skills; Check yourself; Review; Self-assessment rubric Module 3. Space Shape and Measurement; 1. Euclidian geometry*; Revision of concepts; Circle geometry; Circles and chords; Angles at the centre and circumference; Angles on the same and opposite arcs; Concylic points; Tangents and radii; The alternate segment theorem 2. Coordinate geometry; Review of formulae; Compound-angle identities; Double-angle identities; Problems in three dimensions; Angles between planes and other more complex 3-D problems; 4. Transformation geomtery; Transformations; Translations; Reflections; Rotations; Effect of rotation above the origin on the coordinates of a point; Enlargement; Project 4. Networks, fractals and spherical geometry; Language skills; Check yourself; Review; Self-assessment rubric; Module 4. Data Handling and Probability*; 1. Univariate numerical data. populations and samples; Populations; Samples; Simple random sample (SRS); Other sampling methods; Population parameters and sample statistics; Misuse of statistics; 2. Univariate numerical data. normal distribution; Describing z-scores; Properties of the normal distribution; Calculations involving the normal distribution; 3. Bivariate numerical data. correlation coefficient; The scatter plot; Characteristics of a relationship; The correlation coefficient; Calculating Pearson's correlation coefficient; The coefficient of determination; Dependent and independent variables; Correlation and causality; 4. Bivariate numerical data. regression analysis; Fitting lines to data; Simple linear regression; The least squares regression line; Performing a regression analysis; 5. Probability; Probability and sample spaces; Sample space graphs and tree diagrams; Venn diagrams and the additional rule; Multi-stage experiments and the product rule; Probability tree diagrams; Project 5. A statistical analysis; Language skills; Check yourself; Review; Self-assessment rubric; Appendix. Rubrics for assessment.