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Full Description
Study & Master Mathematics Grade 12 has been developed with the help of practising teachers and covers all the requirements of the National Curriculum Statement for Mathematics. Special features of the Learner's Book include: * module openers, clearly explaining the outcomes for that module * language skills activities, assisting learners to master the language of Mathematics * assessment activities, ensuring continuous self, peer and group assessment * module reviews, which provide extra practice as well as more challenging activities * projects, which deal with issues related to the real world, and move learners beyond the confines of the classroom.
Contents
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.
