Essential Mathematical Methods 1 and 2 with CD-ROM

1. Reviewing linear equations, 1.1. Linear equations, 1.2. Solving linear equations in one unknown, 1.3. Constructing linear equations, 1.4. Simultaneous equations, 1.5. Constructing and solving simultaneous linear equations, 1.6. Solving linear inequations, 1.7. Using and transposing formulae; 2. Linear relations, 2.1. The gradient of a straight line, 2.2. The general equation of a straight line, 2.3. Finding the equation of a straight line, 2.4. Equation of a straight line in intercept form, 2.5. Linear models, 2.6. Problems involving simultaneous linear models, 2.7. The tangent of the angle of slope, 2.8. Perpendicular lines, 2.9. The distance between two points, 2.10. Midpoint of a line, 2.11. Angle between intersecting lines; 3. Quadratics, 3.1. Expanding and factorising, 3.2. Quadratic equations, 3.3. Graphing quadratics, 3.4. Completing the square, 3.5. Sketching quadratics in polynomial form, 3.6. The general quadratic formula, 3.7. Iteration, 3.8. The discriminant, 3.9. Solving quadratic inequations, 3.10. Solving simultaneous linear and quadratic equations, 3.11. Determining quadratic rules, 3.12. Quadratic models; 4. A gallery of graphs, 4.1. Rectangular hyperbolas, 4.2. The truncus, 4.3. Circles; 5. Functions and relations, 5.1. Set notations and sets of numbers, 5.2. Relations, 5.3. Functions, 5.4. Special types of functions, 5.5. Miscellaneous exercises, 5.6. Inverse functions, 5.7. Functions and modelling exercises; 6. Cubic functions, 6.1. Cubic functions of the form f:R > R, f(x)= a(x-h)3 + k, 6.2. Division of polynomials, 6.3. Factorisation of polynomials, 6.4. Solving cubic equations, 6.5. Graphs of cubic functions, 6.6. Solving cubic inequations, 6.7. Finding equations for given cubic graphs, 6.8. Graphics calculator exercise, 6.9. Finite differences for sequences generated by polynomials, 6.10. Applications of cubic functions and models; 7. Revision of chapters 2-6, 7.1. Summary of chapters, 7.2. Short answer exercises, 7.3. Multiple choice questions for chapters 2-6, 7.4. Analysis questions, 7.5. Structured problem solving, investigations and computer exercises; 8. Probability, 8.1. Random experiments and events, 8.2. Determining empirical probabilities, 8.3. Determining probabilities by symmetry, 8.4. The addition rule, 8.5. Conditional probability and the multiplication rule, 8.6. Independent events; 9. Counting methods, 9.1. Introduction, 9.2. Addition and multiplication principles, 9.3. Permutations, 9.4. Combinations, 9.5. Pascal's Triangle, 9.6. Applications to probability; 10.The hypergeometric and binomial distributions, 10.1. Introduction, 10.2. The hypergeometric distribution, 10.3. The binomial distribution, 10.4. The binomial approximation to the hypergeometric distribution, 10.5. Graphics calculator exercises; 11. Simulation, 11.1. Solving probability problems using simulation, 11.2. Random number trials, 11.3. How many trials?, 11.4. Simulation with calculators; 12. Revision of chapters 8-11, 12.1. Summary of chapters 8-11, 12.2. Short answer questions, 12.3. Multiple choice questions, 12.4. Analysis questions, 12.5. Problem solving, projects and computer applications; 13. Exponential functions and logarithms, 13.1. Defining exponential functions, 13.2. Graphs of exponential functions, 13.3. Reviewing rules for exponents (indices), 13.4. Rational exponents, 13.5. Solving exponential equations and inequations, 13.6. Logarithms, 13.7. Further solution methods for exponential equations, 13.8. Graph of y = log10x, 13.9. Graphics calculator exercises, 13.10. Exponential models and applications; 14. Circular functions, 14.1. Measuring angles in degrees and radians, 14.2. Defining circular functions - sine and cosine, 14.3. Another circular function - tangent, 14.4. Reviewing trigonometric ratios, 14.5. Symmetry properties of circular functions, 14.6. Exact values of circular functions, 14.