Maths quest 11. Mathematical methods: VCE units 1 & 2

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Title Page Copyright Page Contents Introduction About eBookPLUS and studyON Acknowledgements TOPIC 1 Lines and linear relationships 1.1 Kick off with CAS 1.2 Linearly related variables, linear equations and inequations 1.3 Systems of 3 × 3 simultaneous linear equations 1.4 Linear graphs and their equations 1.5 Intersections of lines and their applications 1.6 Coordinate geometry of the straight line 1.7 Review Answers TOPIC 2 Algebraic foundations 2.1 Kick off with CAS 2.2 Algebraic skills 2.3 Pascal’s triangle and binomial expansions 2.4 The binomial theorem 2.5 Sets of real numbers 2.6 Surds 2.7 Review Answers TOPIC 3 Quadratic relationships 3.1 Kick off with CAS 3.2 Quadratic equations with rational roots 3.3 Quadratics over R 3.4 Applications of quadratic equations 3.5 Graphs of quadratic polynomials 3.6 Determining the rule of a quadratic polynomial from a graph 3.7 Quadratic inequations 3.8 Quadratic models and applications 3.9 Review Answers TOPIC 4 Cubic polynomials 4.1 Kick off with CAS 4.2 Polynomials 4.3 The remainder and factor theorems 4.4 Graphs of cubic polynomials 4.5 Equations of cubic polynomials 4.6 Cubic models and applications 4.7 Review Answers TOPIC 5 Higher-degree polynomials 5.1 Kick off with CAS 5.2 Quartic polynomials 5.3 Families of polynomials 5.4 Numerical approximations to roots of polynomial equations 5.5 Review Answers TOPIC 6 Functions and relations 6.1 Kick off with CAS 6.2 Functions and relations 6.3 The circle 6.4 The rectangular hyperbola and the truncus 6.5 The relation y2 = x 6.6 Other functions and relations 6.7 Transformations of functions 6.8 Review Answers TOPIC 7 Matrices and applications to transformations 7.1 Kick off with CAS 7.2 Addition, subtraction and scalar multiplication of matrices 7.3 Matrix multiplication 7.4 Determinants and inverses of 2 × 2 matrices 7.5 Matrix equations and solving 2 × 2 linear simultaneous equations 7.6 Translations 7.7 Reflections 7.8 Dilations 7.9 Combinations of transformations 7.10 Review Answers TOPIC 8 Probability 8.1 Kick off with CAS 8.2 Probability review 8.3 Conditional probability 8.4 Independence 8.5 Counting techniques 8.6 Binomial coefficients and Pascal’s triangle 8.7 Review Answers TOPIC 9 Trigonometric functions 1 9.1 Kick off with CAS 9.2 Trigonometric ratios 9.3 Circular measure 9.4 Unit circle definitions 9.5 Symmetry properties 9.6 Graphs of the sine and cosine functions 9.7 Review Answers TOPIC 10 Trigonometric functions 2 10.1 Kick off with CAS 10.2 Trigonometric equations 10.3 Transformations of sine and cosine graphs 10.4 Applications of sine and cosine functions 10.5 The tangent function 10.6 Trigonometric relationships 10.7 Review Answers TOPIC 11 Exponential functions 11.1 Kick off with CAS 11.2 Indices as exponents 11.3 Indices as logarithms 11.4 Graphs of exponential functions 11.5 Applications of exponential functions 11.6 Inverses of exponential functions 11.7 Review Answers TOPIC 12 Introduction to differential calculus 12.1 Kick off with CAS 12.2 Rates of change 12.3 Gradients of secants 12.4 The derivative function 12.5 Differentiation of polynomials by rule 12.6 Review Answers TOPIC 13 Differentiation and applications 13.1 Kick off with CAS 13.2 Limits, continuity and differentiability 13.3 Derivatives of power functions 13.4 Coordinate geometry applications of differentiation 13.5 Curve sketching 13.6 Optimisation problems 13.7 Rates of change and kinematics 13.8 Review Answers TOPIC 14 Anti-differentiation and introduction to integral calculus 14.1 Kick off with CAS 14.2 Anti-derivatives 14.3 Anti-derivative functions and graphs 14.4 Applications of anti-differentiation 14.5 The definite integral 14.6 Review Answers Index