Maths in focus : mathematics extension 1, Year 12

Description

Cover Chapter 1 – Sequences and Series 1.01 – General sequences and series 1.02 – Arithmetic sequences 1.03 – Arithmetic series 1.04 – Geometric sequences 1.05 – Geometric series 1.06 – Limiting sum of an infinite geometric series 1.07 – Proof by mathematical induction Test yourself Chapter 2 – Transformations of Functions 2.01 – Vertical translations of functions 2.02 – Horizontal translations of functions 2.03 – Vertical dilations of functions 2.04 – Horizontal dilations of functions 2.05 – Combinations of transformations 2.06 – Graphs of functions with combined transformations 2.07 – Equations and inequalities Test yourself Chapter 3 – Vectors 3.01 – Vectors 3.02 – Adding and subtracting vectors 3.03 – Scalar multiplication 3.04 – Vectors in the Cartesian plane 3.05 – Magnitude and direction of a vector 3.06 – Components of a vector Test yourself Chapter 4 – Trigonometric Functions 4.01 – Transformations of trigonometric functions 4.02 – Combined transformations of trigonometric functions 4.03 – Trigonometric equations 4.04 – Trigonometric identities 4.05 – Further trigonometric equations Test yourself Practice set 1 Chapter 5 – Further Differentiation 5.01 – Differentiation review 5.02 – Derivative of exponential functions 5.03 – Derivative of logarithmic functions 5.04 – Derivative of trigonometric functions 5.05 – Second derivatives 5.06 – Anti-derivative graphs 5.07 – Anti-derivatives 5.08 – Further anti-derivatives 5.09 – Derivative of inverse functions 5.10 – Derivative of inverse trigonometric functions Test yourself Chapter 6 – Geometrical Applications of Differentiation 6.01 – Increasing and decreasing curves 6.02 – Stationary points 6.03 – Concavity and points of inflection 6.04 – Interpreting rates of change graphically 6.05 – Stationary points and the second derivative 6.06 – Curve sketching 6.07 – Global maxima and minima 6.08 – Finding formulas for optimisation problems 6.09 – Optimisation problems Test yourself Chapter 7 – Integration 7.01 – Approximating areas under a curve 7.02 – Trapezoidal rule 7.03 – Definite integrals 7.04 – Indefinite integrals 7.05 – Chain rule 7.06 – Integration involving exponential functions 7.07 – Integration involving logarithmic functions 7.08 – Integration involving trigonometric functions 7.09 – Areas enclosed by the x-axis 7.10 – Areas enclosed by the y-axis 7.11 – Sums and differences of areas Test yourself Chapter 8 – Further Integration 8.01 – Volumes of solids 8.02 – Integration by substitution 8.03 – Definite integrals by substitution 8.04 – Integration of sin2 x and cos2 x 8.05 – Integrals involving inverse trigonometric functions Test yourself Practice set 2 Chapter 9 – Statistics 9.01 – Types of data 9.02 – Displaying numerical and categorical data 9.03 – Measures of central tendency 9.04 – Quartiles, deciles and percentiles 9.05 – Range and interquartile range 9.06 – Variance and standard deviation 9.07 – Shape and modality of data sets 9.08 – Analysing data sets Test yourself Chapter 10 – Further Vectors 10.01 – Scalar (dot) product 10.02 – Parallel and perpendicular vectors 10.03 – Projection of vectors 10.04 – Proofs using vectors 10.05 – Motion and vectors 10.06 – Projectile motion Test yourself Chapter 11 – Correlation and Regression 11.01 – Bivariate data 11.02 – Correlation 11.03 – Line of best fit 11.04 – Least-squares regression line Test yourself Practice set 3 Chapter 12 – Investments, Annuities and Loans 12.01 – Arithmetic growth and decay 12.02 – Geometric growth and decay 12.03 – Compound interest 12.04 – Compound interest formula 12.05 – Annuities 12.06 – Annuities and geometric series 12.07 – Reducing balance loans 12.08 – Loans and geometric series Test yourself Chapter 13 – Differential Equations 13.01 – Solving dy/dx = f(x) 13.02 – Solving dy/dx = g(y) 13.03 – Solving dy/dx = f(x)g(y) 13.04 – Applications of differential equations Test yourself Chapter 14 – Continuous Probability 14.01 – Probability density functions 14.02 – Calculating probabilities 14.03 – Cumulative distribution function 14.04 – Quantiles 14.05 – Normal distribution 14.06 – Empirical rule 14.07 – z-scores 14.08 – Applications of the normal distribution Test yourself Chapter 15 – Binomial Distributions 15.01 – Bernoulli distribution 15.02 – Binomial distribution 15.03 – Mean and variance of a binomial distribution 15.04 – Sample proportions Test yourself Practice set 4 Answers Chapter 1 Chapter 2 Chapter 3 Chapter 4 Practice set 1 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Practice set 2 Chapter 9 Chapter 10 Chapter 11 Practice set 3 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Practice set 4 Index