Table of Contents

Chapter 1 ? Modelling using linear functions. Exercise 1A ? Solving linear equations. Exercise 1B ? Rearrangement and substitution. Exercise 1C ? Gradient of a straight line. Exercise 1D ? Equations of the form y = mx + c. Exercise 1E ? Sketching linear graphs using intercepts. Exercise 1F ? Simultaneous equations. Exercise 1G ? Formula for finding the equation of a straight line. Exercise 1H ? Linear modelling. Chapter review. Modelling and problem solving. Chapter 2 ? Relations and functions. Exercise 2A ? Relations and graphs. Exercise 2B ? Domain and range. Exercise 2C ? Types of relations (including functions). Exercise 2D ? Function notation and special types of functions. Exercise 2E ? Inverse relations and functions. Exercise 2F ? Circles. Exercise 2G ? Functions and modelling. Chapter review. Modelling and problem solving. Chapter 3 ? Other graphs and modelling. Exercise 3A ? Transforming graphs. Exercise 3B ? Sketching graphs using transformations. Exercise 3C ? Sketching graphs using intercepts. Exercise 3D ? The hyperbola. Exercise 3E ? The square root function. Exercise 3F ? The absolute value function. Exercise 3G ? Addition of ordinates. Exercise 3H ? Modelling. Exercise 3I ? Modelling using a graphics calculator. Chapter review. Modelling and problem solving. Chapter 4 ? Triangle trigonometry. Exercise 4A ? Calculating trigonometric ratios. Exercise 4B ? Finding an unknown side. Exercise 4C ? Finding angles. Exercise 4D ? Applications of right-angled triangles. Exercise 4E ? Using the sine rule to find side lengths. Exercise 4F ? Using the sine rule to find angle sizes. Exercise 4G ? Using the cosine rule to find side lengths. Exercise 4H ? Using the cosine rule to find angles. Chapter review. Modelling and problem solving. Chapter 5 ? Graphing periodic functions. Exercise 5A ? Period and amplitude of a periodic function. Exercise 5B ? Radian measure. Exercise 5C ? Exact values. Exercise 5D ? Symmetry. Exercise 5E ? Trigonometric graphs. Exercise 5F ? Applications. Chapter review. Modelling and problem solving. Chapter 6 ? Trigonometric equations. Exercise 6A ? Simple trigonometric equations. Exercise 6B ? Equations using radians. Exercise 6C ? Further trigonometric equations. Exercise 6D ? Identities. Exercise 6E ? Using the Pythagorean identity. Chapter review. Modelling and problem solving. Chapter 7 ? Exponential and logarithmic functions. Exercise 7A ? Index laws. Exercise 7B ? Negative and rational powers. Exercise 7C ? Indicial equations. Exercise 7D ? Graphs of exponential functions. Exercise 7E ? Logarithms. Exercise 7F ? Solving logarithmic equations. Exercise 7G ? Applications of exponential and logarithmic functions. Chapter review. Modelling and problem solving. Chapter 8 ? Applications of exponential and logarithmic functions in financial mathematics. Exercise 8A ? Geometric sequences. Exercise 8B ? Geometric series. Exercise 8C ? Growth and decay functions. Exercise 8D ? Compound interest formula. Exercise 8E ? Loan schedules. Exercise 8F ? The annuities formula. Chapter review. Modelling and problem solving. Chapter 9 ? Presentation of data. Exercise 9A ? Types of variables and data. Exercise 9B ? Collection of data. Exercise 9C ? Bias. Exercise 9D ? Stem plots. Exercise 9E ? Frequency histograms and bar charts. Exercise 9F ? Describing the shape of stem plots and histograms. Exercise 9G ? Cumulative data. Chapter review. Modelling and problem solving. Chapter 10 ? Summary statistics. Exercise 10A ? Measures of central tendency. Exercise 10B ? Range and interquartile range. Exercise 10C ? The standard deviation. Exercise 10D ? Boxplots. Exercise 10E ? Back-to-back stem plots. Exercise 10F ? Parallel boxplots. Chapter review. Modelling and problem solving. Chapter 11 ? Introduction to probability. Exercise 11A ? Informal description of chance. Exercise 11B ? Single event probability. Exercise 11C ? Relative frequency. Exercise 11D ? Modelling probability. Exercise 11E ? Long-run proportion. Chapter review. Modelling and problem solving. Chapter 12 ? Rates of change. Exercise 12A ? Constant rates. Exercise 12B ? Variable rates. Exercise 12C ? Average rates of change. Exercise 12D ? Instantaneous rates. Exercise 12E ? Motion graphs. Exercise 12F ? Relating the gradient function to the original function. Exercise 12G ? Relating velocity-time graphs to position-time graphs. Exercise 12H ? Rates of change of polynomials. Chapter review. Modelling and problem solving. Chapter 13 ? Differentiation and applications. Exercise 13A ? Introduction to limits. Exercise 13B ? Limits of discontinuous, rational and hybrid functions. Exercise 13C ? Differentiation using first principles. Exercise 13D ? Finding derivatives by rule. Exercise 13E ? Rates of change. Exercise 13F ? Solving maximum and minimum problems. Chapter review. Modelling and problem solving. Solutions to investigations. Chapter 2. Investigation ? Interesting relations. Investigation ? A special relation. Chapter 3. Investigation ? Investigating transformations on the basic graphs of y = x2, y = x3 and y = x4. Investigation ? Goal accuracy. Chapter 4. Investigation ? Looking at the tangent ratio. Investigation ? Looking at the sine ratio. Investigation ? Looking at the cosine ratio. Investigation ? Fly like a bird. Investigation ? Derivation of the sine rule. Investigation ? Bearing east and west. Chapter 5. Investigation ? Temperature and tide. Investigation ? Rhythm of life. Investigation ? Ferris wheeling. Investigation ? Finding a radian. Investigation ? The effect of 2. Investigation ? How high. Investigation ? Sunrise to sunset. Chapter 6. Investigation ? Fishing. Investigation ? Further trigonometric identities. Chapter 7. Investigation ? Simulating radioactivity. Investigation ? A world population model. Investigation ? Bode?s Law. Investigation ? Logarithmic graphs. Investigation ? The slide rule. Investigation ? The decibel. Investigation ? The Richter scale. Chapter 8. Investigation ? Crossing the road. Investigation ? Loan schedules using spreadsheets. Investigation ? Spreadsheets and investing for the future. Investigation ? Buying a home. Chapter 9. Investigation ? Types of data. Investigation ? Gallup poll. Investigation ? Identifying the target population. Investigation ? Census or sample. Investigation ? Bias in statistics. Investigation ? Biased sampling. Investigation ? Spreadsheets creating misleading graphs. Investigation ? Cost of a house. Investigation ? Bias. Investigation ? Segmented bar chart. Investigation ? Looking at cost. Investigation ? Using a database. Investigation ? A different display. Chapter 10. Investigation ? Mean and median amount of soft drink. Investigation ? Range of soft drink amounts. Investigation ? Standard deviation of soft drink amounts. Chapter 11. Investigation ? What will the weather be? Investigation ? Comparing theoretical probabilities with experimental results. Investigation ? Experimental or theoretical? Investigations ? Researching relative frequencies, applying relative frequencies. Investigation ? Random choice. Investigation ? Footy season. Chapter 12. Investigation ? Investigating rates of change. Chapter 13. Investigation ? Sneaking up on a limit. Investigation ? Dirichlet?s function. Investigation ? Secants and tangents. Investigation ? Graphs of derivatives. Investigation ? When is a maximum not a maximum?