Maths Quest 12 Further Mathematics 5e Vce Units 3 And 4 & Ebookplus + Studyon Vce Further Mathematics Units 3 And 4 2e

Title Page Copyright Page Contents Introduction About eBookPLUS and studyON Acknowledgements TOPIC 1 Univariate data 1.1 Kick off with CAS Exploring histograms with CAS 1.2 Types of data Types of data Discrete and continuous data 1.3 Stem plots 1.4 Dot plots, frequency tables and histograms, and bar charts Dot plots Frequency tables and histograms Bar charts Segmented bar charts Using a log (base 10) scale 1.5 Describing the shape of stem plots and histograms Symmetric distributions Skewed distributions 1.6 The median, the interquartile range, the range and the mode The median The interquartile range The range The mode 1.7 Boxplots Outliers 1.8 The mean of a sample Calculating the mean of grouped data 1.9 Standard deviation of a sample 1.10 Populations and simple random samples Populations Samples Displaying the data 1.11 The 68–95–99.7% rule and z-scores The 68–95–99.7% rule Standard z-scores Comparing data 1.12 Review Answers TOPIC 2 Comparing data sets 2.1 Kick off with CAS Exploring parallel boxplots with CAS 2.2 Back-to-back stem plots 2.3 Parallel boxplots and dot plots 2.4 Two-way (contingency) frequency tables and segmented bar charts Segmented bar charts 2.5 Review Answers TOPIC 3 Introduction to regression 3.1 Kick off with CAS Lines of best fit with CAS 3.2 Response (dependent) and explanatory (independent) variables 3.3 Scatterplots Fitting straight lines to bivariate data Scatterplots 3.4 Pearson’s product–moment correlation coefficient 3.5 Calculating r and the coefficient of determination Pearson’s product–moment correlation coefficient (r) Correlation and causation Non-causal explanations The coefficient of determination (r 2) 3.6 Fitting a straight line — least-squares regression Calculating the least-squares regression line by hand 3.7 Interpretation, interpolation and extrapolation Interpreting slope and intercept (b and a) Interpolation and extrapolation 3.8 Residual analysis Calculating residuals Introduction to residual analysis 3.9 Transforming to linearity Choosing the correct transformations Testing transformations Using the transformed line for predictions 3.10 Review Answers TOPIC 4 Time series 4.1 Kick off with CAS Time series graphs with CAS 4.2 Time series and trend lines Types of time series Plotting time series Fitting trend lines 4.3 Trend lines and forecasting Association tables and forecasting 4.4 Smoothing time series Moving-mean smoothing Moving-mean smoothing with odd numbers of points Prediction using moving means How many points should be in the moving mean? 4.5 Smoothing with an even number of points 4.6 Median smoothing from a graph 4.7 Seasonal adjustment Deseasonalising time series Forecasting with seasonal time series Seasonal indices 4.8 Review Answers TOPIC 5 Recurrence relations 5.1 Kick off with CAS Generating terms of sequences with CAS 5.2 Generating the terms of a first-order recurrence relation Starting term 5.3 First-order linear recurrence relations First-order linear recurrence relations with a common difference First-order linear recurrence relations with a common ratio 5.4 Graphs of first-order recurrence relations First-order recurrence relations: un + 1 = un + b (arithmetic patterns) First-order recurrence relations: un + 1 = Run Interpretation of the graph of first-order recurrence relations Starting term 5.5 Review Answers TOPIC 6 Interest and depreciation 6.1 Kick off with CAS Calculating interest with CAS 6.2 Simple interest Finding V0, r and n Transposed simple interest formula 6.3 Compound interest tables 6.4 Compound interest formula 6.5 Finding rate or time for compound interest Finding time in compound interest 6.6 Flat rate depreciation Flat rate (straight line) depreciation 6.7 Reducing balance depreciation Effective life 6.8 Unit cost depreciation 6.9 Review Answers TOPIC 7 Loans, investments and asset values 7.1 Kick off with CAS Finance Solver 7.2 Reducing balance loans I Annuities 7.3 Reducing balance loans II Number of repayments Effects of changing the repayment 7.4 Reducing balance loans III Frequency of repayments Changing the rate Interest only loans 7.5 Reducing balance and flat rate loan comparisons 7.6 Effective annual interest rate 7.7 Perpetuities Finding V0 and r 7.8 Annuity investments Superannuation Planning for retirement 7.9 Review Answers TOPIC 8 Matrices 8.1 Kick off with CAS Dominance matrices 8.2 Matrix representation Types of matrices Using matrices to store data 8.3 Addition, subtraction and scalar operations with matrices Addition and subtraction Scalar multiplication Properties of addition of matrices Simple matrix equations 8.4 Multiplying matrices The multiplication rule The identity matrix Permutation matrix Properties of multiplication of matrices 8.5 Multiplicative inverse and solving matrix equations Finding the inverse of a square 2 × 2 matrix Singular and regular matrices Further matrix equations 8.6 Dominance and communication matrices Reachability Dominance Communication 8.7 Application of matrices to simultaneous equations 8.8 Transition matrices Powers of matrices Markov systems and transition matrices Distribution vector and powers of the transition matrix Steady state 8.9 Review Answers TOPIC 9 Undirected graphs and networks 9.1 Kick off with CAS Planar graphs and Euler’s formula 9.2 Basic concepts of a network Definition of a network The degree of a vertex Representations of networks Matrix representation of networks 9.3 Planar graphs and Euler’s formula The regions of a planar graph Converting non-planar graphs Converting three-dimensional solids to planar graphs Euler’s formula 9.4 Walks, trails, paths, cycles and circuits Walks Connected graphs and bridges Euler trails Euler circuits An Euler circuit algorithm Paths and cycles Hamiltonian cycles 9.5 Trees and their applications Graphs and subgraphs Trees Shortest paths A shortest path algorithm Spanning trees Minimum spanning trees and Prim’s algorithm Dijkstra’s algorithm 9.6 Review Answers TOPIC 10 Directed graphs and networks 10.1 Kick off with CAS Directed graphs and networks 10.2 Critical path analysis Activity charts and networks Forward scanning Critical paths Float time and latest start time Drawing network diagrams 10.3 Critical path analysis with backward scanning and crashing Requirements for critical path analysis Backward scanning Dummy activities Crashing 10.4 Network flow Flow capacities and maximum flow Minimum cut–maximum flow method 10.5 Assignment problems and bipartite graphs Bipartite graphs Representing information as bipartite graphs The allocation problem The Hungarian algorithm 10.6 Review Answers TOPIC 11 Geometry: similarity and mensuration 11.1 Kick off with CAS Calculating areas with CAS 11.2 Properties of angles, triangles and polygons Geometry Interior angles of polygons Geometry rules, definitions and notation rules Definitions of common terms Some common notations and rules 11.3 Area and perimeter I Perimeter Area of common shapes Composite areas Conversion of units of area 11.4 Area and perimeter II Arc length Perimeter of composite shapes Area of circles, sectors and segments Composite areas 11.5 Great circles and small circles Latitude and longitude Measuring distances with great circles 11.6 Total surface area Total surface area formulas of common objects Total surface area using a net 11.7 Volume of prisms, pyramids and spheres Conversion of units of volume Volume of prisms Volume of pyramids Volume of spheres and composite objects 11.8 Similar figures Scale factor, k 11.9 Similar triangles 11.10 Triangulation — similarity 11.11 Area and volume scale factors Area of similar figures Volume of similar figures 11.12 Time zones Longitude and time difference 11.13 Review Answers TOPIC 12 Trigonometry 12.1 Kick off with CAS Exploring the sine rule with CAS 12.2 Trigonometry Labelling conventions Pythagoras’ theorem 12.3 Pythagorean triads 12.4 Three-dimensional Pythagoras’ theorem 12.5 Trigonometric ratios Labelling convention Ratio of lengths of sides Sine ratio Cosine ratio Tangent ratio Finding an unknown angle 12.6 The sine rule Introduction — sine and cosine rules 12.7 Ambiguous case of the sine rule 12.8 The cosine rule 12.9 Special triangles 12.10 Area of triangles 12.11 Review Answers TOPIC 13 Applications of geometry and trigonometry 13.1 Kick off with CAS Exploring bearings with CAS 13.2 Angles Adding and subtracting angles Some geometry (angle) laws 13.3 Angles of elevation and depression 13.4 Bearings Standard compass bearings Other compass bearings True bearings 13.5 Navigation and specification of locations 13.6 Triangulation — cosine and sine rules 13.7 Review Answers TOPIC 14 Construction and interpretation of graphs 14.1 Kick off with CAS Solving simultaneous equations with CAS 14.2 Constructing and interpreting straight-line graphs Sketching straight-line graphs Applications of straight-line graphs Extrapolation and interpolation 14.3 Line segments and step functions 14.4 Simultaneous equations and break-even point Solving linear simultaneous equations Break-even analysis 14.5 Interpreting non-linear graphs 14.6 Constructing non-linear relations and graphs Graphical representation of relations of the form y = kx n Finding a non-linear relationship using linear graphs 14.7 Review Answers TOPIC 15 Linear inequalities and linear programming 15.1 Kick off with CAS Shading regions with CAS 15.2 Linear inequalities Graphing a linear inequality 15.3 Simultaneous linear inequalities Graphical solution of simultaneous linear inequalities 15.4 Linear programming The decision variables The constraints Graphing the constraints The objective function 15.5 Applications Blending problems Transportation problems Manufacturing problems Limitations of linear programming techniques 15.6 Review Answers Index