### General Mathematics Year 11 for Queensland

 UNIT ONE 1 Consumer arithmetic Recall 1.1 Percentages, decimals and rates 1.2 Making money 1.3 Taxation and other government charges 1.4 Investing money 1.5 Shares 1.6 Profit, loss and inflation 1.7 Making the most of your money 1.8 Working with finance Chapter summary Chapter review 2 Measurement Recall 2.1 Pythagoras’ theorem 2.2 Perimeter and area 2.3 Volume of prisms and cylinders 2.4 Volume of tapered solids and spheres 2.5 Surface area of prisms and cylinders 2.6 Surface area of tapered solids and spheres Chapter summary Chapter review 3 Similar figures Recall 3.1 Similar shapes and length 3.2 Scale drawing 3.3 Similar shapes and area 3.4 Similar solids and volume Chapter summary Chapter review 4 Linear equations and their graphs Recall 4.1 Linear equations 4.2 Linear graphs 4.3 Sketching linear graphs 4.4 Simultaneous linear equations 4.5 Piece-wise linear graphs and step graphs Chapter summary Chapter review Unit 1 Exam ReviewChapters 1 – 4 UNIT TWO 5 Applications of trigonometryRecall 5.1 Sine, cosine and tangent 5.2 Angles of elevation and depression 5.3 Directions and compass points 5.4 The sine rule 5.5 The cosine rule 5.6 Alternative formulas for triangle area Chapter summary Chapter review 6 Algebra and matricesRecall 6.1 Linear and non-linear expressions 6.2 Matrix properties 6.3 Matrix addition, subtraction and scalar multiplication 6.4 Matrix multiplication 6.5 Networks and Power Matrices Chapter summary Chapter review 7 Univariate data analysis Recall 7.1 Categorising and organising data 7.2 Categorical data 7.3 Numerical data 7.4 Median, range and interquartile range 7.5 Cumulative frequency 7.6 Mean and standard deviation 7.7 Comparing data Chapter summary Chapter review Unit 2 Exam ReviewChapters 5 – 7Unit 1 & 2 Exam Review Chapters 1 – 7

### General Mathematics Year 12 for Queensland

 UNIT THREE 1 Bivariate data analysisRecall 1.1 Association between categorical variables 1.2 Scatterplots and association 1.3 Modelling and the line of best fit 1.4 Residual analysis 1.5 The statistical investigation process Chapter summary Chapter review 2 Time series analysisRecall 2.1 Time series 2.2 Seasonal variation 2.3 Smoothing 2.4 The statistical investigation process Chapter summary Chapter review 3 Growth and decay in sequencesRecall 3.1 Arithmetic sequences 3.2 Applications of arithmetic sequences 3.3 Geometric sequences 3.4 Applications of geometric sequences Chapter summary Chapter review 4 Earth geometry and time zonesRecall 4.1 Latitude and Longitude 4.2 Angular distances 4.3 Time Zones 4.4 Time and Travel Chapter summary Chapter review Unit 3 Exam ReviewChapters 1 – 4 UNIT FOUR 5 Compound interest loans and investmentsRecall 5.1 Financial sequences 5.2 Compound interest and recursion 5.3 The compound interest formula 5.4 Compound interest parameters 5.5 Effective annual rate of interest 5.6 Depreciation and appreciation Chapter summary Chapter review 6 Reducing balance loans, annuities and perpetuitiesRecall 6.1 Repaying a loan 6.2 Reducing balance loans 6.3 Changing parameters 6.4 Annuities and perpetuities 6.5 Annuity investments Chapter summary Chapter review 7 Graphs and networksRecall 7.1 Describing graphs 7.2 Practical networks 7.3 Adjacency matrices 7.4 Walks, trails, paths and cycles 7.5 Weighted networks Chapter summary Chapter review 8 Networks and decision mathematicsRecall 8.1 Minimum spanning trees 8.2 Network flow 8.3 Allocation problems 8.4 Project networks Chapter summary Chapter review Unit 4 Exam ReviewChapters 5 – 8Unit 3 & 4 Exam Review Chapters 1 – 8

### Mathematical Methods Year 11 for Queensland

 UNIT ONE 1 Linear relations Recall 1.1 Linear relations and functions 1.2 Solving simultaneous linear equations 1.3 Piece-wise functions 1.4 Artithmetic sequences and series 1.5 Linear growth and decay Chapter summary Chapter review 2 Quadratic functionsRecall 2.1 Introduction to quadratic functions 2.2 Transformations of quadratic functions 2.3 Solving quadratic equations 2.4 Determining the rule of a quadratic function Chapter summary Chapter review 3 Polynomial functionsRecall 3.1 Polynomials 3.2 Expanding cubic polynomials 3.3 Factorising cubiv polynomials 3.4 Graphs of power functions 3.5 Graphs of cuvic functions 3.6 Solving polynomial equations Chapter summary Chapter review Mixed Review Chapters 1 – 3 4 Advanced functions and relationsRecall 4.1 Inverse proportion and graphs of rectangular hyperbolas 4.2 The graph of x = y2 4.3 Circles Chapter summary Chapter review 5 ProbabilityRecall 5.1 Probability review 5.2 Probability and set notation 5.3 Conditional probability 5.4 Independent events 5.5 Counting techniques 5.6 Combinations  Chapter summary Chapter review 6 Index LawsRecall 6.1 Review of index laws 6.2 Scientific notation 6.3 Geometric sequences and series 6.4 Financial mathematics Chapter summary Chapter review Unit 1 Exam ReviewChapters 1 – 6 UNIT TWO 7 Exponential and logarithmic functionsRecall 7.1 Equations with exponentials 7.2 Graphs of exponentials functions 7.3 Indices and logarithms 7.4 Modelling with exponentials Chapter summary Chapter review 8 Trigonometric functionsRecall 8.1 Circular measure and radian measure 8.2 The unit circle 8.3 Dilations of trigonometric graphs 8.4 Translation of trigonometric  graphs 8.5 Solving trigonometric equations 8.6 Applications of trigonometric functions Chapter summary Chapter review 9 Rates of changeRecall 9.1 Average and instantaneous rates of change 9.2 Functions and rates of change 9.3 Derivatives from first principles 9.4 Differentiation using the power rule Chapter summary Chapter review Mixed ReviewChapters 1 – 9 10 Differential calculusRecall 10.1 Gradients of functions and equations of tangents 10.2 Calculus and rates of change 10.3 Curve sketching 10.4 Maximum and minimum problems 10.5 Calculus and linear motion 10.6 Composite functions and their derivatives 10.7 Derivatives of products and quotients Chapter summary Chapter review 11 Discrete random variablesRecall 11.1 Random variables and probability 11.2 Statistics of discrete probability distributions 11.3 Uniform distributions 11.4 Probability distributions in practical applications Chapter summary Chapter review Unit 2 Exam ReviewChapters 7 – 11 Unit 1 & 2 Exam ReviewChapters 1 – 11

### Mathematical Methods Year 12 for Queensland

 UNIT THREE 1 Derivatives of exponential functions Recall 1.1 Euler’s number and index laws 1.2 Graphing exponential functions 1.3 Differentiating exponential functions 1.4 Applications of exponential functions 1.5 Further differentiation Chapter summary Chapter review 2 Trigonometric functions and derivativesRecall 2.1 Radians and the unit circle 2.2 Solving trigonometric equations 2.3 Graphs of trigonometric functions 2.4 Derivatives of trigonometric functions 2.5 Applications of trigonometric functions Chapter summary Chapter review 3 Logarithmic functions and their derivativesRecall 3.1 Logarithmic functions and their properties 3.2 Logarithmic equations 3.3 Logarithmic bases and exponential equations 3.4 Graphs of logarithmic functions 3.5 Logarithmic scales 3.6 The derivative of the natural logarithm 3.7 Applications of logarithms Chapter summary Chapter review Mixed Review Chapters 1 – 3 4 Anti-differentiationRecall 4.1 Introduction to anti-differentiation 4.2 Anti-differentiation of power functions 4.3 Anti-differentiation of binomial power functions 4.4 Anti-differentiation of exponential functions 4.5 Anti-differentiation of sine and cosine functions 4.6 Anti-derivatives of reciprocal functions 4.7 Further anti-differentiation Chapter summary Chapter review 5 Definite integralsRecall 5.1 Estimating area beneath curves 5.2 Finding definite integrals 5.3 Calculating area beneath curves 5.4 Finding area between curves 5.5 Kinematics applications of integration Chapter summary Chapter review Unit 3 Exam ReviewChapters 1 – 5 UNIT FOUR 6 Further applications of differentiationRecall 6.1 The derivative and curve sketching 6.2 Motion and derivatives 6.3 The second derivative and curve sketching 6.4 Maximum and minimum problems Chapter summary Chapter review 7 Sine and Cosine rulesRecall 7.1 Trigonometry review 7.2 The sine rule and the cosine rule 7.3 Areas of triangles 7.4 Bearings Chapter summary Chapter review 8 Binomial distributionsRecall 8.1 Discrete probability distributions review 8.2 Bernoulli trials and binomial distributions 8.3 Statistics of binomial probability distributions Chapter summary Chapter review Mixed ReviewChapters 1 – 8 9 Continuous random variables and the normal distributionRecall 9.1 Continuous random variables 9.2 The normal distribution 9.3 Standard normal distributions 9.4 Inverse of standard normal Chapter summary Chapter review 10 Interval estimates for proportionsRecall 10.1 Random sampling 10.2 The central limit theorem 10.3 Proportions 10.4 Estimating with confidence Chapter summary Chapter review Unit 4 Exam ReviewChapters 6 – 10 Unit 3 & 4 Exam ReviewChapters 1 – 10

### Specialist Mathematics Year 11 for Queensland

 UNIT ONE 1 Combinatorics Recall 1.1 Counting techniques 1.2 The multiplication and addition principles 1.3 Permutations 1.4 Combinations 1.5 Applications to probability 1.6 Pascal's triangle 1.7 The Pigeon-hole principle Chapter summary Chapter review 2 Vectors in the plane Recall 2.1 Introduction to vectors 2.2 Vectors in two dimensions 2.3 Vectors in component form 2.4 Scalar product of vectors 2.5 Projections of vectors 2.6 Vectors in geometric proofs 2.7 Displacement and velocity problems 2.8 Problems involving forces Chapter summary Chapter review 3 Introduction to proofRecall 3.1 Rational and irrational numbers 3.2 The language and logic of proof 3.3 Methods of proof Chapter summary Chapter review 4 Geometric properties and proof Recall 4.1 Review of congruence and similarity 4.2 Geometric proof 4.3 Circle theorems, part 1 4.4 Circle theorems, part 2 Chapter summary Chapter review Unit 1 Exam Review Chapters 1 – 4 UNIT TWO 5 Real and complex numbers Recall 5.1 Complex numbers 5.2 The complex plane 5.3 Radian measure 5.4 Complex arithmetic using polar form 5.5 Complex solutions of real quadratic functions Chapter summary Chapter review 6 Graphing functions Recall 6.1 Absolute value functions 6.2 Reciprocal functions 6.3 Rational functions Chapter summary Chapter review 7 TrigonometryRecall 7.1 Solving trigonometric equations 7.2 Graphing and modelling with trigonometric functions 7.3 The reciprocal trigonometric functions 7.4 The Pythagorean trigonometric identities 7.5 Compound and double-angle formulas 7.6 Transformations of trigonometric Chapter summary Chapter review 8 Introduction to matricesRecall 8.1 Matrix properties and arithmetic 8.2 Matrix multiplication 8.3 Inverse matrices 8.4 Solving simultaneous linear equations with matrices 8.5 Translations in the plane 8.6 Linear transformations in the plane 8.7 Reflections, rotations and dilations 8.8 Applying transformations in the plane 8.9 Determining the transformation matrix 8.10 Combining transformations 8.11 Establishing geometric results by using matrix multiplication Chapter summary Chapter review Unit 2 Exam ReviewChapters 5 – 8 Unit 1 & 2 Exam Review Chapters 1 – 8

### Specialist Mathematics Year 12 for Queensland

 UNIT THREE 1 Mathematical InductionRecall 1.1 Proof by induction 1.2 Proving results for sums 1.3 Proving divisibility Chapter summary Chapter review 2 Vectors and MatricesRecall 2.1 Vectors review 2.2 Vectors in three dimensions 2.3 Scalar product of vectors and projections of vectors 2.4 Linearly dependent and independent vectors 2.5 Vector proofs of geometric theorems 2.6 The vector product 2.7 Vector equation of a straight line in the Cartesian plane 2.8 Straight lines in three dimensional space 2.9 Systems of linear equations 2.10 Dominance and Leslie matrices 2.11 Further applications of matrices Chapter summary Chapter review 3 Vector calculus Recall 3.1 Position vectors as a function of time 3.2 Differentiation of vector functions 3.3 Velocity and acceleration vectors 3.4 Investigating curvilinear motion Chapter summary Chapter review 4 Complex numbersRecall 4.1 Complex numbers review 4.2 Modulus and argument form of complex numbers 4.3 Powers and Roots of complex numbers 4.4 The complex plane 4.5 The remainder and factor theorem 4.6 Complex factors of polynomials Chapter summary Chapter review Unit 3 Exam ReviewChapters 1 – 4 UNIT FOUR 5 Integration techniques Recall 5.1 Inverse trigonometric functions 5.2 Derivatives of inverse trigonometric functions 5.3 Integrals involving inverse trigonometric and logarithmic functions 5.4 Integration by substitution 5.5 Integration with trigonometric identities 5.6 Partial fractions 5.7 Integration by parts Chapter summary Chapter review 6 Applications of integration Recall 6.1 Areas between curves 6.2 Volumes of solids of revolution 6.3 Numerical approximations of integration 6.4 The exponential distribution 6.5 Arc Lengths 6.6 Graphs of anti-derivatives Chapter summary Chapter review 7 Rates of change and differential equations Recall 7.1 Implicit differentiation 7.2 Related rates 7.3 Introduction to differential equations 7.4 Qualitative and numerical solutions of differential equations 7.5 Analytical solutions of differential Chapter summary Chapter review Mixed ReviewChapters 1 – 7 8 Modelling motion Recall 8.1 Linear motion with constant acceleration 8.2 Linear motion with non-constant acceleration 8.3 Newton’s laws of motion 8.4 Simple harmonic motion Chapter summary Chapter review 9 Statistical inferenceRecall 9.1 Sample means 9.2 Sampling distributions 9.3 Confidence intervals 9.4 Hypothesis testing Chapter summary Chapter review Unit 4 Exam Review Chapters 5 – 9 Unit 3 & 4 Exam Review Chapters 1 – 9