Pearson Queensland Senior Mathematics

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Supporting teaching and learning from the classroom and home, the eBooks help engage learners as they consolidate understanding of concepts and ideas. They feature:

• online and offline access to student book content
• digital activities
• interactive videos
• investigations
• exam preparation material.

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Developed to support senior maths students in their preparation for the QCAA external exams, the workbooks feature:

• past external exam questions from other states, selected based on their alignment with the QCAA syllabus, and then categorised using the QCAA three levels of question difficulty: simple familiar, complex familiar and complex unfamiliar.
• a 5-Step exam preparation approach to support students in their revision and help them identify gaps and areas of strength
• extra support for year 12 students to build confidence for exams
• worked solutions and notes on common errors.

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Focused on saving teachers time and teach with confidence, this series features:

• curriculum-aligned teaching programs
• curriculum grids
• question banks
• Interactives
• technology integration support
• formative and summative assessment tasks
• problem solving and modeling tasks to support internal assessment.

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See how the series guides students over both senior years to prepare them for the new external exams.

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See how the series supports students and teachers with additional support materials including problem solving and modeling tasks for both year 11 and 12.

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Learn more about the work solutions and the content structure based on the syllabus mapping.

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We listened to what teachers have been telling us they need. Learn more about the exercises we’ve designed to help students solve questions without the use of a calculator. 

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Learn how the new resources accommodate the technology active teaching components, and how questions are presented to help students identify when a calculator is required to solve.

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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 

5 Applications of trigonometry 

Recall 

• 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 matrices 

Recall 

• 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 

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1 Bivariate data analysis

Recall

• 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 analysis

Recall

• 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 sequences

Recall

• 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 zones

Recall

• 4.1 Latitude and Longitude
• 4.2 Angular distances
• 4.3 Time Zones
• 4.4 Time and Travel
• Chapter summary
• Chapter review

5 Compound interest loans and investments
Recall

• 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 perpetuities

Recall

• 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 networks

Recall

• 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 mathematics

Recall

• 8.1 Minimum spanning trees
• 8.2 Network flow
• 8.3 Allocation problems
• 8.4 Project networks
• Chapter summary
• Chapter review

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1 Linear relations

Recall

• 1.1 Linear relations and functions
• 1.2 Solving simultaneous linear equations
• 1.3 Piece-wise functions
• 1.4 Arithmetic sequences and series
• 1.5 Linear growth and decay
• Chapter summary
• Chapter review

2 Quadratic functions

Recall

• 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 functions

Recall

• 3.1 Polynomials
• 3.2 Expanding cubic polynomials
• 3.3 Factorising cubic polynomials
• 3.4 Graphs of power functions
• 3.5 Graphs of cubic functions
• 3.6 Solving polynomial equations
• Chapter summary
• Chapter review

4 Advanced functions and relations

Recall

• 4.1 Inverse proportion and graphs of rectangular hyperbolas
• 4.2 The graph of x = y²
• 4.3 Circles
• Chapter summary
• Chapter review

5 Probability

Recall

• 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 Laws

Recall

• 6.1 Review of index laws
• 6.2 Scientific notation
• 6.3 Geometric sequences and series
• 6.4 Financial mathematics
• Chapter summary
• Chapter review

7 Exponential and logarithmic functions

Recall

• 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 functions

Recall

• 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 change

Recall

• 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

10 Differential calculus

Recall

• 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 variables

Recall

• 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

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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 derivatives

Recall

• 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 derivatives

Recall

• 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

4 Anti-differentiation

Recall

• 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 integrals

Recall

• 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

6 Further applications of differentiation

Recall

• 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 rules

Recall

• 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 distributions

Recall

• 8.1 Discrete probability distributions review
• 8.2 Bernoulli trials and binomial distributions
• 8.3 Statistics of binomial probability distributions
• Chapter summary
• Chapter review

9 Continuous random variables and the normal distribution

Recall

• 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 proportions

Recall

• 10.1 Random sampling
• 10.2 The central limit theorem
• 10.3 Proportions
• 10.4 Estimating with confidence
• Chapter summary
• Chapter review

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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 proof

Recall

• 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

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 Trigonometry

Recall

• 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 matrices

Recall

• 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

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1 Mathematical Induction

Recall

• 1.1 Proof by induction
• 1.2 Proving results for sums
• 1.3 Proving divisibility
• Chapter summary
• Chapter review

2 Vectors and Matrices

Recall

• 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 numbers

Recall

• 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

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

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 inference

Recall

• 9.1 Sample means
• 9.2 Sampling distributions
• 9.3 Confidence intervals
• 9.4 Hypothesis testing
• Chapter summary
• Chapter review

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Greg teaches senior mathematics and philosophy at Toowoomba Grammar School. He’s served on the executive of the Queensland Association of Mathematics Teachers (QAMT) for many years and is currently president of the association.

In 2009, Greg received an Australian Award for Teaching Excellence for his use of technology in the mathematics classroom. He holds a Master of Leadership and Management in Education from the University of Newcastle.

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Peter is the Head of Curriculum Development: Mathematics including Head of Mathematics C/Specialist Mathematics at Brisbane Girls Grammar School, Queensland. He has a PhD in Pure Mathematics from The University of Queensland, and has published a number of articles in International Mathematics Journals.

In addition to teaching Mathematics at the tertiary level over a number of years, he has spent the past ten years teaching mathematics at the secondary school level to all year levels, and remains a member of the Brisbane Central Review Panel for Mathematics C.

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Nicola has worked in Queensland public and private schools across her 40+ year teaching career, including 24 years at Somerville House. She also taught probability and statistics at QUT for two years part-time.

Nicola has been authoring school mathematics books since 1999, including Maths Zone Queensland 7-10, Pearson Mathematics 7-10 and making significant contributions to the online senior Pearson Lightbook Mathematics Western Australia Years 11 and 12 series for Mathematics Methods.

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Gillian is a former head of mathematics at Lauriston Girls’ School, Victoria, and has been a teacher of VCE Specialist Mathematics, Mathematics Methods, and Further Mathematics for many years.

She has taught Higher Level and Standard Level International Baccalaureate Mathematics and was a teacher workshop presenter for IB Higher Level Mathematics. She is currently an IB examination assessor.