CambridgeMATHS NSW Syllabus for the Australian Curriculum is a complete teaching and learning program to support the implementation of the NSW Syllabus for the Australian Curriculum. Developed by highly experienced maths educators to reflect the NSW syllabus for the Australian Curriculum - Developed by highly experienced educators with years of knowledge and experience in maths teaching and in preparing exceptional maths resources, and who are committed to the principles of the NSW Syllabus and the Australian Curriculum. As lead author on the series, Stuart Palmer has advised on implementation of NSW syllabuses and on all aspects of mathematics teaching in the state. Close alignment of chapters with the NSW Syllabus in an effective teaching program - The authors have devised a workable, time-saving implementation of the syllabus, laid out in a detailed teaching program. Comprehensively integrated Working Mathematically components - Every exercise contains questions relating to Working Mathematically under headings for Understanding, Fluency, Problem Solving, Reasoning, while Communication is covered in all sections using symbols and words. Caters for all ability levels - Offers two levels of resources at Stage 5 to cover the 5.1/5.2 and 5.1/5.2/5.3 courses. At Stage 4, Gold editions of Essential Mathematics for the Australian Curriculum focus on consolidating core mathematics concepts for those that require additional support. Builds on a successful formula for teaching and learning - Combines logical topic development, carefully graded questions, linked examples, investigations, and opportunities for differentiated learning in an uncluttered layout that is easy to follow.
Author(s): David Sadler; William Pender; Julia Shea; Brian Dorofaeff; Derek Ward
Series: CambridgeMATHS Stage 6
Publisher: Cambridge University Press
Year: 2019
Language: English
Pages: 572
City: Port Melbourne, Victoria
Tags: HSC
Rationale
Overview
Acknowledgements
About the authors
1 Methods in algebra
1A Arithmetic with pronumerals
1B Expanding brackets
1C Factoring
1D Algebraic fractions
1E Solving linear equations
1F Solving quadratic equations
1G Solving simultaneous equations
1H Completing the square
Chapter 1 Review
2 Numbers and surds
2A Whole numbers, integers and rationals
2B Real numbers and approximations
2C Surds and their arithmetic
2D Further simplification of surds
2E Rationalising the denominator
Chapter 2 Review
3 Functions and graphs
3A Functions and function notation
3B Functions, relations and graphs
3C Review of linear graphs
3D Quadratics functions — factoring and the graph
3E Completing the square and the graph
3F The quadratic formulae and the graph
3G Powers, polynomials and circles
3H Two graphs that have asymptotes
3I Four types of relations
Chapter 3 Review
4 Transformations and symmetry
4A Translations of known graphs
4B Reflections in the x-axis and y-axis
4C Even and odd symmetry
4D The absolute value function
4E Composite functions
Chapter 4 Review
5 Trigonometry
5A Trigonometry with right-angled triangles
5B Problems involving right-angled triangles
5C Three-dimensional trigonometry
5D Trigonometric functions of a general angle
5E Quadrant, sign, and related acute angle
5F Given one trigonometric function, find another
5G Trigonometric identities
5H Trigonometric equations
5I The sine rule and the area formula
5J The cosine rule
5K Problems involving general triangles
Chapter 5 Review
Appendix: Proofs of the sine, cosine and area rules
6 The coordinate plane
6A Lengths and midpoints of intervals
6B Gradients of intervals and lines
6C Equations of lines
6D Further equations of lines
6E Using pronumerals in place of numbers
Chapter 6 Review
7 Exponential and logarithmic functions
7A Indices
7B Fractional indices
7C Logarithms
7D The laws for logarithms
7E Equations involving logarithms and indices
7F Exponential and logarithmic graphs
7G Applications of these functions
Exponential data investigation (ITB)
Chapter 7 Review
8 Differentiation
8A Tangents and the derivative
8B The derivative as a limit
8C A rule for differentiating powers of x
8D Tangents and normals — dy/dx notation
8E Differentiating powers with negative indices
8F Differentiating powers with fractional indices
8G The chain rule
8H The product rule
8I The quotient rule
8J Rates of change
8K Continuity
8L Differentiability
Chapter 8 Review
Appendix: Proving differentiation rules
9 Extending calculus
9A The exponential function base e
9B Transformations of exponential functions
9C Differentiation of exponential functions
9D Differentiation and the graph
9E The logarithmic function base e
9F Exponential rates using the base e
9G Radian measure of angle size
9H Solving trigonometric equations
9I Arcs and sectors of circles
9J Trigonometric graphs in radians
Chapter 9 Review
10 Probability
10A Probability and sample spaces
10B Sample space graphs and tree diagrams
10C Sets and Venn diagrams
10D Venn diagrams and the addition theorem
10E Multi-stage experiments and the product rule
10F Probability tree diagrams
10G Conditional probability
Chapter 10 Review
11 Probability distributions
11A The language of probability distributions
11B Expected value
11C Variance and standard deviation
11D Sampling
Chapter 11 Review
Answers
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Index
