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Specialist Mathematics Units 1 and 2 20th Edition by Michael Evans, Douglas Wallace, Kay Lipson, David Treeby ISBN 1107567653 9781107567658

Name: Specialist Mathematics Units 1 and 2 20th Edition by Michael Evans, Douglas Wallace, Kay Lipson, David Treeby ISBN 1107567653 9781107567658
SKU: EB-36352034
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Specialist Mathematics 20th Edition Michael Evans Digital Instant Download

Author(s): Michael Evans, Douglas Wallace, Kay Lipson, David Treeby

ISBN(s): 9781107567658, 1107567653

Edition: 20

File Details: PDF, 48.25 MB

Year: 2016

Language: English

SKU: EB-36352034 Category: Mathematics - Lectures Tags: David Treeby, Douglas Wallace, Kay Lipson, Michael Evans

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Specialist Mathematics Units 1&2 20th Edition by Michael Evans, Douglas Wallace, Kay Lipson, David Treeby – Ebook PDF Instant Download/Delivery: 1107567653, 978-1107567658

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ISBN 10: 1107567653

ISBN 13: 978-1107567658

Author: Michael Evans, Douglas Wallace, Kay Lipson, David Treeby

Specialist Mathematics Units 1&2 20th Edition:

Cambridge Senior Mathematics: Australian Curriculum/VCE builds on a proven teaching and learning formula to support the new AC/VCE Mathematics Study Designs implemented in 2016. Our authors have unrivalled expertise in writing examples and problems to prepare students for exams, as well as proven experience interpreting the Australian Curriculum and VCE Study Designs for VCE students. Developed from the popular Cambridge Essential Mathematics VCE series, the new series combines logical topic development with a wealth of examples, exercises, exam-style questions and a focus on what is important to guide students to VCE success. Carefully-developed creative and rigorous questions help students understand concepts and develop mathematical skills, apply Maths to real life and prepare for exams. Drawing on the successful Cambridge Essential Mathematics VCE style, the questions are now fully updated for the new study designs and latest exams. A new level of digital support, powered by Cambridge HOTMaths, allows effortless and immediate navigation from the Interactive Textbook to interactive animations, video examples, complete worked solutions (solutions must be switched on by a connected teaching account), automarked questions, online testing and a powerful learning management system.

Specialist Mathematics Units 1&2 20th Edition Table of contents:

1. Reviewing algebra
- Indices
- Standard form
- Solving linear equations and simultaneous linear equations
- Solving problems with linear equations
- Solving problems with simultaneous linear equations
- Substitution and transposition of formulas
- Algebraic fractions
- Literal equations
- Using a CAS calculator for algebra
- Review of Chapter 1
2. Number systems and sets
- Set notation
- Sets of numbers
- Surds
- Natural numbers
- Problems involving sets
- Review of Chapter 2
3. Sequences and series
- Introduction to sequences
- Arithmetic sequences
- Arithmetic series
- Geometric sequences
- Geometric series
- Applications of geometric sequences
- Recurrence relations of the form tn = rtn–1 + d
- Zeno’s paradox and infinite geometric series
- Review of Chapter 3
4. Additional algebra
- Polynomial identities
- Quadratic equations
- Applying quadratic equations to rate problems
- Partial fractions
- Simultaneous equations
- Review of Chapter 4
5. Revision of Chapters 1–4
- Technology-free questions
- Multiple-choice questions
- Extended-response questions
- Investigations
6. Proof
- Direct proof
- Proof by contrapositive
- Proof by contradiction
- Equivalent statements
- Disproving statements
- Mathematical induction
- Review of Chapter 6
7. Logic
- The algebra of sets
- Switching circuits
- Boolean algebra
- Logical connectives and truth tables
- Valid arguments
- Logic circuits
- Karnaugh maps
- Review of Chapter 7
8. Algorithms
- Introduction to algorithms
- Iteration and selection
- Introduction to pseudocode
- Further pseudocode
- Review of Chapter 8
9. Combinatorics
- Basic counting methods
- Factorial notation and permutations
- Permutations with restrictions
- Permutations of like objects
- Combinations
- Combinations with restrictions
- Pascal’s triangle
- The pigeonhole principle
- The inclusion–exclusion principle
- Review of Chapter 9
10. Revision of Chapters 6–9
- Technology-free questions
- Multiple-choice questions
- Extended-response questions
- Investigations
11. Matrices
- Matrix notation
- Addition, subtraction and multiplication by a real number
- Multiplication of matrices
- Identities, inverses and determinants for 2 x 2 matrices
- Solution of simultaneous equations using matrices
- Inverses and determinants for n x n matrices
- Simultaneous linear equations with more than two variables
- Review of Chapter 11
12. Graph theory
- Graphs and adjacency matrices
- Euler circuits
- Hamiltonian cycles
- Using matrix powers to count walks in graphs
- Regular, cycle, complete and bipartite graphs
- Trees
- Euler’s formula and the Platonic solids
- Appendix: When every vertex has even degree
- Review of Chapter 12
13. Revision of Chapters 11–12
- Technology-free questions
- Multiple-choice questions
- Extended-response questions
- Investigations
14. Simulation, sampling and sampling distributions
- Expected value and variance for discrete random variables
- Distribution of sums of random variables
- Populations and samples
- Investigating the distribution of the sample mean using simulation
- Review of Chapter 14
15. Trigonometric ratios and applications
- Reviewing trigonometry
- The sine rule
- The cosine rule
- The area of a triangle
- Circle mensuration
- Angles of elevation, angles of depression and bearings
- Problems in three dimensions
- Angles between planes and more difficult 3D problems
- Review of Chapter 15
16. Trigonometric identities
- Reciprocal circular functions and the Pythagorean identity
- Compound and double angle formulas
- Simplifying a cos x + b sin x
- Sums and products of sines and cosines
- Review of Chapter 16
17. Graphing functions and relations
- The inverse circular functions
- Reciprocal functions
- Graphing the reciprocal circular functions
- The modulus function
- Locus of points
- Parabolas
- Ellipses
- Hyperbolas
- Parametric equations
- Polar coordinates
- Graphing using polar coordinates
- Review of Chapter 17
18. Complex numbers
- Starting to build the complex numbers
- Multiplication and division of complex numbers
- Argand diagrams
- Solving quadratic equations over the complex numbers
- Solving polynomial equations over the complex numbers
- Polar form of a complex number
- Sketching subsets of the complex plane
- Review of Chapter 18
19. Revision of Chapters 15–18
- Technology-free questions
- Multiple-choice questions
- Extended-response questions
- Investigations
20. Transformations of the plane
- Linear transformations
- Geometric transformations
- Rotations and general reflections
- Composition of transformations
- Inverse transformations
- Transformations of straight lines and other graphs
- Area and determinant
- General transformations
- Review of Chapter 20
21. Vectors in the plane
- Introduction to vectors
- Components of vectors
- Scalar product of vectors
- Vector projections
- Geometric proofs
- Applications of vectors: displacement and velocity
- Applications of vectors: relative velocity
- Applications of vectors: forces and equilibrium
- Vectors in three dimensions
- Review of Chapter 21
22. Revision of Chapters 20–21
- Technology-free questions
- Multiple-choice questions
- Extended-response question

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