Maths in Focus 12 Extension 1 has been rewritten and updated to cover the new senior mathematics courses: Mathematics Advanced and Mathematics Extension 1 and 2. Each chapter begins with a Chapter Outline that includes a list of objectives and a Terminology glossary and graded exercises include multiple-choice questions, HSC-style questions and realistic applications. Investigations explore the syllabus in more detail, providing ideas for research projects and modelling activities, while Did you know? sections contain interesting facts and applications of the mathematics learned in a chapter. The student book specifically highlights the Mathematics Extension 1 content and includes syllabus grids and codes, answers and an index to meet the new 2019 senior maths course requirements.
Author(s): Margaret Grove
Series: Maths in focus
Edition: 3rd edition.
Publisher: Nelson,Cengage Learning Australia
Year: 2019
Language: English
Pages: 835
City: South Melbourne, Victoria
Tags: HSC
PREFACE
CONTENTS
SYLLABUS REFERENCE GRID
ABOUT THIS BOOK
STUDY SKILLS
MATHEMATICAL VERBS
Chapter 1 SEQUENCES AND SERIES
1.01 General sequences and series
1.02 Arithmetic sequences
1.03 Arithmetic series
1.04 Geometric sequences
1.05 Geometric series
1.06 Limiting sum of an infinite geometric series
1.07 EXT1 Proof by mathematical induction
Test yourself 1
Challenge exercise 1
Chapter 2 TRANSFORMATIONS OF FUNCTIONS
2.01 Vertical translations of functions
2.02 Horizontal translations of functions
2.03 Vertical dilations of functions
2.04 Horizontal dilations of functions
2.05 Combinations of transformations
2.06 Graphs of functions with combined transformations
2.07 Equations and inequalities
Test yourself 2
Challenge exercise 2
Chapter 3 VECTORS
3.01 EXT1 Vectors
3.02 EXT1 Adding and subtracting vectors
3.03 EXT1 Scalar multiplication
3.04 EXT1 Vectors in the Cartesian plane
3.05 EXT1 Magnitude and direction of a vector
3.06 EXT1 Components of a vector
Test yourself 3
Challenge exercise 3
Chapter 4 TRIGONOMETRIC FUNCTIONS
4.01 Transformations of trigonometric functions
4.02 Combined transformations of trigonometric functions
4.03 Trigonometric equations
4.04 EXT1 Trigonometric identities
4.05 EXT1 Further trigonometric equations
Test yourself 4
Challenge exercise 4
PRACTICE SET 1
Chapter 5 FURTHER DIFFERENTIATION
5.01 Differentiation review
5.02 Derivative of exponential functions
5.03 Derivative of logarithmic functions
5.04 Derivative of trigonometric functions
5.05 Second derivatives
5.06 Anti-derivative graphs
5.07 Anti-derivatives
5.08 Further anti-derivatives
5.09 EXT1 Derivative of inverse functions
5.10 EXT1 Derivative of inverse trigonometric functions
Test yourself 5
Challenge exercise 5
Chapter 6 GEOMETRICAL APPLICATIONS OF DIFFERENTIATION
6.01 Increasing and decreasing curves
6.02 Stationary points
6.03 Concavity and points of inflection
6.04 Interpreting rates of change graphically
6.05 Stationary points and the second derivative
6.06 Curve sketching
6.07 Global maxima and minima
6.08 Finding formulas for optimisation problems
6.09 Optimisation problems
Test yourself 6
Challenge exercise 6
Chapter 7 INTEGRATION
7.01 Approximating areas under a curve
7.02 Trapezoidal rule
7.03 Definite integrals
7.04 Indefinite integrals
7.05 Chain rule
7.06 Integration involving exponential functions
7.07 Integration involving logarithmic functions
7.08 Integration involving trigonometric functions
7.09 Areas enclosed by the x-axis
7.10 Areas enclosed by the y-axis
7.11 Sums and differences of areas
Test yourself 7
Challenge exercise 7
Chapter 8 FURTHER INTEGRATION
8.01 EXT1 Volumes of solids
8.02 EXT1 Integration by substitution
8.03 EXT1 Definite integrals by substitution
8.04 EXT1 Integration of sin2 x and cos2 x
8.05 EXT1 Integrals involving inverse trigonometric functions
Test yourself 8
Challenge exercise 8
PRACTICE SET 2
Chapter 9 STATISTICS
9.01 Types of data
9.02 Displaying numerical and categorical data
9.03 Measures of central tendency
9.04 Quartiles
9.05 Range and interquartile range
9.06 Variance and standard deviation
9.07 Shape and modality of data sets
9.08 Analysing data sets
Test yourself 9
Challenge exercise 9
Chapter 10 FURTHER VECTORS
10.01 EXT1 Scalar (dot) product
10.02 EXT1 Parallel and perpendicular vectors
10.03 EXT1 Projection of vectors
10.04 EXT1 Proofs using vectors
10.05 EXT1 Motion and vectors
10.06 EXT1 Projectile motion
Test yourself 10
Challenge exercise 10
Chapter 11 CORRELATION AND REGRESSION
11.01 Bivariate data
11.02 Correlation
11.03 Line of best fit
11.04 Least-squares regression line
Test yourself 11
Challenge exercise 11
PRACTICE SET 3
Chapter 12 INVESTMENTS
12.01 Arithmetic growth and decay
12.02 Geometric growth and decay
12.03 Compound interest
12.04 Compound interest formula
12.05 Annuities
12.06 Annuities and geometric series
12.07 Reducing balance loans
12.08 Loans and geometric series
Test yourself 12
Challenge exercise 12
Chapter 13 DIFFERENTIAL EQUATIONS
13.01 EXT1 Solving dy/dx = f(x)
13.02 EXT1 Solving dy/dx = g(y)
13.03 EXT1 Solving dy/dx = f(x)g(y)
13.04 EXT1 Applications of differential equations
Test yourself 13
Challenge exercise 13
Chapter 14 CONTINUOUS PROBABILITY DISTRIBUTIONS
14.01 Probability density functions
14.02 Calculating probabilities
14.03 Cumulative distribution function
14.04 Quantiles
14.05 Normal distribution
14.06 Empirical rule
14.07 z-scores
14.08 Applications of the normal distribution
Test yourself 14
Challenge exercise 14
Chapter 15 BINOMIAL DISTRIBUTIONS
15.01 EXT1 Bernoulli distribution
15.02 EXT1 Binomial distribution
15.03 EXT1 Mean and variance of a binomial distribution
15.04 EXT1 Sample proportions
Test yourself 15
Challenge exercise 15
PRACTICE SET 4
ANSWERS
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Practice Set 1
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Practice Set 2
Chapter 9
Chapter 10
Chapter 11
Practice Set 3
Chapter 12
Chapter 13
Chapter 14
Chapter 15
Practice Set 4
INDEX
