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PRE-CALCULUS 12 Richard N.S. Seong Key points concisely summarized More than 450 complete guided examples All the formulae provided with complete proofs 3000 carefully crafted questions with full solutions! 1400 graphs and diagrams to help explain and solve problems! Infinite Challenge Publishing Ltd.
Transcript of PRE-CALCULUS 12 › app › uploads › 2018 › 03 › Precalcul… · the mathematical...
PRE-CALCULU
S 12
Richard N.S. Seong
CAD $37.50
Key points concisely summarized More than 450 complete guided examplesAll the formulae provided with complete proofs 3000 carefully crafted questions with full solutions! 1400 graphs and diagrams to help explain and solve problems!
Infinite Challenge Publishing Ltd.
Chapter 1. FunctionsChapter 2. TransformationsChapter 3. Polynomial Equations and FunctionsChapter 4. Rational Functions and ConicsChapter 5. Exponents and LogarithmsChapter 6. Sequences and SeriesChapter 7. Trigonometric EquationsChapter 8. Graphs of Trigonometric FunctionsChapter 9. Trigonometric Identities
At all levels of mathematics, the best way to learn new concepts is by solving numerous questions. Through this Pre-calculus 12 workbook, students master the mathematical foundations required to succeed in Calculus. Following a short review of the fundamental concepts and guided examples, students are challenged with exercise questions ranging in difficulty. There are over 450 guided examples and 3000 questions, with full solutions, because practice makes perfect.
Table of ContentsChapter 1. Functions Functions and Relations........................................................................................................................................ Operations with Functions.................................................................................................................................... Composition of Functions..................................................................................................................................... Inverse Functions................................................................................................................................................. Even and Odd Functions..................................................................................................................................... Piecewise-Defined Functions................................................................................................................................
Chapter Review Exercises....................................................................................................................................
Chapter 2. Transformations Translations............................................................................................................................................................ Reflections............................................................................................................................................................. Stretches............................................................................................................................................................... Combined Transformations................................................................................................................................... Graphing .............................................................................................................................. Reciprocal Transformations.................................................................................................................................. Absolute Value Transformations......................................................................................................................... Square Root Transformations.............................................................................................................................
Chapter Review Exercises..................................................................................................................................
Chapter 3. Polynomial Equations and Functions Polynomials.......................................................................................................................................................... Dividing Polynomials........................................................................................................................................... Remainder Theorem........................................................................................................................................... Factor Theorem.................................................................................................................................................. Solving Polynomial Equations by Factoring...................................................................................................... Graphing Polynomial Functions......................................................................................................................... Applications of Polynomial Functions Using a Graphing Calculator .............................................................
Chapter Review Exercises.................................................................................................................................
Chapter 4. Rational Functions and Conics Asymptotes and Holes........................................................................................................................................ Graphing Rational Functions.............................................................................................................................. Slant Asymptotes of Rational Functions (Oblique Asymptote)........................................................................ Circle................................................................................................................................................................... Parabola............................................................................................................................................................. Ellipse.................................................................................................................................................................. Hyperbola............................................................................................................................................................ Classifying Conic Sections.................................................................................................................................
Chapter Review Exercises.................................................................................................................................
Chapter 5. Exponents and Logarithms Review of Exponent Laws................................................................................................................................. Solving Exponential Equations with the same base, ....................................................................... Graphing Exponential Functions........................................................................................................................ Converting between Exponential Form and Logarithmic Form.......................................................................
7 14 18 25 37 39
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Graphing Logarithmic Functions........................................................................................................................ Laws of Logarithms............................................................................................................................................ Solving Exponential and Logarithmic Equations............................................................................................... Applications of Exponential and Logarithmic functions...................................................................................
Chapter Review Exercises................................................................................................................................
Chapter 6. Sequences and Series Sequences.......................................................................................................................................................... Arithmetic Sequence........................................................................................................................................... Arithmetic Series................................................................................................................................................. Geometric Sequence......................................................................................................................................... Geometric Series............................................................................................................................................... Infinite Geometric Series................................................................................................................................... Sigma Notation...................................................................................................................................................
Chapter Review Exercises...............................................................................................................................
Chapter 7. Trigonometric Equations Angular Measure................................................................................................................................................ Trigonometric Ratios.......................................................................................................................................... Special Angles and Solving Simple Trigonometric Equations........................................................................ Unit Circle........................................................................................................................................................... Radians............................................................................................................................................................... Solving Trigonometric Equations Using a Calculator: Algebraic Method....................................................... General Solutions............................................................................................................................................... Trigonometric Equations Involving Multiple Angles.......................................................................................... Solving Trigonometric Equations Using a Graphing Calculator: Graphical Method...................................... Arc Length and Sector Area.............................................................................................................................
Chapter Review Exercises................................................................................................................................
Chapter 8. Graphs of Trigonometric Functions Graphing Primary Trigonometric Functions...................................................................................................... Graphing Transformed Trigonometric Functions.............................................................................................. Finding the Equation of a Trigonometric Graph.............................................................................................. Applications of Sinusoidal Functions............................................................................................................... Graphing Reciprocal Trigonometric Functions..................................................................................................
Chapter Review Exercises.................................................................................................................................
Chapter 9. Trigonometric Identities Basic Trigonometric Identities........................................................................................................................... Proving Trigonometric Identities........................................................................................................................ Sum and Difference Identities........................................................................................................................... Double Angle Identities...................................................................................................................................... Solving Trigonometric Equations Involving Double Angle Identities...............................................................
Chapter Review Exercises...............................................................................................................................
*Solutions..................................................................................................................................................
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287289292302304313316318320322
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333340344348354
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363368373379387
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403 ― 522
ISBN: 978-0-9916987-6-9
ISBN: 978-0-9916987-5-2ISBN: 978-0-9916987-3-8
ISBN: 978-0-9916987-4-5
PRE-CALCULU
S 12
Richard N.S. Seong
CAD $37.50
Key points concisely summarized More than 450 complete guided examplesAll the formulae provided with complete proofs 3000 carefully crafted questions with full solutions! 1400 graphs and diagrams to help explain and solve problem!
Infinite Challenge Publishing Ltd.
Chapter 1. FunctionsChapter 2. TransformationsChapter 3. Polynomial Equations and FunctionsChapter 4. Rational Functions and ConicsChapter 5. Exponents and LogarithmsChapter 6. Sequences and SeriesChapter 7. Trigonometric EquationsChapter 8. Graphs of Trigonometric FunctionsChapter 9. Trigonometric Identities
At all levels of mathematics, the best way to learn new concepts is by solving numerous questions. Through this Pre-calculus 12 workbook, students master the mathematical foundations required to succeed in Calculus. Following a short review of the fundamental concepts and guided examples, students are challenged with exercise questions ranging in difficulty. There are over 450 guided examples and 3000 questions, with full solutions, because practice makes perfect.
