At all levels of mathematics, the best way to learn new concepts is by solving 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. PRE-CALCULUS 12 numerous questions. Through this Pre-calculus 12 workbook, students master 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! CAD $37.50 Infinite Challenge Publishing Ltd.
Table of Contents Functions and Relations... 7 Operations with Functions... 14 Composition of Functions... 18 Inverse Functions... 25 Even and Odd Functions... 37 Piecewise-Defined Functions... 39 Chapter Review Exercises... 41 Translations... 47 Reflections... 52 Stretches... 57 Combined Transformations... 64 Graphing... 73 Reciprocal Transformations... 77 Absolute Value Transformations... 84 Square Root Transformations... 92 Chapter Review Exercises... 96 Polynomials... 103 Dividing Polynomials... 105 Remainder Theorem... 110 Factor Theorem... 114 Solving Polynomial Equations by Factoring... 119 Graphing Polynomial Functions... 123 Applications of Polynomial Functions Using a Graphing Calculator... 132 Chapter Review Exercises... 135 Asymptotes and Holes... 141 Graphing Rational Functions... 144 Slant Asymptotes of Rational Functions (Oblique Asymptote)... 152 Circle... 155 Parabola... 161 Ellipse... 168 Hyperbola... 175 Classifying Conic Sections... 182 Chapter Review Exercises... 186 Review of Exponent Laws... 192 Solving Exponential Equations with the same base,... 196 Graphing Exponential Functions... 199 Converting between Exponential Form and Logarithmic Form... 203
Graphing Logarithmic Functions... 206 Laws of Logarithms... 213 Solving Exponential and Logarithmic Equations... 222 Applications of Exponential and Logarithmic functions... 233 Chapter Review Exercises... 242 Sequences... 249 Arithmetic Sequence... 252 Arithmetic Series... 256 Geometric Sequence... 262 Geometric Series... 267 Infinite Geometric Series... 273 Sigma Notation... 277 Chapter Review Exercises... 282 Angular Measure... 287 Trigonometric Ratios... 289 Special Angles and Solving Simple Trigonometric Equations... 292 Unit Circle... 302 Radians... 304 Solving Trigonometric Equations Using a Calculator: Algebraic Method... 313 General Solutions... 316 Trigonometric Equations Involving Multiple Angles... 318 Solving Trigonometric Equations Using a Graphing Calculator: Graphical Method... 320 Arc Length and Sector Area... 322 Chapter Review Exercises... 327 Graphing Primary Trigonometric Functions... 333 Graphing Transformed Trigonometric Functions... 340 Finding the Equation of a Trigonometric Graph... 344 Applications of Sinusoidal Functions... 348 Graphing Reciprocal Trigonometric Functions... 354 Chapter Review Exercises... 358 Basic Trigonometric Identities... 363 Proving Trigonometric Identities... 368 Sum and Difference Identities... 373 Double Angle Identities... 379 Solving Trigonometric Equations Involving Double Angle Identities... 387 Chapter Review Exercises... 396 *Solutions... 403 522
ISBN: 978-0-9916987-4-5 ISBN: 978-0-9916987-6-9 ISBN: 978-0-9916987-3-8 ISBN: 978-0-9916987-5-2
At all levels of mathematics, the best way to learn new concepts is by solving 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. PRE-CALCULUS 12 numerous questions. Through this Pre-calculus 12 workbook, students master 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 problem! CAD $37.50 Infinite Challenge Publishing Ltd.