Calculus Subjects (What you'll take) 

Algebra and Trigonometry Background (What you'll need) 




Numbers and Their Disguises 



Brackets, multiplying and dividing fractions, adding and subtracting fractions, exponents, roots, percent, scientific notation, calculators, rounding, intervals 


1  (24) 





Completing the square in one and two variables 


25  (5) 





Equations of degree 1 and 2, solving other types of equations, rational equations, the zerofactor property 


30  (17) 



Functions and Their Graphs 



Introduction, equations of lines, power functions, shifting graphs, intersection of curves 


47  (28) 



Changing the Form of a Function 



Factoring, canceling, long division, rationalizing, extracting a factor from under a radical 


75  (14) 



Simplifying Algebraic Expressions 



Working with difference quotients and rational functions, canceling common factors, rationalizing expressions 


89  (7) 

Derivatives of Trig Functions 



Cyclic Phenomena: The Six Basic Trigonometric Functions 



Angles, definitions of the six trigonometric functions, special angles, graphs involving sin x and cos x 


96  (20) 



Composition and Decomposition of Functions 



Composite functions; inner, outer, and outermost functions: decomposing composite functions 


116  (4) 



Equations of Degree 1 Revisited 



Solving linear equations involving derivatives 


120  (4) 

Related Rates, Applied MaxMin Problems 



Word Problems, Algebraic and Trigonometric 



Algebraic word problems; the geometry of rectangles, circles, and spheres; trigonometric word problems; right angled triangles; the law of sines and the law of cosines 


124  (12) 

Integrating Trigonometric Functions 





Rewriting trigonometric expressions using identities 


136  (5) 

Appendices (Use as needed) 




141  (6) 


147  (9) 


156  (13) 

D. Inverse Trigonometric Functions 


169  (13) 


182  (3) 

F. Derivation of the Quadratic Formula 


185  (2) 
Answers to OddNumbered Exercises 

187  (21) 
Index 

208  