Contents

Preface
1Prerequisites
2Equations and Inequalities
3Functions
4Linear Functions
5Polynomial and Rational Functions
6Exponential and Logarithmic Functions
7The Unit Circle: Sine and Cosine Functions
8Periodic Functions
9Trigonometric Identities and Equations
10Further Applications of Trigonometry
11Systems of Equations and Inequalities
12Analytic Geometry
13Sequences, Probability, and Counting Theory
AProofs, Identities, and Toolkit Functions
Answer Key
Index

Practice Test

For the following exercises, identify the number as rational, irrational, whole, or natural. Choose the most descriptive answer.

$−13 −13$

$\sqrt{2} \sqrt{2}$

For the following exercises, evaluate the expression.

$2 (x + 3) - 12; x = 2 2 (x + 3) - 12; x = 2$

$y {(3 + 3)}^{2} - 26; y = 1 y {(3 + 3)}^{2} - 26; y = 1$

Write the number in standard notation: $3.1415 \times 10^{6} 3.1415$

Write the number in scientific notation: 0.0000000212.

For the following exercises, simplify the expression.

$−2 \cdot {(2 + 3 \cdot 2)}^{2} + 144 −2 \cdot {(2 + 3 \cdot 2)}^{2} + 144$

$4 (x + 3) - (6 x + 2) 4 (x + 3) - (6 x + 2)$

$3^{5} \cdot 3^{−3} 3^{5} \cdot 3^{−3}$

10.

${(\frac{2}{3})}^{3} {(\frac{2}{3})}^{3}$

11.

$\frac{8 x^{3}}{{(2 x)}^{2}} \frac{8 x^{3}}{{(2 x)}^{2}}$

12.

$(16 y^{0}) 2 y^{−2} (16 y^{0}) 2 y^{−2}$

13.

$\sqrt{441} \sqrt{441}$

14.

$\sqrt{490} \sqrt{490}$

15.

$\sqrt{\frac{9 x}{16}} \sqrt{\frac{9 x}{16}}$

16.

$\frac{\sqrt{121 b^{2}}}{1 + \sqrt{b}} \frac{\sqrt{121 b^{2}}}{1 + \sqrt{b}}$

17.

$6 \sqrt{24} + 7 \sqrt{54} - 12 \sqrt{6} 6 \sqrt{24} + 7 \sqrt{54} - 12 \sqrt{6}$

18.

$\frac{\sqrt[3]{−8}}{\sqrt[4]{625}} \frac{\sqrt[3]{−8}}{\sqrt[4]{625}}$

19.

$(13 q^{3} + 2 q^{2} - 3) - (6 q^{2} + 5 q - 3) (13 q^{3} + 2 q^{2} - 3) - (6 q^{2} + 5 q - 3)$

20.

$(6 p^{2} + 2 p + 1) + (9 p^{2} −1) (6 p^{2} + 2 p + 1) + (9 p^{2} −1)$

21.

$(n - 2) (n^{2} - 4 n + 4) (n - 2) (n^{2} - 4 n + 4)$

22.

$(a - 2 b) (2 a + b) (a - 2 b) (2 a + b)$

For the following exercises, factor the polynomial.

23.

$16 x^{2} - 81 16 x^{2} - 81$

24.

$y^{2} + 12 y + 36 y^{2} + 12 y + 36$

25.

$27 c^{3} - 1331 27 c^{3} - 1331$

26.

$3 x {(x - 6)}^{- \frac{1}{4}} + 2 {(x - 6)}^{\frac{3}{4}} 3 x {(x - 6)}^{- \frac{1}{4}} + 2 {(x - 6)}^{\frac{3}{4}}$

For the following exercises, simplify the expression.

27.

$\frac{2 z^{2} + 7 z + 3}{z^{2} - 9} \cdot \frac{4 z^{2} - 15 z + 9}{4 z^{2} - 1} \frac{2 z^{2} + 7 z + 3}{z^{2} - 9} \cdot \frac{4 z^{2} - 15 z + 9}{4 z^{2} - 1}$

28.

$\frac{x}{y} + \frac{2}{x} \frac{x}{y} + \frac{2}{x}$

29.

$\frac{\frac{a}{2 b} - \frac{2 b}{9 a}}{\frac{3 a - 2 b}{6 a}} \frac{\frac{a}{2 b} - \frac{2 b}{9 a}}{\frac{3 a - 2 b}{6 a}}$