Practice Test

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

$−13$

$\sqrt{2}$

For the following exercises, evaluate the expression.

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

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

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

Write the number in scientific notation: 0.0000000212.

For the following exercises, simplify the expression.

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

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

$3^{5} \cdot 3^{−3}$

10.

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

11.

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

12.

$(16 y^{0}) 2 y^{−2}$

13.

$\sqrt{441}$

14.

$\sqrt{490}$

15.

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

16.

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

17.

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

18.

$\frac{\sqrt[3]{−8}}{\sqrt[4]{625}}$

19.

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

20.

$(6 p^{2} + 2 p + 1) + (9 p^{2} −1)$

21.

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

22.

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

For the following exercises, factor the polynomial.

23.

$16 x^{2} - 81$

24.

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

25.

$27 c^{3} - 1331$

26.

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

For the following exercises, simplify the expression.

27.

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

28.

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

29.

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