Algebra and Trigonometry

# Practice Test

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

1.

$−13 −13$

2.

$2 2$

For the following exercises, evaluate the equations.

3.

$2(x+3)−12=18 2(x+3)−12=18$

4.

$y (3+3) 2 −26=10 y (3+3) 2 −26=10$

5.

Write the number in standard notation:$3.1415 × 10 6 3.1415 × 10 6$

6.

Write the number in scientific notation: 0.0000000212.

For the following exercises, simplify the expression.

7.

$−2⋅ ( 2+3⋅2 ) 2 +144 −2⋅ ( 2+3⋅2 ) 2 +144$

8.

$4( x+3 )−( 6x+2 ) 4( x+3 )−( 6x+2 )$

9.

$3 5 ⋅ 3 −3 3 5 ⋅ 3 −3$

10.

$( 2 3 ) 3 ( 2 3 ) 3$

11.

$8 x 3 ( 2x ) 2 8 x 3 ( 2x ) 2$

12.

$( 16 y 0 )2 y −2 ( 16 y 0 )2 y −2$

13.

$441 441$

14.

$490 490$

15.

$9x 16 9x 16$

16.

$121 b 2 1+ b 121 b 2 1+ b$

17.

$6 24 +7 54 −12 6 6 24 +7 54 −12 6$

18.

$−8 3 625 4 −8 3 625 4$

19.

$(13 q 3 +2 q 2 −3)−(6 q 2 +5q−3) (13 q 3 +2 q 2 −3)−(6 q 2 +5q−3)$

20.

$( 6 p 2 +2p+1 )+( 9 p 2 −1 ) ( 6 p 2 +2p+1 )+( 9 p 2 −1 )$

21.

$(n−2)( n 2 −4n+4) (n−2)( n 2 −4n+4)$

22.

$(a−2b)(2a+b) (a−2b)(2a+b)$

For the following exercises, factor the polynomial.

23.

$16 x 2 −81 16 x 2 −81$

24.

$y 2 +12y+36 y 2 +12y+36$

25.

$27 c 3 −1331 27 c 3 −1331$

26.

$3x (x−6) − 1 4 +2 (x−6) 3 4 3x (x−6) − 1 4 +2 (x−6) 3 4$

For the following exercises, simplify the expression.

27.

$2 z 2 +7z+3 z 2 −9 ⋅ 4 z 2 −15z+9 4 z 2 −1 2 z 2 +7z+3 z 2 −9 ⋅ 4 z 2 −15z+9 4 z 2 −1$

28.

$x y + 2 x x y + 2 x$

29.

$a 2b − 2b 9a 3a−2b 6a a 2b − 2b 9a 3a−2b 6a$