Practice Test

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

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 × 10 6 3.1415 × 10 6

Write the number in scientific notation: 0.0000000212.

For the following exercises, simplify the expression.

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

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

3 5 ⋅ 3 −3 3 5 ⋅ 3 −3

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

( 16 y 0 ) 2 y −2 ( 16 y 0 ) 2 y −2

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

6 24 + 7 54 − 12 6 6 24 + 7 54 − 12 6

−8 3 625 4 −8 3 625 4

( 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 )

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

( n − 2 ) ( n 2 − 4 n + 4 ) ( n − 2 ) ( n 2 − 4 n + 4 )

( a − 2 b ) ( 2 a + b ) ( a − 2 b ) ( 2 a + b )

For the following exercises, factor the polynomial.

16 x 2 − 81 16 x 2 − 81

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

27 c 3 − 1331 27 c 3 − 1331

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

For the following exercises, simplify the expression.

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

x y + 2 x x y + 2 x

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

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