Download Quiz I Solutions 1. (3 points) Determine which numbers in the set are

Quiz I Solutions
1. (3 points) Determine which numbers in the set are (a) integers, (b) rational numbers
and (c) irrational numbers.
√ 1
{−3, π, 2, , 0}
3
Solution:
(a) {−3, 0}
(b) {−3, 0, 31 }.
√
(c) {π, 2}.
2. (1 point) Evaluate the following expression.
|3 − 9|
Solution: |3 − 9| = | − 6| = 6
3. Evaluate the following expressions for the given value of x.
(a) (2 points) x2 + 2x − 7, x = −2
Solution: (−2)2 + 2(−2) − 7 = 4 − 4 − 7 = −7
(b) (2 points) −20x2 , x = − 12
2
1
1
Solution: −20 −
= −20
= −5
2
4
(c) (2 points) 4x0 , x = 100
Solution: 4(100)0 = 4 · 1 = 4
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4. Rewrite each expression with positive exponents and simplify.
(a) (2 points) (−2x2 )2 (6x3 )−1
Solution: (−2x2 )2 (6x3 )−1 =
(b) (2 points)
x−1 y 4
3
Solution:
(−2x2 )2
(−2)2 (x2 )2
4x4
2x
=
=
=
3
1
3
3
(6x )
6x
6x
3
−3
x−1 y 4
3
−3
=
(x−1 )−3 (y 4 )−3
x3 y −12
33 x3
27x3
=
=
=
3−3
3−3
y 12
y 12
5. Simplify each radical expression.
s
16x5
(a) (3 points) 3
y4
s
Solution:
3
√
√
√
3
3
3
16x5
16x5
8 · 2 · x3 · x2
2x 2x2
p
p
= 3
=
=
√
3
y4
y3y
y4
y3 · y
√
√
(b) (3 points) 2 50 + 10 8
√
√
√
√
√
√
√
√
√
Solution: 2 50+10 8 = 2 25 · 2+10 4 · 2 = 2·5 2+10·2 2 = 10 2+20 2 = 30 2
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