Chapter 1 Review Worksheet
1. Given: A= {-5, -4, -3, -2, -1, 0, 1, 2}, Tell whether the following are true or false.
a.
6∈A
b.
{-5, -3} ⊂ A
c.
{-5, -3} ∈ A
d.
-2 ⊂ A
e.
∅⊂A
2. Simplify. (4𝑥 3 + 12𝑦)(16𝑥 2 − 7𝑦 2 ) − [18𝑦 6 + 𝑥 2 𝑦]
12𝑥
3. Simplify.
𝑥 2 −𝑥−12
+
4𝑦
2𝑥 2 +18𝑥+36
3
4
+
𝑦 𝑥+ℎ
5𝑦
𝑥+ℎ
4. Simplify.
5. Factor. 14ab + 8ax - 7by - 4xy
Simplify.
6.
[(
𝑎−2 𝑏−6 𝑐 −5
2𝑎10 𝑏−14 𝑐 3
4
3
8. (−125)
4
10.
√16𝑎21 𝑏9
2𝑎𝑏
−1 2
)
]
7.
9.
(
4𝑥 2 𝑦−3 𝑧 8
24𝑥 −1 𝑦 6 𝑧 2
(
27𝑎−27
64𝑏125
−2
)
1/3
)
11. Simplify.
12. Simplify.
13. Simplify.
14. Simplify.
2√2 − 3√5
−3√5 − 5√2
2 + 4𝑥 −2
2𝑥 −1 + 𝑥
5
5
√3𝑚2 𝑛3 ∙ √4𝑚2 𝑛7
(
10𝑢2 𝑣 3
−5𝑤 −1 𝑢−1
)
2
1. Please match each property to the equation that represents it.
a. Distributive property:
3+7+2=2+3+7
b. Commutative property:
(3 + 7) + 2 = (2 + 7) + 3
c. Zero property:
7 × 21 × 48 × 0= 0
d. Associative property:
4(9 + 2)=4(9)+4(2)
e. Inverse property:
1
24.5× 24.5= 1
2. Label whether the statements are true or false given: A={1,3,4,5,7,8,22}, B={2,3,7,8,9,11,23}
a. 1, 2, 3 ⊂ A
b. 2, 3, 10 ⊂ B
c. 22 ∈ A
d. 4 ∉ B
e. 7 ∈ A, B
3. Express as a simple fraction reduced to the lowest terms.
3
3−𝑥
1
𝑥−𝑥
4. Perform the indicated operations and simplify.
(5x – 10y)(10x – 5y) – [26𝑥 2 +7y(2x + 3y)]
5. Perform the indicated operations and reduce answers to lowest terms.
64 − 𝑥 2
𝑥 2 + 6𝑥 − 16
6. Factor completely
581𝑥 2 +28x +249xy +12𝑦
7. Simplify
(
3𝑥 2 𝑦 −5
4𝑥 −2 𝑦 −3
−2
)
8. Simplify.
𝑥 2 + 6𝑥 − 16
𝑥 2 + 5𝑥 − 24
÷ 2
2𝑥 2 − 5𝑥 − 7
2𝑥 − 17𝑥 + 35
9. Simplify.
4
√16𝑘 34 𝑦 6
10. Find c such that 3𝑠 5𝑐 (9𝑠 2𝑐−2 + 7𝑠 3𝑐+5 )=27𝑠 47 + 21𝑠 61