Download Practice Problems in Essential Algebra Skills

Math 120-121
Name ___________________
Practice Problems in Essential Algebra Skills
1. Label the numbers below: N if they are integers; R if they are rational numbers (but
not integers); and I if they are irrational numbers.
a)  72
b) 0
c) 6
d) 13
e) 1.4
f)
g) 
2
3
h) –0.08
2. Place the correct inequality symbol (< or >) between the two numbers:
1
1
a) 10 ___ 4 b) –8 ___ 3 c) ___
d) 2.75 ___ 
3
4
3. Plot the number and its opposite on the real number line:
a) 7
b) –5
4.
Evaluate: a) –16 + 84
b) –22 – 6
c) 5.8 – 6.2 + 1.1
5.
Evaluate the product:
1
a)  6 
2
b)  7 5
6.
Evaluate:
c) 72 – 8(6 2  4)
a) 16 – 6 – 10
d)
5 1

6 4
 2  15 
c)    
 5  4 
b) 28  4 + 3  5
d) 18 – [4 + (17 – 12)]
7.
If you earn $350 per week for 2 years, how much money will you earn during
that time? [let 52 weeks equal one year.]
8.
Rewrite using the Distributive Property:
a) 20(7 + 5)
b) (x + 3)(2)
c) 3(2 x 2  3x  4)
9.
10.
11.
Give the a) additive inverse and b) the multiplicative inverse of the quantity
⅓.
Identify the terms of the algebraic expression:
3 4
a)  3 y 2 2 y  8
b) 2   6
t
t
Simplify:
a)  23  24
d) (2 x)( x 2 y 2 )
12.
b)  (4 x 2 ) 2
e) 6n(3n 2 ) 2
13.
f) (a 3 ) k
Simplify by combining like terms: a) 2x  5x
c) 7 x 2  2 x  x 2
Simplify the expressions:
c) 4( x) 2
b) 2 y  3 y  y
d) 6x  4  3x  7
a) 2( x  5)  7 x  1
c) x( x 2  3)  3( x  4)
b) 5(a + 2) – 4(3a – 1)
d) 2 x  3 y  ( x  2 y )
14. Evaluate each expression for the specified values of the variables:
a) x 2  4 x  3 for x = 2.
b) x 2  4 x  3 for x = −3
x
x
c)
for x = 0 and y = 10.
d)
for x = 4 and y = 4.
x y
x y
e) 6x – 5y for x = −2 and y = −3.
f) 6x – 5y for x = 1 and y = 1.
15. Translate the verbal phrase into an algebraic expression:
a) Five more than a number n.
b) Twelve decreased by twice a number n.
c) The ratio of y to 5.
d) Forty percent of the cost C.
e) 10 less than a number n.
Answers to Practice Problems from Chapter 1
1. a) R
b) N
c) I
e) R
f) R
g) I
2. a) >
b) <
c) >
3. a) [a number line with dots at −7 and 7]
4. a) 68
b) −28
c) 0.7
5. a) −3
b) 35
d) N
h) R
d) <
b) [dots at −5 and 5]
d) 7
12
c) − 3
2
6. a) 0
b) 22
c) 0
d) 9
7. $36,400
8. a) 140 + 100 = 240
b)  2x  6
c) 6 x 2  9 x  12
9. a) −⅓
b) 3
10.
First term
2nd term
3rd term
a)
−8
2y
 3y 2
b)
6
3
4

2
t
t
11. a)  2 7  128 b)  16x 4
c) 4x 2
d) 2 x 3 y 2
e) 54n 5
f) a 3 k
12. a)  3x
b) 4y
c) 6 x 2  2 x
d) 3x  3
3
13. a)  5x  11 4x  3
b)  7a  14 c) x  12
d) x  5 y
14. a) −7; b) 18; c) 0; d) undefined;
e) 3; f) 1
15. a) n + 5 b) 12  2n
c) y : 5, or y
d) 0.4C
e) n  10
5