M115 Beginning Algebra Ch1 Practice Test

M115 Beginning Algebra
Ch1 Practice Test
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Classify as an expression or an equation.
1) 2x + 9
A) Expression
2) 6x - 10y = 7
A) Expression
Evaluate.
3)
1)
B) Equation
2)
B) Equation
x+y
, for x = 9 and y = 16
5
A)
144
5
3)
B)
61
5
C)
189
5
D) 5
Solve the problem.
4) The area of a triangle with base b and height h is given by the formula A =
1
bh. Find the area of a
2
4)
triangle when the base is 19.1 cm and the height is 8.6 cm. Round your answer to the nearest
hundredth.
A) 164.26 cm2
B) 82.13 cm2
C) 1.11 cm2
D) 65.704 cm2
5) Bill takes four times as long to do a job as Jose. Suppose t represents the time it takes Bill to do the
job. Then t/4 represents the time it takes Jose. How long does it take Jose if it takes Bill 33 minutes?
A) 132.00 minutes
B) 8.25 minutes
C) 37.00 minutes
D) 29.00 minutes
Translate to an algebraic expression.
6) 10 decreased by b
A) b ÷ 10
B) 10b
C) 10 - b
7) 3 less than 6 times a number
A) 3 - 6x
B) 3x - 6
C) 6x - 3
D) 10 + b
D) 3x
5)
6)
7)
Decide if the given number is a solution to the given equation.
8) 5p + 4p - 2 = 70; 8
A) Yes
B) No
8)
Translate the problem to an equation. Do not solve.
9) Twice a number less 7 equals 3.
A) 7 - 2x = 3
B) 2x - 7 = 3
9)
C) 2(x - 7) = 3
10) Four times a number increased by 4 divided by 2 is 2.
4
4x + 4
=2
A) 4x + = 4
B)
2
2
4(x + 4)
=4
C)
2
11) 44 minus twice a number equals 11 more than the number.
A) 44 - 2 = 11 + x
B) 44 - 2x = 11 + 2x
C) 44 - 2x = 11 + x
1
10)
11)
Translate to an algebraic expression.
12) Monica had $29 before spending y dollars for a snack. How much money remains?
A) $29 - y
B) $29y
C) y - $29
D) $29 + y
Name the correct property to make the sentence true.
13) 8 + p is equivalent to p + 8 by the
A) commutative law for multiplication.
C) distributive law.
12)
13)
B) commutative law for addition.
D) associative law for addition.
14) 4t is equivalent to t4 by the
A) commutative law for multiplication.
C) associative law for multiplication.
B) distributive law.
D) commutative law for addition.
15) n + (6 + g) is equivalent to (n + 6) + g by the
A) distributive law.
C) commutative law for multiplication.
B) associative law for multiplication.
D) associative law for addition.
14)
15)
16) (8p)g is equivalent to 8(pg) by the
A) commutative law for multiplication.
C) distributive law.
B) associative property for multiplication.
D) commutative property for addition.
17) 9(z + m) is equivalent to 9z + 9m by the
A) distributive law.
C) associative law for multiplication.
B) commutative law for addition.
D) associative law for addition.
Use the commutative law of addition to write an equivalent expression.
18) 2x + 3y
A) x2 + 2y
B) x2 + y3
C) 3x + y2
19) 4a + 9b
A) 4a + b9
20) 6(y + 6)
A) (y + 6)6
B) a4 + b9
C) 9b + 4a
B) 6(6 + y)
C) 36 + y
17)
18)
D) 3y + 2x
19)
D) a4 + 9b
20)
D) 6y + 36
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Use the commutative and/or associative laws to write a series of steps verifying the given statement.
21) 9 + (a + b) is equivalent to b + (9 + a)
21)
22) x(y5) is equivalent to 5(xy)
22)
23) ( 2)m is equivalent to 2( m)
23)
24) s(t2) is equivalent to 2(ts)
24)
25) (y + z) + 7 is equivalent to (7 + z) + y
25)
2
16)
26) (9 + y) + 3 is equivalent to y + 12
26)
27) (x + 8) + 6 is equivalent to 14 + x
27)
28) (8w)5 is equivalent to 40w
28)
29) (z2)6 is equivalent to 12z
29)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use the distributive law to multiply.
30) 8(4x + 9y + 5)
A) 32x + 9y + 5
B) 32x + 72y + 40
C) 32x + 72y + 5
D) 32x + 9y + 40
List the terms of the expression.
3p
31) 7x + m +
s
A) x, m, p
31)
B) 7x, m,
3p
s
Use the distributive law to factor the given expression.
32) 5 + 35a + 55b
A) 5(0 + 7a + 11b)
B) 5(1 + 35a + 55b)
34)
22
45
B) -
22
45
D) x, m,
C) 35(1 + a + b)
D) 5(1 + 7a + 11b)
C) -
55
18
D)
13
90
33)
34)
B) 1
C)
49
64
D) -
49
64
Perform the indicated operation and, if possible, simplify.
7
2
- 35)
10
3
A) -
32)
55
18
-7
8
÷
8
-7
A) -1
p
s
C) 7, 3
Perform the indicated operation and, if possible, simplify. If a quotient is undefined state this.
-11
2
÷ 33)
9
5
A)
30)
B)
35)
1
30
C)
Write the expression using exponents.
36) 5p · 5p · 5p · 5p
A) (5p)4
B) 20p
41
30
C) 5p4
3
D) -
41
30
D) 54 p
36)
Simplify.
37) (-2y)4
A) -8y
38) 74 - 2 · 9 + 210 ÷ (-15)
A) -1051
39) -90 ÷ -6 · A)
3
2
B) 42
C) -19
D) 634
2
3
B) -150
C) -
B) 415
C) 36
D) -
21
2
38)
3
2
D) 56
40)
41)
B) 10
2
7
C) 18
D) 2
27 - 2 · 3
2 3 ÷ 2 2 - (-2)2
A) -
37)
39)
4 · (3 + 8) + 4 · 7
4 · (2 - 1)
A) 24
42)
C) 16y
D) -2y4
1
10
40) 15 + 62 (8) - (-7)
A) 310
41)
B) 16y4
42)
B) 1
7
2
C) - 1
D)
Write an equivalent expression without using parentheses.
43) -(2x3 - 4x + 9)
A) -2x3 + 4x - 9
B) -2x3 + 4x + 9
C) -2x3 - 4x - 9
D) -2x3 - 4x + 9
Simplify.
44) 7x - y - 6(2x - 9y + 2z)
A) -5x - 10y + 2z
C) -5x - 55y + 12z
D) -5x + 8y - 2z
B) -5x + 53y - 12z
45) 9x3 + x - 7(3x2 - 8x)
A) 9x3 - 21x2 - 55x
C) 9x3 - 21x2 + x + 56
B) 9x3 - 21x2 + 57x
D) 9x3 - 3x2 - 7x
4
43)
44)
45)
Answer Key
Testname: CH1TEST
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
14)
15)
16)
17)
18)
19)
20)
21)
22)
23)
24)
25)
26)
27)
28)
29)
30)
31)
32)
33)
34)
35)
A
B
D
B
B
C
C
A
B
B
C
A
B
A
D
B
A
D
C
B
9 + (a + b) = (9 + a) + b
Using the associative law
Using the commutative law
= b + (9 + a)
x(y5) = (xy)5
Using the associative law
Using the commutative law
= 5(xy)
( 2)m = (2 )m
Using the commutative law
Using the associative law
= 2( m)
s(t2) = (t2)s Using the commutative law
= (2t)s Using the commutative law
= 2(ts) Using the associative law
(y + z) + 7 = 7 + (y + z)
Using the commutative law
Using the commutative law
= 7 + (z + y)
= (7 + z) + y
Using the associative law
(9 + y) + 3 = (y + 9) + 3
Using the commutative law
Using the associative law
= y + (9 + 3)
= y + 12
Simplifying
(x + 8) + 6 = x + (8 + 6)
Using the associative law
Simplifying
= x + 14
= 14 + x
Using the commutative law
(8w)5 = 5(8w)
Using the commutative law
Using the associative law
= (5·8)w
= 40w
Simplifying
(z2)6 = z(2·6)
Using the associative law
Simplifying
= z(12)
= 12z
Using the commutative law
B
B
D
D
C
C
5
Answer Key
Testname: CH1TEST
36)
37)
38)
39)
40)
41)
42)
43)
44)
45)
A
B
B
D
A
C
A
A
B
B
6