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Math 251: Practice Exam 1
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Disclaimer
You should use this practice exam to assess your speed and to
improve your ability to correctly identify different problem types.
The questions on this practice exam are taken from exams given in
previous semesters, but they may not be representative of the
questions that will appear on this semester's exam. You should also
invest time re-reading the relevant parts of your textbook, reviewing
your notes, and practicing homework problems.
Math 251: Practice Exam 1
Questions
You will not receive full credit if you do not clearly show how you are obtaining your
answers. Show all work on this exam; do not attach other work. Circle your answers.
1.
Decide whether each statement is an example of the commutative, associative, identity, inverse, or distributive property.
a.
2(3x − 7) + 5 = 2 ⋅ 3x − 2 ⋅ 7 + 5 a. distributive
b.
1
7 ⋅ x = x 7
b. inverse
c.
(3x + 2y) + 4 = (2y + 3x) + 4 c. commutative
d.
2x + 17 + (−17) = 2x + 0 d. inverse
e.
15x − 3x + 2 = (15 − 3)x + 2 e. distributive
f.
5x(3y ⋅ 7) = (5x ⋅ 3y) ⋅ 7 f. associative
g.
0 + 4(12x + 1) = 4(12x + 1) g. identity
h.
3 ⋅ (2x − 1) = (2x − 1) ⋅ 3 h. commutative
2.
Find the measure of an angle whose complement is five times its measure.
x = the measure of the angle
90° − x = the measure of the angle's complement
90° − x = 5x
90° = 6x
15° = x
(16 points)
(4 points)
Page 2
3.
Solve each equation and check your solution.
a.
7.7r − 6 = 6.7r − 6
7.7r − 6 = −6.7r − 6
−6.7r − 6 = −6.7r − 6
r − 6 = −6
r + 6 = +6
r=0
b.
3
− z = −21
4
3
− z = −21
4
⎛ 4 ⎞ ⎛ 3 ⎞ ⎛ 4 ⎞ ⎛ 21 ⎞
⎜⎝ − ⎟⎠ ⎜⎝ − z ⎟⎠ = ⎜⎝ − ⎟⎠ ⎜⎝ − ⎟⎠
3
4
3
1
⎛ 4⎞ ⎛ 7⎞
z=⎜ ⎟⎜ ⎟
⎝ 1⎠ ⎝ 1⎠
z = 28
c.
5(2m + 3) − 4m = 2m + 25
10m + 15 − 4m = 2m + 25
6m + 15 = 2m + 25
4m + 15 = 25
4m = 10
10
m=
4
5
m=
2
(12 points)
Page 3
4.
Perform each indicated operation. (4 points)
a.
−8 − [(−4 − 1) + (9 − 2)] −8 − [(−5) + (7)]
−8 − [2]
−10
5.
Tell whether each statement is TRUE or FALSE
a.
3[5(2) − 3] > 20 b.
− 12 > − 15
3[10 − 3] > 20
3[7] > 20 21 > 20
−12 > 15
TRUE
FALSE
6.
Evaluate the expression 5x − 4a 2 + 2y for x = 6 , y = −4 , and a = 3 .
5x − 4a 2 + 2y = 5(6) − 4(3)2 + 2(−4) = 30 − 4 ⋅ 9 + (−8) = 30 − 36 + (−8) = −6 + (−8) = −14
7.
Decide whether 20 is a solution to the equation 0.5(x − 4) = 80 0.5(x − 4) = 0.5(20 − 4) = 0.5(16) = 8 ≠ 80
So 20 is not a solution.
8.
Write the word statement “nine is greater than five minus four” in symbols.
9>5−4
b.
−8−2 − −9−3
− 10 − − 12
10 − 12
−2
(4 points)
(2 points)
(2 points)
(2 points)
Page 4
9.
Simplify each expression. a.
5y 3 + 6y 3 − 3y 2 − 4y 2 (8 points)
b.
7
1
− (t − 15) − t
5
2
⎛ 7⎞ ⎛ 7⎞
⎛1 ⎞
⎜⎝ − ⎟⎠ t − ⎜⎝ − ⎟⎠ 15 − ⎜⎝ t ⎟⎠
5
5
2
11y − 3y − 4y
3
2
11y 3 − 7y 2
2
⎛ 2⎞ ⎛ 7 ⎞ ⎛ 7⎞
⎛ 5⎞ ⎛ 1 ⎞
⎜⎝ ⎟⎠ ⋅ ⎜⎝ − t ⎟⎠ + ⎜⎝ ⎟⎠ ⋅ 3 − ⎜⎝ ⎟⎠ ⋅ ⎜⎝ t ⎟⎠
2
5
1
5
2
⎛ 14 ⎞
⎛ 5 ⎞
⎜⎝ − ⎟⎠ t + 21 − ⎜⎝ t ⎟⎠
10
10
21 −
c.
100[0.06(x + 5)] 6(x + 5)
6x + 30
d.
6(3p − 2) − (5 p + 1)
6(3p − 2) − (5 p + 1)
18 p − 12 − 5 p − 1
13p − 13
10.
Find the value of each expression.
a.
9(4 2 − 3)
4 ⋅ 5 − 17
9(16 − 3)
20 − 17
9(13)
3
3(13)
39
19
t
10
(4 points)
b.
7[3 + 6(32 )]
7[3 + 6(9)]
7[3 + 54]
7[57]
399
Page 5
11.
Write the word statement “three times a number is equal to 8 more than twice
the number” as an equation. Use x as the variable.
3x = 2x + 8
32 − 4 2
12.
Perform the indicated operation.
7(−8 + 9)
(2 points)
32 − 4 2
7(−8 + 9)
9 − 16
7(1)
−7
7
−1
13.
Simplify − −
− −
4
.
5
(2 points)
4
4
=−
5
5
14.
Select the lesser of the two given numbers.
(4 points)
a.
−9, − 11 b.
− 3.5 , − 4.5
3.5, 4.5
15.
Write the word phrase “three-fifths of a number added to twelve” as an algebraic expression, using x as the variable.
(2 points)
12 +
3
x
5
(2 points)
Page 6
16.
Solve each equation and check your solution.
a.
b.
1
1
x+5=− x
2
2
⎛1
⎞
⎛ 1 ⎞
2 ⎜ x + 5⎟ = 2 ⎜ − x ⎟
⎝2
⎠
⎝ 2 ⎠
x + 10 = −x
2x + 10 = 0
2x = −10
x = −5
−3.9x = 32.76
32.76
−3.9
x = −8.4
x=
c.
3(6 − 4x) = 2(−6x + 9)
18 − 12x = −12x + 18
18 = 18
Since the statement is always true, all real numbers are solutions.
(12 points)
Page 7
17.
Perform each indicated operation.
a.
5 ⎛ 17 ⎞
+ ⎜ − ⎟ 8 ⎝ 12 ⎠
(8 points)
b.
5.7 − (−11.6)
5.7 + 11.6
17.3
3 5 2 ⎛ 17 ⎞
⋅ + ⋅⎜− ⎟
3 8 2 ⎝ 12 ⎠
15 ⎛ 34 ⎞
+ ⎜− ⎟
24 ⎝ 24 ⎠
19
−
24
c.
3 ⎛ 10 ⎞
− ⋅ ⎜ − ⎟ 8 ⎝ 9⎠
d.
3 ⎛ 10 ⎞ 1 ⎛ 5 ⎞ 5
⋅⎜ ⎟ = ⋅⎜ ⎟ =
8 ⎝ 9 ⎠ 4 ⎝ 3 ⎠ 12
18.
Evaluate the expression
−0.46
0.23
−2
x
+ 4y for x = 6 and y = 3 .
3
(2 points)
x
6
+ 4y = + 4(3) = 2 + 12 = 14
3
3
19.
Two apartments have numbers that are consecutive integers. The sum of the numbers
is 59. What are the two apartment numbers?
n = first integer
n + 1 = second integer
(n) + (n + 1) = 59
2n + 1 = 59
2n = 58
n = 29
So the two integers are 29 and 30.
(8 points)