Math 351: Practice Exam 1
Answers
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 351: Practice Exam 1
Answers
You will not receive full credit if you do not clearly show work as demonstrated
in class. Show all work in the space provided on this exam. Circle your answers.
1.
Determine whether each equation is an example of the commutative, associative, or distributive property.
(6 points)
a)
9 + 2 = 2 + 9 ________________commutative____________________
b)
7 ( 5 ⋅ 4 ) = ( 7 ⋅5 ) ⋅ 4 ________________associative_____________________
c)
3( x +1) = 3⋅ x + 3⋅1 ________________distributive_____________________
d)
5 ( 3× 4 ) = 5 ( 4 × 3) ________________commutative____________________
e)
( 2 +1) + 3 = 2 + (1+ 3) ________________associative_____________________
f)
4 ⋅6 = 6 ⋅ 4 ________________commutative____________________
2.
List the terms and coefficients of the given expression. Also identify the constant.
5xy2 − xy + 6y − 3
(7 points)
terms
coefficients
5xy2
5
−xy
−1
6y
6
−3
← constant
Page 2
3.
Round each number to the indicated place value.
a)
352 to the nearest ten
350
b)
15,264,124 to the nearest hundred-thousand
15,300,000
c)
6,983 to the nearest hundred
7,000 to the nearest hundred
d)
18,494 to the nearest one-thousand
18,000
4.
Simplify each expression.
a)
4 ( a + 3) − 2a +1 4 ( a + 3) − 2a +1
4a + 4 ⋅ 3− 2a +1
4a +12 − 2a +1
4a +12 + ( −2a ) +1 4a + ( −2a ) +12 +1
2a +12 +1
2a +13
(4 points)
(6 points)
b)
2 ( 3x −1) − 5 ( x + 6 )
2 ( 3x −1) − 5 ( x + 6 )
2 ( 3x −1) + ( −5 ) ( x + 6 )
2 ⋅ 3x − 2 ⋅1+ ( −5 ) x + ( −5 ) 6
6x − 2 + ( −5x ) + ( −30 )
6x + ( −2 ) + ( −5x ) + ( −30 )
6x + ( −5x ) + ( −2 ) + ( −30 )
x − 32
Page 3
5.
Find the value of each expression.
a)
−24 ÷ ( −6 ) b)
27 −3
c)
6 × ( −20 )
4 −9 −120
d)
−15 5
e)
−2 ( −5 ) f)
−7 ⋅ 3
−3 −10 −21
6.
Use the rule for the order of operations to simplify the expressions.
a)
−32
⎡
− 2⎢
⎣
(−3)
2
⎤
+ 2 ⎥ ⎦
(12 points)
b)
−32 − 2 ⎢( −3) + 2 ⎥
⎡
2
⎣
−32
⎤
⎦
− 2 ⎡⎣ 9 + 2 ⎤⎦
−32 − 2 ⎡⎣11⎤⎦
−9 − 2 ⎡⎣11⎤⎦
−9 − 22
−31
(8 points)
⎡
−5 − ⎢1+
⎢⎣
2⎤
(−5 + 2) ⎥⎥⎦
2
⎡
−5 − ⎢1+
⎢⎣
(−5 + 2) ⎥⎥⎦
2
⎡
−5 − ⎢1+
⎣
2⎤
(−3)
2⎤
−5 − ⎡⎣1+ 9 ⎤⎦
−5 − ⎡⎣10 ⎤⎦
2
−5 −100
−105
⎥
⎦
2
2
Page 4
7.
Identify the place value of the digit 4 in each whole number.
(3 points)
a)
2,473,677 b)
241,236,097 c)
1,284
hundred thousands
ten millions
ones
8.
Find the value of each expression.
a)
6 −13 b)
−4 + ( −7 ) c)
−9 − ( −2 )
6 + ( −13)
−7
−11 −9 + 2
−7
d)
−5 − 5 e)
−8 + 3 f)
−8 +10
−5 + ( −5 )
−10
−5 2
9.
Simplify each expression by combining like terms.
a)
(12 points)
5a − 3b −11a − 2b + 3 b)
(6 points)
3( −r − 2q ) − 2 ( 2q − 3r )
3( −r − 2q ) − 2 ( 2q − 3r )
5a − 3b −11a − 2b + 3
5a + ( −3b ) + ( −11a ) + ( −2b ) + 3
5a + ( −11a ) + ( −3b ) + ( −2b ) + 3 −6a + ( −5b ) + 3
−6a − 5b + 3
3( −r − 2q ) + ( −2 ) ( 2q − 3r )
3( −r ) + 3( −2q ) + ( −2 ) ( 2q ) + ( −2 ) ( −3r )
(−3r ) + (−6q) + (−4q) + (6r )
(−3r ) + (−10q) + (6r )
(−3r ) + (6r ) + (−10q)
( 3r ) + (−10q)
3r −10q
Page 5
10.
Fill in the blank with < or > to make the statement true.
(6 points)
a)
−33 ____ − 27 b)
−17 ____ − 20 c)
23 ____ 21
−33 < − 27 −17 > − 20 23 > 21
11.
Use the rule for the order of operations to simplify the expressions.
a)
−2 4 − 8 + 8 b)
−2 4 − 8 + 8
−2 ( −4 ) + 8
−8 + 8
0
c)
( −4 ) − − 6 − 7
( −4 ) − − 6 − 7
2
( −4 ) − −13
2
( −4 ) − ( −13)
2
16 − ( −13)
16 +13
29
40 ÷ 2 ( 5 )
20 ( 5 )
100
d)
2
5 64 ÷ 2 25
5 64 ÷ 2 25
5 (8) ÷ 2 (5)
−2 − 4 + 8
(12 points)
−5
⎞
⎠
2
15 + ⎛⎝ 9 − − 5
⎞
⎠
2
15 + ⎛⎝ 9 −
15 + ( 9 − 5 )
2
15 + ( 4 )
2
15 +16
31
Page 6
12.
Evaluate each expression.
a)
(6 points)
− 10 + ( −5 ) b)
− 10 + ( −5 )
7 − 22
c)
− ( −2 ) + −14
7 − 22
− (10 ) + ( −5 ) −15
−15
a)
−2x + 4y −1 −2x + 4y −1
−2 ( −2 ) + 4 ( 3) −1
4 + 4 ( 3) −1 4 +12 −1
16 −1
15
c)
−x 2 y2 d)
b)
− ( 4 )(9)
(−4 )(9)
−36
2
−5x 3y
−5 ( −2 ) ( 3)
−5 ( −8 ) ( 3)
( 40 )( 3)
120
3
− ( −2 ) ( 3)
(12 points)
−5x 3y
−x 2 y2
2
(2) + (14 )
16
15
13.
Evaluate each expression where x = −2 and y = 3 .
− ( −2 ) + −14
2y
4−x
2y
4−x
2 ( 3)
4 − ( −2 )
6
4+2
6
6
1