MATHEMATICS FOR ELEMENTARY TEACHERS I
FINAL EXAM REVIEW
Find the GCD or LCM as indicated.
1) Given 56 and 96, find the LCM.
Evaluate.
12) Let f(x) = x + 1. Find f(83).
2) Given 208 and 135, find the GCD.
Solve the problem.
13) A group of 9 people wants to buy a boat. The
boat costs $414. If they all pay the same
amount, how much is each person's share?
Find the LCM for the given numbers by an appropriate
method.
3) 45, 56, and 150
14) Tom earned $35 a week for washing cars. How
much has he earned in the last 9 weeks?
Use least common multiple or greatest common divisor to
solve the problem.
4) Rob can complete his bus route in 6 hours.
Joan can complete her bus route in 3 hours. If
they both left the terminal at 3:00 am and after
each completed route returned to the terminal,
determine the next time they would leave the
terminal at the same time.
Evaluate.
15) (6 · 0) ÷ (- 8 · 9)
Compute.
16) -4 2 + 3(- 4)2
Simplify.
17) 5 + 2(5w + 3) - w
5) A brick layer is hired to build three walls of
equal length. He has bricks which are 9 inches,
27 inches, and 15 inches long. He plans to build
one wall out of each type of brick. What is the
shortest length of wall possible?
Provide the proper response. Show all fractions in
simplest form.
18) Write a fraction to represent the shaded
portion of the figure.
Compute or simplify as much as possible.
6) (-13) - (- 3)
7) 8 - (3 - 2x)
Add.
8) 3 + -9
9) - 5 + - 8
19) Write a fraction to represent the shaded
portion of the figure.
Write as an addition problem and find the sum.
10) Jack's checking account was overdrawn by $95.
He deposited $44 into his account. What is the
balance in his account?
Write the fraction in simplest form.
18xy2
20)
45x2 y
Perform the indicated computation.
11) - 14 - (20 + 17)
1
Find the requested fraction.
-9
?
=
21)
16 96
Solve the problem. Express your answer in simplest form.
2
31) The second tallest child in a class is 36 inches
3
tall. The tallest child is 3
Determine whether the fractions are equal.
1
19
22) and
7
133
tall is the tallest child in the class?
Find the product. Write your answer in simplest form.
15
4
·4
32) 2
31
5
Answer the question. Give your answer in simplest form.
23) For lunch, Jamie bought a 8-inch submarine
sandwich. What fraction of a foot was Jamie's
sandwich? (1 foot = 12 inches)
Solve for x in the following.
2
7 17
33) x - =
5
5
2
24) A teacher bought a package of 48 markers for
her first-grade class. After one school year, 5
markers were still working. What fraction of
the package of markers was working? Express
the result using a simple, convenient fraction
that is close in value to the exact answer.
Solve the problem.
34) A recipe calls for
2
cup of milk. How much
5
milk should be used to make
Arrange the fractions in ascending order. Or, if the
fractions are equivalent, answer "Equivalent".
5 10
,
25)
36 12
1
of the recipe?
2
Write the following in simplest form using positive
exponents.
35) 5 5 · 5 3
Perform the indicated operation. Express your answer in
simplest form.
5
1
26)
12 7
27)
11
inches taller. How
12
36) 7 8 ÷ 7 4
Solve for n in the following.
37) n 2 = 9
9
1
+
13 7
Write the following as a sum using powers of 10 to show
place value.
38) 540.81
Change the following fraction to a mixed number.
19
28)
3
Rewrite as a numeral.
39) Two thousand and twenty-five
hundred-thousandths
Change the following mixed number to a fraction in the
a
form , where a and b are integers and b 0.
b
Write the terminating decimal as
3
29) 4
5
where a, b I and b 0.
40) 6.95
Choose the best estimate from the list.
11
21
1
2
+ 10
is approximately 13, 13 , 13 , 14.
30) 3
32
62
3
3
2
a
in simplest form
b
54) 503 to base five
Mentally determine if the number can be written as a
terminating decimal
2
41)
34
Write the numeral in base ten.
55) 436eight
Order the decimals from least to greatest.
42) 2.854, 2.548, 2.584, 2.458
Provide an appropriate response.
56) Write the base-four numeral for the base-four
blocks shown.
Rewrite the number or expression as requested.
43) 32,000,000,000 (Rewrite in scientific notation.)
Round the number as specified.
44) 4.479 to the nearest hundredth
Find the Cartesian product or cardinal number as
requested.
57) A = {i, a}
B = {t, d, m}
Find A × B.
Write the fraction in decimal notation.
3
45)
7
Convert the repeating decimal to a fraction.
46) 0.67
58) n(A) = 2
n(B) = 5
n(C) = 3
n(A × B × C) = ?
Rewrite the following as indicated.
1
(Write as a percent.)
47)
15
Shade the portion of the diagram that represents the given
set.
Find the simple interest and the final value of the deposit
that earns the given rate for the indicated length of time.
Round your answers to the nearest cent.
48) $45,469 earning 12.9% for 21 months
59) A B
For the following, write an equivalent numeral in the
Hindu-Arabic system.
49) MCMLXVI
Use set notation to identify the shaded region.
60)
For the given Hindu-Arabic numeral, write an equivalent
numeral in the indicated system.
50) 3063; Egyptian
Write the place value of the underlined numeral.
51) 210,152
Write the following as a base-ten numeral.
52) 6 · 103 + 8 · 102 + 4
Convert the base-ten number to a number in the indicated
base.
53) 329 to base six
3
Use sets to solve the problem.
61) The circles in the Venn diagram represent
customers who prefer products A, B, and C,
respectively. Which of the regions numbered
one through eight describe customers who
prefer Products A or C?
Fill in the missing numbers.
73)
() 3 4
4 5
×
74)
2
7
1 ()
3 6
0
0
()
9
5
0
3
36
a 147
- 12
27
- 24
3
Rewrite the subtraction problem as an equivalent addition
problem.
62) 85 - x = 51
Find the solutions in the set W.
63) 2 + (6 + 3) = (x + 6) + 3
Solve the problem.
75) An elementary school has 14 classrooms, each
of which can take 28 children. How many
children can the school accept for admission?
Find, if possible, the whole number that makes the
equation true.
=2·
+
·7
64) (2 + 7) ·
65)
2
Estimate the following mentally.
76) 92 + 246 + 254 + 108
÷ 0 = undefined
Provide an appropriate response.
77) Pam uses front-end estimation and adds 345,
211, 418 as 900 + (50 + 10 + 20) to get the
answer 980. Pat rounds up the numbers and
adds 350 + 200 + 400 to get 950. Who has the
better answer?
State the property that is illustrated.
66) 1(15 · 11) = 15 · 11
67) 2 · 11 = 11 · 2
Round the number to the place value indicated.
78) 265,945
68) (4 + 6)(9 + 15) = (4 + 6)9 + (4 + 6)15
69) 3(6 · 5) = (3 · 6)5
Estimate by rounding.
79) 804 ÷ 18
Find the solution.
70) (x - 7) ÷ 5 = 9
80) 122 · 5859
71) 4(x + 4) = 28
Estimate the answer to the problem.
81) A mobile library has 1029 books in its
collection. If there are 21 shelves in the library,
then how many books, on average, are stacked
on each shelf?
Solve the problem.
72) 3 times Gail's salary is equal to 6 times Nancy's
salary. If Gail's salary is $28,200, what is
Nancy's salary?
Determine all possible digits to place in the square that
make the statement true. If none exist, state this.
82) 4,3 6 is divisible by 4.
4
Compute.
83) 74,3 2 is divisible by 6.
97) -2 2
Solve the problem.
84) A group of teachers order markers for their
classrooms. The bill was $3.91. If the original
price per marker was 17¢ and the price has
risen, how much does each marker cost now?
Simplify.
98) 3 + 4(5w + 2) - w
Factor the expression, then simplify if possible.
99) 6xy + 10x - xz
Provide the appropriate response.
85) There is a number that has 2, 5, and 8 as
divisors. This number has exactly seven
additional divisors. What is the number?
100) x2 - 36y2
Find the prime factorization.
86) 1606
Find the GCD or LCM as indicated.
87) Given 48, 162, and 9, find the LCM.
88) Given 21, 24, and 27 , find the GCD.
Find the GCD for the given numbers by an appropriate
method.
89) 1296 and 1944
Write as an addition problem and find the sum.
90) Jack's checking account was overdrawn by $59.
He deposited $17 into his account. What is the
balance in his account?
Perform the indicated computation.
91) - 10 + [(- 9) - (- 13)]
Evaluate.
92) Let f(x) = - x - 1. Find f(60).
93) Let f(x) = 11 - x . Find f(80).
Solve the problem.
94) Ajay averages 20 miles per gallon of gasoline
in his car. How far can he travel on 17 gallons
of gasoline?
Evaluate.
95) (-30 - - 21) ÷ 3
96) - 36 ÷ (3 - 12)
5
Answer Key
Testname: FINAL EXAM REVIEWSPR2015
1)
2)
3)
4)
5)
672
1
12,600
9:00 am
135 inches
6) -10
7) 5 + 2x
8) - 6
32) 11
9) - 13
10) - $95 + $44 = - $51
11) - 51
84
$46
$315
0
32
9w + 11
2
18)
5
48) $10,264.63; $55,733.63
49) 1966
50)
51) Hundred thousands
52) 6804
53) 1305six
54) 4003five
55) 286
56) 213four
57) {(i, t), (i, d), (i, m), (a, t), (a, d), (a, m)}
58) 30
59)
23
26)
84
27)
76
91
28) 6
29)
1
58
2
47) 6 %
3
22) Yes
2
23) ft
3
5 10
,
36 12
35)
45) 0.428571
67
46)
99
96
25)
1
cup
5
44) 4.48
- 54
1
10
34)
41) No
42) 2.458, 2.548, 2.584, 2.854
43) 3.2 · 1010
2y
5x
24)
99
4
39) 2000.00025
139
40)
20
3
19)
8
21)
33)
36) 7 12
37) 3 or 3
38) 5 · 102 + 4 · 101 + 0 · 100 + 8 · 10-1 + 1 · 10-2
12)
13)
14)
15)
16)
17)
20)
143
155
1
3
23
5
30) 13
2
3
60)
61)
62)
63)
64)
7
in.
31) 40
12
6
B A
1,2,4,5,6,7
x + 51 = 85
2
Any whole number
Answer Key
Testname: FINAL EXAM REVIEWSPR2015
65)
66)
67)
68)
69)
70)
71)
72)
73)
Any whole number
identity property of multiplication
commutative property of multiplication
distributive property of multiplication over addition
associative property of multiplication
52
3
$14,100
(4)
3
4
4
5
1
3
(7)
6
0
0
×
1
74)
75)
76)
77)
78)
79)
80)
81)
82)
83)
84)
85)
86)
87)
88)
89)
90)
2
7
(1) 9 5
3
0
a=4
392
700
Pam, as her adjustments to the actual numbers are
much closer.
270,000
40
600,000
50
1, 3, 5, 7, 9
2, 5, 8
23¢
80
2 · 11 · 73
1296
3
648
- $59 + $17 = - $42
91) - 6
92) - 61
93) 69
94) 340 miles
95) - 3
96) - 4
97) - 4
98) 19w + 11
99) x(6y + 10 - z)
100) (x + 6y)(x - 6y)
7