Florida Gateway College Mathematics Department
MGF 1100 Final Exam Review
Formulas and Conversions:
mi
1.6 km,
12 in
ft,
ft
in
2.54 cm,
yd, 5280 ft
kg
2.2 lbs,
mi,
yd
fl oz
c,
0.9 m,
ft
pt,
9
5
C + 32, C = (F 32)
5
9
30.48 cm,
pts
qt,
qt
gal, 16 oz
lb.
PART 1: Free Response. NO Calculators Allowed.
Write the fraction as a decimal. If necessary, use repeating decimal notation.
19
1) 20
2)
13
15
Write the percent as a decimal.
3) 600%
4) 0.8%
Write the percent as a fraction or mixed number in simplest form.
1
5) 9 %
4
6) 8.5%
Write the decimal as a percent.
7) 0.4056
Write the fraction or mixed number as a percent.
33
8)
4
Solve. If necessary, round percents to the nearest tenth, dollar amounts to the nearest cent, and all other numbers to the
nearest whole.
9) In a recent survey of 500 people, 20 said that their favorite color of car was black. What percent of the people
surveyed liked black cars?
10) Ben is taking Ellie out to dinner. He has $84.00 to spend. He wants to tip the server 20% of the cost of the meal.
How much can he spend on the meal?
11) The enrollment at a local college decreased by 13% over last year's enrollment of 3000. Find the current
enrollment.
201610-MGF 1100 Final Exam Review-1
12) A watch has a purchase price of $16. If the sales tax on this purchase is $1.52, find the sales tax rate.
Simplify using order of operations.
13) 4(8 - 10)2 - 3(1 - 3)3
14) -9 + (5 · 4 + 20) ÷ 5
15)
[81 ÷ (-9) + 1]
[2 - (-2)]
16)
16(-1) - (-5) (-5)
2 [-8 ÷ (-2 - 2)]
PART 2: Multiple Choice. Circle the best answer to each problem. Scientific
Calculators Allowed.
17) A school has just purchased new computer equipment for $25,000.00. Write a linear equation in slope-intercept
form that models the value of the equipment, y, x years after purchase. Use the model to predict the value of the
equipment after 2 years.
A) y = - 5000x + 25,000;
value after 2 years is $15,000.00;
C) y = 25,000x + 5;
value after 2 years is $15,000.00
B) y = 5000x - 25,000;
value after 2 years is $15,000.00
D) y = - 25,000x + 25,000;
value after 2 years is $-25,000.00
List all the elements of set B that are of the indicated type.
0
18) B = 19, 5, -13, 0, , 4
4
Natural numbers
B) 19, 0,
A) 19, 0
19) B = 8,
8, -15, 0,
0
,
2
0
3
16
4
D) 19, 0,
16
Integers
A) 8, 0,
C) 19,
B) 8, -15, 0,
0
,
2
16
C) 8, -15, 0
201610-MGF 1100 Final Exam Review-2
D) 8, 0
4
Evaluate the expression for x = -2, y = 3, and a = -4.
20) 4x2 - 9y -a
A) -7
21)
B) -10
C) -9
D) -13
y + 3x
y - 2a
A) -
1
5
Simplify the expression.
22) 8x - 3 + 4x - 3
A) 6x
B) -
3
11
C) -
5
11
D) -
2
11
B) 4x - 6
C) 12x - 6
D) 6
23) 9b + 4a + 5c + 2b - 9a
A) -5a + 11b + 5c
B) 11a - 5b + 5c
C) 13a + 11b + 5c
D) -5a + 11b
24) -5(x + 1) + 8x
A) -13x - 5
B) 3x + 5
C) 3x - 5
D) 13x + 5
25) -(4wx - 7) + 6(3wx + 8)
A) 22wx + 1
B) 22wx + 15
C) -14wx + 41
D) 14wx + 55
26) 22 2 - 7 2
A) 29 2
B) 30
C) 15 2
D) 15
27) 4 10 + 5 10 + 2 10 + 11
A) 11 10 + 11
B) 11 21
C) 22 10
D) 32
Write the English phrase as an algebraic expression. Let x represent the number.
28) 7 more than 3 times a number
A) 3x + 7
B) 10x
C) 3(7 + x)
29) 45 less than a number
A) x + 45
B) 45
30) 19 decreased by 4 times the sum of 2 and a number
A) 19 - [-4(2 + x)]
B) 19 - [-4(2 + x)]
Solve and check the equation.
31) 7y - 2 = -8 + 5y
1
A) 3
32) 4(3x - 2) + 2(2x + 2) = 3x - 56
A) {-8}
B) -
6
5
B) {-4}
D) 7x + 3
C) 45 - x
D) 45x
C) 19 - [4(2 + x)]
D) 19 - [4(2 + x)]
C) - 3
D)
C) {-10}
D) {1}
201610-MGF 1100 Final Exam Review-3
1
3
Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set.
33) -8x - 42 + 2(4x + 23) = 0
A) Contradiction;
B) Conditional; {4}
C) Conditional; {1}
D) Identity; {all real numbers}
34) 5(4x - 4) - 20x + 20 = 0
A) Identity; {all real numbers}
C) Contradiction;
B) Conditional; {0}
D) Conditional; {4}
35) 3(28x + 16) = 12(5x + 12)
A) Identity; {all real numbers}
C) Contradiction;
B) Conditional; {4}
D) Conditional; {-8}
Find the indicated function value.
36) Find f(1) when f(x) = x2 + 5x + 3.
A) -1
37) Find f(-1) when f(x) =
B) 3
C) 9
1
8
C) -
D) -7
x2 - 2
.
x3 + 7x
A) 1
B)
Decide whether the relation is a function.
38) {(-3, -5), (-1, 2), (2, -9), (2, 6)}
A) function
39) {(-4, -6), (-3, -8), (3, 3), (7, -5)}
A) function
1
6
D) -
1
8
B) not a function
B) not a function
Calculate the slope of the line passing through the given points. If the slope is undefined, so state. Then indicate whether
the line rises, falls, is horizontal, or is vertical.
40) (-2, -4), (4, 5)
1
3
3
2
A) , rises
B) , rises
C) - , falls
D) , rises
2
2
2
3
41) (-7, -9), (-2, -9)
A) 0, is horizontal
C) -
B) 2, rises
18
, falls
5
42) (9, 6), (8, 9)
15
, rises
A)
17
43) (1, 8), (1, 6)
A) 0, is horizontal
C) 1, rises
D) undefined, is vertical
B) 3, rises
C) - 3, falls
B) undefined, is vertical
D) 7, rises
201610-MGF 1100 Final Exam Review-4
D) -
1
, falls
3
Find the slope and the y-intercept of the line.
7
44) y = - x - 2
5
A) m = - 2; b = -
7
5
45) 3x + 5y = -34
3
34
A) m = - ; b = 5
5
7
; b=- 2
5
C) m =
7
; b=2
5
D) m = -
5
; b=2
7
3
34
; b=5
5
C) m =
5
34
; b=
3
5
D) m = -
3
34
; b=
5
5
B) m = -
B) m =
Plot the point in the rectangular coordinate system.
46) (1, 4)
A)
C)
B)
D)
201610-MGF 1100 Final Exam Review-5
47) (-5, 4)
A)
B)
C)
D)
Use the graph to find the indicated function value.
48) y = f(x). Find f(-5)
A) 5
B) 2
C) -5
201610-MGF 1100 Final Exam Review-6
D) 17
49) y = f(x). Find f(3)
A) 1
B) -7
C) 5
D) 7
Use the theoretical probability formula to solve the problem. Express the probability as a fraction reduced to lowest
terms.
50) A die is rolled. The set of equally likely outcomes is {1, 2, 3, 4, 5, 6}. Find the probability of getting a 6.
1
A) 1
B) 6
C)
D) 0
6
51) You are dealt one card from a standard 52-card deck. Find the probability of being dealt a picture card.
3
3
3
1
A)
B)
C)
D)
52
13
26
13
52) You are dealt one card from a standard 52-card deck. Find the probability of being dealt an ace or a 7.
4
13
2
A)
B)
C) 8
D)
13
2
13
53) Use the spinner below to answer the question. Assume that it is equally probable that the pointer will land on
any one of the five numbered spaces. If the pointer lands on a borderline, spin again. Find the probability that
the arrow will land on 3 or 4.
A)
4
3
B) 1
C)
2
5
201610-MGF 1100 Final Exam Review-7
D) 3
54) Use the spinner below to answer the question. Assume that it is equally probable that the pointer will land on
any one of the five numbered spaces. If the pointer lands on a borderline, spin again. Find the probability that
the arrow will land on an odd number.
A) 0
B) 1
C)
3
5
D)
2
5
Use the empirical probability formula to solve the exercise. Express the answer as a fraction. Then express the probability
as a decimal, rounded to the nearest thousandth, if necessary.
55) In 1999 the stock market took big swings up and down. A survey of 991 adult investors asked how often they
tracked their portfolio. The table shows the investor responses. What is the probability that an adult investor
tracks his or her portfolio daily?
How frequently?
Response
Daily
236
Weekly
284
Monthly
277
Couple times a year 137
Don't track
57
277
137
236
284
; 0.28
; 0.138
; 0.238
; 0.287
A)
B)
C)
D)
991
991
991
991
The chart below shows the percentage of people in a questionnaire who bought or leased the listed car models and were
very satisfied with the experience.
Model A
Model B
Model C
Model D
Model E
Model F
81%
79%
73%
61%
59%
57%
56) With which model was the greatest percentage satisfied? Estimate the empirical probability that a person with
this model is very satisfied with the experience. Express the answer as a fraction with a denominator of 100.
81
57
0.57
0.81
A) Model A;
B) Model F;
C) Model F;
D) Model A:
100
100
100
100
The exercise presents numerical information. Describe the population whose properties are analyzed by the data.
57) During 2001, there were 574 crimes in a certain city per 100,000 residents.
A) criminals in the city
B) criminals in the country
C) residents of the city
D) residents of the country
201610-MGF 1100 Final Exam Review-8
Solve the problem.
58) The city council of a small town needs to determine if the town's residents will support the building of a new
library. The council decides to conduct a survey of a sample of the town's residents. Which one of the following
procedures would be most appropriate for obtaining a sample of the town's residents?
A) Survey every 14th person who enters the old library on a given day.
B) Survey 400 individuals who are randomly selected from a list of all people living in the state in which the
town is located.
C) Survey a random sample of librarians who live in the town.
D) Survey a random sample of persons within each neighborhood of the town.
This double-bar graph shows the number of male (M) and female (F) athletes at a university over a four-year period.
Answer the question.
YEAR
59) What percentage of all students involved in athletics in 1986 was female? (Round to the nearest percent.)
A) 57%
B) 14%
C) 75%
D) 43%
60) What is the only year in which the number of female athletes declined from its previous value?
A) 1986
B) 1988
C) 1989
D) 1987
61) Which year had the smallest number of male athletes?
A) 1987
B) 1989
C) 1988
Determine which scatterplot shows the strongest linear correlation.
62) Which shows the strongest linear correlation?
A)
B)
Convert the given measurement to the unit indicated.
63) 10 ft to in.
A) 40 in.
B) 30 in.
64) 18 in. to yd
A) 108 yd
B) 0.50 yd
D) 1986
C)
C) 360 in.
D) 120 in.
C) 324 yd
D) 0.25 yd
201610-MGF 1100 Final Exam Review-9
Convert the measurement as indicated.
65) 26,400 ft to miles
A) 5 mi
B) 6 mi
C) 5.5 mi
D) 132 mi
66) 70.09 mm to m
A) 0.07009 m
B) 0.701 m
C) 7009 m
D) 70,090 m
67) 0.443 dam to cm
A) 44.3 cm
B) 443 cm
C) 4.43 cm
D) 4430 cm
68) 56 kg to g
A) 5600 g
B) 0.56 g
C) 56,000 g
D) 0.056 g
69) 0.084 mg to g
A) 0.0084 g
B) 0.000084 g
C) 0.00084 g
D) 84 g
70) 655 mi to km
A) 2.4 km
B) 409.4 km
C) 0.001 km
D) 1048.0 km
71) 9 m to ft
A) 29.5 ft
B) 8.1 ft
C) 10.0 ft
D) 2.7 ft
B) 93 oz
C) 92 oz
D) 112 oz
C) 8.3 lb
D) 11.6 lb
72) 5
3
lb to ounces
4
A) 62 oz
73) 116 oz to the nearest tenth of a pound, if necessary
A) 7.3 lb
B) 17.3 lb
74) 11 c to pints
3
A) 2 pt
4
75) 44 c to gallons
3
A) 2 gal
4
76) 4
B) 5
1
pt
2
C) 44 pt
D) 22 pt
B) 5
1
gal
2
C) 11 gal
D) 1
C) 38 fl oz
D) 152 fl oz
3
gal
8
3
qt to fluid ounces
4
A) 76 fl oz
B) 304 fl oz
201610-MGF 1100 Final Exam Review-10
Find the measure of angle A for the triangle shown.
77)
38°
100°
A) 222°
B) 52°
C) 10°
D) 42°
B) 78°
C) 88°
D) 168°
78)
12°
A) 90°
PART 3: Free Response. Please justify all answers with work below each
problem. Scientific Calculators Allowed.
Solve the equation.
x x
79) - = 6
5 8
80)
x+6
13 x - 2
=
2
4
4
81)
1
1
(x + 6) - (x - 9) = x - 6
3
9
Solve the problem.
82) Jill is 10 kilometers away from Joe. Both begin to walk toward each other at the same time. Jill walks at 2
kilometers per hour. They meet in 2 hours. How fast is Joe walking?
83) Tom Quig traveled 270 miles east of St. Louis. For most of the trip he averaged 60 mph, but for one period of
time he was slowed to 10 mph due to a major accident. If the total time of travel was 7 hours, how many miles
did he drive at the reduced speed?
Write an equation for the line described. Give your answer in slope-intercept form.
84) m = -8, through (-4, 9)
85) through (-7, -2) and (0, 2)
201610-MGF 1100 Final Exam Review-11
In the following problems:
a. Put the equation in slope-intercept form.
b. Identify the slope and y-intercept.
c. Graph the line.
86) 3x + 8y = 24
87) 6x + y = 6
Construct the specified histogram.
88) The frequency table below shows the number of days off in a given year for 30 police detectives.
Days off Frequency
0- 1
10
2 -3
1
4-5
7
6-7
7
8-9
1
10 -11
4
Construct a histogram.
201610-MGF 1100 Final Exam Review-12
89) In a survey, 20 voters were asked their age. The results are summarized in the frequency table below. Construct a
histogram .
Age of Number of
voters
voters
20-29
5
30-39
5
40-49
6
50-59
0
60-69
4
A set of data points is given together with the equation of the regression line.
a. Create a Scatter Plot of the Data
b. Draw an approximate trend (best fit) line on the scatter plot.
c. Determine an approximate equation of best fit.
x
1
3
5
7
9
90)
y
73
46
30
28
20
91) x 10 14 20 6 6 14 16 24 32 36
y 19 23 29 12 17 23 25 33 37 45
201610-MGF 1100 Final Exam Review-13
In a school survey, students showed these preferences for instructional materials. Answer the question.
92) About how many students would you expect to prefer lectures in a school of 1000 students?
93) About how many students would you expect to prefer films in a school of 850 students?
94) 355°C to degrees Fahrenheit
95) 32°C degrees Fahrenheit
96) 563°F to degree Celsius
97) 93°F to degrees Celsius
Solve.
98) The two sticks used to make a kite have lengths of 1.2 m and 54 cm. What total length of wood must be ordered
for the sticks if 28 kites are to be built?
99) The total pages of a hardbound book are 3 cm thick. The front and back covers are each 1.6 mm thick. How high
would a stack of 9 of these books be?
Find the measure of x.
100)
63°
140°
101)
116°
14°
201610-MGF 1100 Final Exam Review-14
Answer Key
Testname: MGF 1100 EXAM REVIEW FALL 2015
1) -0.95
2) 0.86
3) 6
4) 0.008
37
5)
400
6)
17
200
7) 40.56%
8) 825%
9) 4%
10) $70.00
11) 2610 students
12) 9.5%
13) 40
14) -1
15) -2
16) -10.25
17) A
18) C
19) B
20) A
21) B
22) C
23) A
24) C
25) D
26) C
27) A
28) A
29) C
30) D
31) C
32) B
33) A
34) A
35) B
36) C
37) B
38) B
39) A
40) B
41) A
42) C
43) B
44) B
45) A
46) B
47) A
48) A
49) D
50) C
51) B
52) D
53) C
54) C
55) C
56) A
57) C
58) D
59) D
60) C
61) D
62) C
63) D
64) B
65) A
66) A
67) B
68) C
69) B
70) D
71) A
72) C
73) A
74) B
75) A
76) D
77) D
78) B
79) 80
80) {1}
81
81)
7
82) 3 km/hr
83) 30 mi
84) y = -8x - 23
4
85) y = x + 2
7
201610-MGF 1100 Final Exam Review-15
Answer Key
Testname: MGF 1100 EXAM REVIEW FALL 2015
86) a. y = -
3
x+3
8
b. slope = -
88)
3
, y-intercept = 3
8
c.
89)
87) a. y = -6x + 6
b. slope = -6, y-intercept = 6
c.
90) a. and b.
c. Equation of regression line: y = 70.4 - 6.2x
201610-MGF 1100 Final Exam Review-16
Answer Key
Testname: MGF 1100 EXAM REVIEW FALL 2015
91) a and b.
c. Equation of regression line: y = 9.3 + .95x
92) About 180 students
93) About 170 students
94) 671°F
95) 89.6°F
96) 295°C
97) 33.9°C
98) 48.72 m
99) 29.88 cm
100) 77°
101) 50°
201610-MGF 1100 Final Exam Review-17