MTH 157 – Math For Elementary Teachers II
Week #9 Final Cumulative Test
Chapters 8 - 13
Name:
Score: x/250 (p%)
Please show your work or justify your answer. Work or justification must
be shown for full credit, including multiple choice questions.
Multiple choice questions: The correct answer may not be among the
listed answers. Always be sure to check your work. If you are certain of
your answer, you may write your answer in the work area.
Be sure to use the Equation editor as needed.
Each question is worth 5 points.
1. A medical research team studied the ages of patients who had strokes caused
by stress. The ages of 34 patients who suffered stress strokes were as follows.
29 30 36 41 45 50 57 61 28 50 36 58 60 38 36 47 40 32 58 46 61 40
55 32 61 56 45 46 62 36 38 40 50 27
Construct a Frequency table for these ages. Group the data into 8 equal
intervals starting with the interval 25-29.
Age
25 – 29
30-- 34
35--39
40--44
45--49
50--54
55--59
60—64
Frequency
Relative Frequency
3
3/34
3
3/34
6
6/34
4
4/34
5
5/34
3
3/34
5
5/34
5
5/34
Instructor’s comments
2. The weights (in pounds) of a group of high school students are listed below in a
stem-and-leaf plot.
What is the difference between the lowest and highest weights?
MTH 157 Week #9 Final Cumulative Test
MTH 157 – Math For Elementary Teachers II
Week #9 Final Cumulative Test
Chapters 8 - 13
a) 60
b) 61
c) 53
d) 98
Answer:
b
Work or justification:
Lowest weight is 98, highest weight is 159 so the difference is 159-98=61
Instructor’s comments
3. Use the high closing values of Naristar Inc. stock from the years 1990 - 2001 to
construct a line graph. (Let x = 0 stand for 1990 and so on...)
Year
1990
1991
1992
1993
1994
1995
High
42
40
31
42
44
47
Year
1996
1997
1998
1999
2000
2001
High
47
60
61
57
54
30
Create a Line graph to illustrate the data. Identify a trend.
Naristar Stock
70
H
I
G
H
C
L
O
S
I
N
G
60
50
40
30
20
10
0
1
2
3
4
5
6
7
8
9
10
11
12
YEAR
Values are decreasing between 1990 and 1992 , after that there is appositive trend
but at the end values are lower. So there is no trend
MTH 157 Week #9 Final Cumulative Test
MTH 157 – Math For Elementary Teachers II
Week #9 Final Cumulative Test
Chapters 8 - 13
Instructor’s comments
4. What type of correlation is there for the data shown in the scatterplot below?
a) Positive
Correlation
b) Negative
Correlation
c) No
Correlation
Answer:
C
Work or justification:
We don´t see any relation between variables
Instructor’s comments
5. Bill kept track of the number of hours he spent exercising each week. The
results for 15 weeks are shown below.
7.2
8.0
8.5
6.8
6.8
6.8
7.2
8.1
8.0
7.5
8.5
8.9
7.9
7.5
7.9
Find the midrange.
a) 7.65
b) 7.85
c) 2.1
d) 7.9
Answer:
b
Work or justification:
Midrange= (Max+Min)/2=(8.9+6.8)/2=7.85
MTH 157 Week #9 Final Cumulative Test
MTH 157 – Math For Elementary Teachers II
Week #9 Final Cumulative Test
Chapters 8 - 13
Instructor’s comments
6. A gymnast needs to score an average of 8.4 in order for her team to win the
competition. Her score was 9.7 on her uneven bars, 7.8 on the floor exercise, and
8.8 on the vault. What must her score be on the balance beam for her team to
win?
a) 8.8
b) 8.3
c) 7.3
d) 8.4
Answer:
c
Work or justification:
Let x=score on the balance beam
(9.7+7.8+8.8+x)/4=8.4
26.3+x=8.4*4=33.6
x= 33.6-26.3=7.3
Instructor’s comments
7. Identify the misuse or misrepresentation of statistics:
60% of those attending the folk festival said that they prefer to buy organic food. So, most
Americans prefer to buy organic food.
We can´t say that most American prefer to buy organic food because
the sample was not representative.
Instructor’s comments
8. An 8-sided die is rolled. The sides contain the numbers 1, 2, 3, 4, 5, 6, 7, 8.
List the sample space of rolling one die.
a) {64}
c) {8}
b) {1, 2, 3, 4, 5, 6, 7, 8}
d) None of these
Answer:
b
Work or justification:
S={1, 2, 3, 4, 5, 6, 7, 8}
MTH 157 Week #9 Final Cumulative Test
MTH 157 – Math For Elementary Teachers II
Week #9 Final Cumulative Test
Chapters 8 - 13
Instructor’s comments
9. Consider the experiment of selecting a card from an ordinary deck of 52 playing
cards. Determine the probability that a face card or a 4 is drawn.
a)
5
13
b)
1
13
c)
4
13
d) 0
Answer:
c
Work or justification:
There are 12 face cards and 4 fours so favorable cases are 12+4=16
P(face card or4)=16/52=4/13
Instructor’s comments
10. A lumber company sells shelves. A customer can choose from 5 types of
wood, 4 different widths, and 4 different lengths. How many different types of
shelves are available?
a) 13 types
b) 100 types c) 80 types
d) 36 types
Answer:
c
Work or justification:
5*4*4=80
Instructor’s comments
11. A bag contains seven blue marbles and five red marbles. One marble is
drawn at random without replacement, and then a second marble is drawn. What
is the probability that the second marble is blue if the first marble was blue?
a)
7
11
b)
6
11
c)
7
12
d)
1
2
Answer:
b
Work or justification:
If the first marble was blue total number of cases are 7+5-1=11
And there are 7-1=6 blue marbles available
So P(2nd blue/1st blue)=6/11
Instructor’s comments
MTH 157 Week #9 Final Cumulative Test
MTH 157 – Math For Elementary Teachers II
Week #9 Final Cumulative Test
Chapters 8 - 13
12. A bag contains 13 balls numbered 1 through 13. What are the odds in favor
of selecting a ball that has an even number?
a) 13 : – 7
b) 6 : 13
c) 2 : 11 d) 6 : 7
Answer:
d
Work or justification:
There are 6 even numbers so P(even)=6/(6+7) then odds are 6:7
Instructor’s comments
13. Suppose you pay $ 3.00 to roll a fair die with the understanding that you will
get back $ 5.00 for rolling a 1 or a 2, nothing otherwise. What is your expected
value?
a) –$ 1.33
b) $ 3.00
c) $ 5.00 d) –$ 3.00
Answer:
a
Work or justification:
Expected value is -3(4/6)+2(2/6)=-12/6+4/6=-8/6=-4/3=-1.33
Instructor’s comments
14. If the odds in favor of an event A are 2 to 4, what is the probability
associated with event A occurring?
a)
2
3
b)
3
2
c) 3
d)
1
3
Answer:
D
Work or justification:
2/(2+4)=2/6=1/3
Instructor’s comments
15. Assume that a researcher randomly selects 14 newborn babies and counts
the number of girls selected, x. The probabilities corresponding to the 14 possible
values of x are summarized in the given table.
MTH 157 Week #9 Final Cumulative Test
MTH 157 – Math For Elementary Teachers II
Week #9 Final Cumulative Test
Chapters 8 - 13
Find the probability of selecting exactly 4 girls.
a) 0.061
b) 0.022
c) 0.122
d) 0.001
Answer:
a
Work or justification:
Value is in the table at the 5th row
Instructor’s comments
16. How many different ways can a teacher line up 9 students for lunch?
a) 40,320
b) 362,880
c) 9
d) 3,628,800
Answer:
b
Work or justification:
P9=9!=362,880
Instructor’s comments
17. A deli offers its cheese sandwich with various combinations of mayonnaise,
lettuce, tomatoes, pickles, and sprouts. 8 types of cheese are available. How
many different cheese sandwiches are possible?
a) 128
b) 256
c) 512
d) 16
Answer:
a
Work or justification:
Instructor’s comments
MTH 157 Week #9 Final Cumulative Test
MTH 157 – Math For Elementary Teachers II
Week #9 Final Cumulative Test
Chapters 8 - 13
18. Find the area.
Parallelogram ABCD
a) 30
square units
b) 36
square units
c) 15
square units
d) 18
square units
Answer:
a
Work or justification:
Instructor’s comments
19. Describe the curve as simple closed, nonsimple closed, or not closed.
a) Simple closed
b) Nonsimple closed
c) Not closed
Answer:
b
Work or justification:
Instructor’s comments
MTH 157 Week #9 Final Cumulative Test
MTH 157 – Math For Elementary Teachers II
Week #9 Final Cumulative Test
Chapters 8 - 13
20. Find a traversable path that begins at vertex A.
a)
b)
c)
d)
A → D → B → A→ C → E → D→ C→ A
A → B → D → E → C →A
A→B→D→C→E→D→A
No such path exists.
Answer:
b
Work or justification:
Instructor’s comments
21. What is the name for the point where the three medians of a triangle are
concurrent?
a)
centroid
b)
orthocenter
c)
circumcenter
d)
incenter
Answer: a
Work or justification:
Instructor’s comments
MTH 157 Week #9 Final Cumulative Test
MTH 157 – Math For Elementary Teachers II
Week #9 Final Cumulative Test
Chapters 8 - 13
22. Identify all pairs of corresponding angles
a)
b)
c)
d)
∠ 4 and ∠ 8, ∠ 5 and ∠ 1, ∠ 3 and ∠ 7, ∠ 6 and ∠ 2
∠ 4 and ∠ 1, ∠ 3 and ∠ 2, ∠ 5 and ∠ 8, ∠ 6 and ∠ 7
∠ 3, ∠ 2, ∠ 7 and ∠ 6
∠ 4 and ∠ 2, ∠ 5 and ∠ 7, ∠ 3 and ∠ 1, ∠ 6 and ∠ 8
Answer:
d
Work or justification:
Instructor’s comments
23. Find the measure of the indicated exterior angle, given that
∠ x = (4n – 20)º
∠ y = (n + 10)º
∠ z = (166 – 6n)º
a) 84º
b) 70º
c) 160º
d) 134º
Answer:
b
Work or justification:
X+y=z
(4n-20)+(n+10)=166-6n
5n-10=166-6n
11n=176
n=176/11=16
z=166-6(16)=166-96=70
MTH 157 Week #9 Final Cumulative Test
MTH 157 – Math For Elementary Teachers II
Week #9 Final Cumulative Test
Chapters 8 - 13
Instructor’s comments
24. Which property (if any) should be used to show that the triangles are
congruent?
a) SAS
b) SSS
c) ASA
d) SSA
Answer:
A
Work or justification:
Instructor’s comments
25. A painter leans a ladder against one wall of a house (as depicted below). The
ladder is 14 ft long. The base of the ladder is 10 ft from the house. How high above
the ground does the ladder touch the wall?
a) 48 ft
b) 12 ft
c) 9.798 ft
d) 4.889ft
Answer:
c
Work or justification:
MTH 157 Week #9 Final Cumulative Test
MTH 157 – Math For Elementary Teachers II
Week #9 Final Cumulative Test
Chapters 8 - 13
Let x the missing side:
10^2+x^2=14^2
100+x^2=196
X^2=96
X=96=9.798
Instructor’s comments
26. Choose the word "rectangle," "square," or "rhombus" to fill in the blank and
make the statement true. (If none of the words can be used, then write "none.")
A quadrilateral is a __square__ if and only if all of its sides are congruent and its
diagonals are congruent.
a) rhombus
b) rectangle
c) square
d) none
Answer:
c
Work or justification:
Instructor’s comments
27. Suppose that a given parallelogram is not a rhombus. Which of the
following can you conclude about this parallelogram?
a)
b)
c)
d)
Its diagonals are perpendicular bisectors of each other.
Its sides are not all congruent.
It is a square.
All of the above
Answer:
B
Work or justification:
Instructor’s comments
MTH 157 Week #9 Final Cumulative Test
MTH 157 – Math For Elementary Teachers II
Week #9 Final Cumulative Test
Chapters 8 - 13
28. Find the image of the figure obtained from the given transformation.
TCD
a)
b)
c)
d)
Answer:
b
Work or justification:
Instructor’s comments
MTH 157 Week #9 Final Cumulative Test
MTH 157 – Math For Elementary Teachers II
Week #9 Final Cumulative Test
Chapters 8 - 13
29. Find the image of the figure obtained from the given transformation.
Mm
a)
b)
c)
d)
Answer:
c
Work or justification:
Instructor’s comments
MTH 157 Week #9 Final Cumulative Test
MTH 157 – Math For Elementary Teachers II
Week #9 Final Cumulative Test
Chapters 8 - 13
30. List the vertex arrangements:
a) 3, 4, 6, 4
c) 3, 4, 3, 6
b) 3, 4, 6, 4 and 3, 4, 4, 6
d) 3, 4, 3, 6 and 3, 4, 6, 4
Answer:
a
Work or justification:
Instructor’s comments
7 
31. Describe the figure or polygon produced by interpreting the symbol   .
3
a) hexagon
c) star polygon
b) heptagon
d) None of these
Answer:
D
Work or justification:
Instructor’s comments
32. Use Euler's formula to answer the question.
A polyhedron has 36 edges and 19 faces. How many vertices does it have?
a) 53
b) 55
c) 19
d) 16
Answer:
c
Work or justification:
V+F=E+2
V+19=36+2
V+19=38
V=19
MTH 157 Week #9 Final Cumulative Test
MTH 157 – Math For Elementary Teachers II
Week #9 Final Cumulative Test
Chapters 8 - 13
Instructor’s comments
33. Indicate the metric unit that would be best used to express the mass of the
object:
A Computer Desk
a) milligrams b) grams
c) kilograms
d) meters
Answer: c
Work or justification:
Instructor’s comments
34. Convert the units:
1008 in2 =
a) 7
b) 8
c) 6
ft2
d) 112
Answer:
A
Answer:
B
Work or justification:
1ft = 12 in
1 ft2 = 144 in2
X ft2= 1008in2
X=1008/144=7
Instructor’s comments
35. Convert the units:
220 g =
a) 22,000
b) 0.22
c) 220,000
d) 0.022
kg
Work or justification:
Instructor’s comments
MTH 157 Week #9 Final Cumulative Test
MTH 157 – Math For Elementary Teachers II
Week #9 Final Cumulative Test
Chapters 8 - 13
36. Complete the following. Round to the nearest tenth:
226 mi =
km
a) 140.3
b) 239.6
c) 363.9
d) 213.8
Answer:
C
Work or justification:
Instructor’s comments
37. Maha checked the outside temperature at noon one day and found it was
27° C. At 10 PM when he checked, the outside temperature was 20° C. How
much, in degrees Fahrenheit, did the temperature drop between noon and 10
PM? Round your answer to the nearest hundredth if necessary.
a) 12.6ºF
b) -9ºF
c) 3.89ºF
d) – 19.4ºF
Answer:
44.6
Answer:
c
Work or justification:
F=(9/5)C+32
Drops 27-20=7C
C=7 then F=(9/5)7+32=12.6+32=44.6 ºF
Instructor’s comments
38. Find the perimeter:
a) 55 m
b) 75 m
c) 110 m
d) 90 m
Work or justification:
P=2(20+35)=110 m
Instructor’s comments
MTH 157 Week #9 Final Cumulative Test
MTH 157 – Math For Elementary Teachers II
Week #9 Final Cumulative Test
Chapters 8 - 13
39. Two corresponding sides of similar polygons are in the ratio of 2 : 7. If the
area of the smaller figure is 8 square meters, what is the area of the larger
figure?
a) 56 m2
b) 98 m2
c) 512 m2
d) 256 m2
Answer:
b
Work or justification:
Instructor’s comments
40. Find the surface area of the solid: Use 3.14 for π.
Hemisphere with radius = 9 m
a) 423.63 m2
c) 1017.36 m2
b) 763.02 m2
d) 508.68 m2
Answer:
b
Work or justification:
Area of the sphere = 4(pi)r2=4(3.14)81=1017.36
Area of the semisphere=1017.36/2=508.68
Area of the circle = r2pi=81*3.14=254.34
Total area = 508.68+254.34=763.02 m2
Instructor’s comments
41. Find the volume. Use 3.14 for π and round to the nearest hundredth, if
necessary. : Use 3.14 for π.
MTH 157 Week #9 Final Cumulative Test
MTH 157 – Math For Elementary Teachers II
Week #9 Final Cumulative Test
Chapters 8 - 13
Right circular cylinder
a) 1061.32 ft3
c) 163.28 ft3
b) 4245.28 ft3
d) 326.56 ft3
Answer:
a
Work or justification:
Instructor’s comments
42. Today the Center City baseball team scored 7 runs. The day before yesterday they
scored x runs. How many runs did they score in these two days?
a) 7x
b) 7 – x
c) 7 + 2x
d) 7 + x
Answer: D
Work or justification:
Instructor’s comments
43. Substitute to find the value of the expression:
A train must cover a distance of 581 miles. The velocity, in miles per hour, of the
581
train is
where t is the time, in hours, to complete the trip. If the train completes
t
the trip in 7 hours, what is its velocity?
MTH 157 Week #9 Final Cumulative Test
MTH 157 – Math For Elementary Teachers II
Week #9 Final Cumulative Test
Chapters 8 - 13
a) 83 mi/h
b) 78 mi/h
c) 0.01 mi/h
d) 4067 mi/h
Answer:
a
Work or justification:
Instructor’s comments
44. Solve the linear equation.
3n – 5 = 25
Work:
3n-5=25
3n=20
n=20/3
Instructor’s comments
45. Solve the linear equation.
x 1
  4
4 4
Work:
x/4=-4+1/4
x/4=(-16+1)/4
x/4=-15/4
x=-15
Instructor’s comments
46. Solve the quadratic equation:
x2 + 2x – 35 = 0
a) 7, 5
b) –7, 5
c) 7, –5
d) –7, 1
Answer:
b
Work:
x = [-2±2^2-4(1)(-35)]/2=[-2±144]/2=[-2±12]/2=-1±6
Answer: x=-1+6=5 or x=-1-6=-7
MTH 157 Week #9 Final Cumulative Test
MTH 157 – Math For Elementary Teachers II
Week #9 Final Cumulative Test
Chapters 8 - 13
Instructor’s comments
47. Without graphing, identify the slope and the y-intercept:
3x + 7y = 27
3
a) Slope  ;
7
 27 
y-intercept  0, 
 7 
7
c) Slope  ;
3
 7 
y-intercept  0, 
 27 
Answer:
7
;
3
 7 
y-intercept  0, 
 27 
3
d) Slope
;
7
 27 
y-intercept  0, 
 7 
b) Slope
a
Work or justification:
Instructor’s comments
48. Find the slope of the line passing through the pair of points:
(8, –2) and (1, 4)
a) 
7
2
b) 
6
7
c)
2
9
d)
7
2
Answer: B
Work or justification:
Slope is [4-(-2)]/[1-8]=6/(-7)=-6/7
MTH 157 Week #9 Final Cumulative Test
MTH 157 – Math For Elementary Teachers II
Week #9 Final Cumulative Test
Chapters 8 - 13
Instructor’s comments
49. Find the midpoint of the line segment having the given endpoints
(–1, –6) and (8, 8)
a)
7 
M  ,1 
2 
b)
M  9, 14 
c)
 9

M   , 7 
 2

d)
M  7, 2
Answer: A
Work or justification:
Midpoint is ((-1+8)/2,(-6+8)/2)=(7/2,1)
Instructor’s comments
50. Find the distance between the two points. Round an approximate result to the
nearest hundredth.
(–2, –1) and (4, –8)
a) 36
b) 39
c) 10.82
d) 10.39
Answer:
9.22
Work or justification:
D=[(-8-(-1))^2+(4-(-2))^2]= [(-7)^2+(6)^2]= 85=9.22
Instructor’s comments
MTH 157 Week #9 Final Cumulative Test
MTH 157 – Math For Elementary Teachers II
Week #9 Final Cumulative Test
Chapters 8 - 13
Correct and complete answer, all work is
Full credit
shown and is Correct.
Full and complete answer, some minor
Partial credit
errors or omissions in work
Minor errors* in answer or partial answer.
Partial credit
Work is complete and correct except for
these errors in the final answer
Incorrect or incomplete answer with no
No credit
work shown or major errors in work
* A minor error is defined as a small mistake that may affect the results, but does not
reflect misunderstanding or misapplication of the concepts. An example would be a
missing sign in a step, when it had been present in previous steps. Incorrect digits and
rounding errors are not considered minor.
MTH 157 Week #9 Final Cumulative Test