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009
Subject
Mathematics
Date
Apr 3, 2024
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10
Uploaded by GrandReindeerMaster147
MATH 009 - Bohner
Midterm Exam
Instructions
:
●
The midterm is worth 100 points (25 questions total; 4 points apiece).
●
This midterm is
open book
and
open notes
, and you may take as long as you like on it
provided that you submit the midterm no later September 13
th
11:59PM. You may refer to
your textbook, notes, and online classroom materials,
but you may not consult anyone
.
●
You should show all of your work (where applicable) to receive full credit. If you do not
show work, you may earn only partial or no credit.
●
Please type your work in your copy of the midterm, or if you prefer, create a document
containing your work. Scanned work is also acceptable. Be sure to include your name in
the document. If you are using your camera as a “scanner” please be sure that the
document you create is in *.pdf format, and not a *.gif or *.jpeg. I cannot comment on a
picture.
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Upload your midterm to the Midterm assignment link in Week 4 Content area.
●
If you have any questions, please contact me by e-mail
(kathy.bohner@faculty.umuc.edu).
1. 4(3 + 6) – 3(2)
2
3 + 6 = 9
2 squared = 4
4 ( 9 ) - 3 ( 4 )
4 x 9 = 36
MATH 009 - Bohner
Midterm Exam
3 x 4 = 12
36 - 12 = 24
4(3 + 6) – 3(2)
2
= 24
2. [13 + 12] ÷ [2
3
– 3]
13 + 12 = 25
2 ^ 3 = 8
8 - 3 = 5
25 / 5 = 5
[13 + 12] ÷ [2
3
– 3] = 5
3.
3
14
×
7
9
3 x 7 = 21
14 x 9 = 126
21 / 126 = 7 / 42
= 7/ 42
3
14
×
7
9
4.
4
1
3
÷2
3 x 4 + 1 = 13
(13/3 ) / (2 / 1)
MATH 009 - Bohner
Midterm Exam
13 / 3 x 1 / 2
13 x 1 = 13
3 x 2 = 6
13 / 6 = 2 1/6
= 2 1/6
4
1
3
÷2
5.
Find the area of a triangle with base length
inches and altitude 10
3
3
4
inches.
A = ( h * b ) / 2
h = 10
b = 3 ¾
4 * 3 + 3 = 15
10/1 * 15/4 = 150 / 4 = 75/2 = 37 ½
The area of a triangle with base length
inches and altitude 10 inches is 37 ½
3
3
4
inches
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MATH 009 - Bohner
Midterm Exam
6.
(
5
9
−
5
12
)÷(
1
2
−
1
4
)
2
a. 9 * 4 = 36
b. 1 * 2 = 4
5 * 4 = 20
2 * 2 = 4
3 * 5 = 15
12 * 3 = 36
( 20/36 - 15/36 ) / ( 2/4 - ¼) ^2
( 5/36 ) / ( ¼ ) ^2
¼ ^2 = (1 * 1) / (4 *4) = 1/16
( 5/36) / ( 1/16 ) = ( 5/36)(16/1) = 80/36 = 2 2/9
= 2 2/9
5
9
−
5
12
)÷(
1
2
−
1
4
)
2
7.
5
9
÷
1
3
×
1
6
(5/9) * (3/1) = 15/9
15/9 *
⅙
= 15/54 = 5/18
=
5/18
5
9
÷
1
3
×
1
6
8. A chef has
pounds of beef. How many one-third burgers can he
16
2
3
make?
MATH 009 - Bohner
Midterm Exam
(16 ⅔ ) / (⅓) = (16 ⅔ ) * (3/1) =
3 * 16 + 2 = (50/3) * (3/1) = 150/3 = 50
A chef has
pounds of beef. How many one-third burgers can he make? 50
16
2
3
burgers
9. Find the perimeter and area of a square that has side length 7.35 cm.
Round, if necessary, to the nearest hundredth of a unit. Include units in
your answer.
P = 7.35 cm x 4
P = 29.4 cm
A = 7.35cm^2
A = 54.02 cm
10. Diane stopped at Sheetz and filled the tank in her RV; the odometer read
51, 456.6. After the next fill up, the odometer read 51, 801.5. It took 21.5
gallons to fill the tank. How many miles per gallon did the RV get between
fill-ups?
51,801.5 - 51, 456.6 = Diane traveled 344.9 miles
344.9miles / 21.5gallons = 16.04 miles per gallon
11. The diameter of the Ferris wheel at Six Flags is 205 feet. Use 3.14 as an
approximation for π to find the circumference of the wheel and round your
MATH 009 - Bohner
Midterm Exam
answer to the nearest foot. How far would a person travel if they rode the
Ferris wheel 5 times? Round to the nearest foot.
radius is = ½ d
205ft / 2 = 102.5ft
3.14 x 2 = 6.28
6.28 x 102.5ft = 644 ft
C = 644 ft
644 ft x 5 = 3,222 ft
12. The American Psychological Association reports that 12 out of every 100
people in Maryland are depressed. If there are 6 million people in the state,
how many are depressed? Use a proportion to solve the problem.
12 : 100 = x : 6,000,000
12 * 6,000,000 = 72,000,000
72,000,000 = 100x
72,000,000/100 = 720,000
x = 720,000
12 : 100 = 720,000 : 6,000,000
13. At 5 PM, my shadow is 0.95 meters long. My height is 1.75 meters. At the
same time, a tree’s shadow is 6.51 meters long. Use a proportion to find the
height of the tree.
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MATH 009 - Bohner
Midterm Exam
0.95 : 1.75 = x : 6.51
0.95 * 6.51 = 6.18
6.18 = 1.75x
6.18 / 1.75 = 3.53
x = 3.53
14. It takes 80 ounces of grass seed to seed 4000 square feet of lawn. Janelle’s
lawn is 90.5 feet wide and 98 feet long. How many ounces of grass seed should
she buy if she wants to seed the entire lawn? Use a proportion to solve the
problem.
Area of Janelle’s lawn = 90.5ft * 98ft = 8,869 sft
80 : 4000 sft = x : 8,869
8,869 * 80 = 709,520
709,520 = 80x
4,000 * x = 4,000x
709,520 / 4,000 = 177.38
Janelle should buy 178 ounces of grass seed.
15. Which of the following bottles of shampoo is the most economical?
32 fluid ounces for $5.69
48 fluid ounces for $7.65
62 fluid ounces for $11.99
MATH 009 - Bohner
Midterm Exam
$5.69 / 32 = 0.18 ℅
$7.65 / 48 = 0.16 ℅
$11.99 / 62 = 0.19 ℅
The 48 fluid ounce bottle is the most economical because it has the lowest ℅ .
16. Brian digs two circular holes for fish ponds, one 3 meters in radius and
the other is 6 meters in radius. How much greater in area is the larger fish
pond? Use 3.14 as an approximation for π.
3.14 * 3m ^2
3^2 = 9
9 * 3.14 = 28.26
3.14 * 6^2
6^2 = 36
36 * 3.14 = 113.04
113.04 - 28.26 = 84.78
17. I stopped at McDonald’s on my way home from work (don’t judge me)
and ordered a Big Mac combo costing me $6.79. I gave the cashier a twenty
dollar bill. What change did I receive?
$20 - $6.79 = $13.21
18. Convert the number
to a percent and round your answer to the
3
5
7
nearest tenth of a percent.
3 5/7 = 3 + (5/7)
MATH 009 - Bohner
Midterm Exam
5/7 = 0.714
0.714 +3 = 3.714
3.714 * 100 = 371.4 %
19. Convert 56% to a fraction in lowest terms and to a decimal number.
56 % = 0.56
0.56 / 1 * 100 / 100
56 / 100 = 14 / 25
20. What is 90% of 85? Write an equation to solve the problem using a
variable to represent the unknown quantity.
.90 * 85 = x
x = 76.5
90% of 85 is 76.5
21. The original price of a Sony TV was $1899.90. Monica had a 20% off
coupon to use for this purchase. If sales tax of 6% was added after the
discount was taken, how much did Monica pay altogether for the TV?
$1899.9 * .20 = $379.98
$1899.9 - $379.98 = $1519.92
$1519.92 * .06 = $91.20
$1519.92 + $91.20 = $1611.12
Monica paid $1611.12 for the TV
22. Steve borrowed $65,000 at 6.5% interest and repaid the loan at the end of
10 years. How much interest did he pay on the loan?
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MATH 009 - Bohner
Midterm Exam
$65,000 * .065
$65000 * .065 = $4,225
23. Evaluate the expression 9x – 6 when x = 2.
9 * 2 = 18
18 - 6 = 12
9x - 6 = 12
24. Evaluate the expression (2x – 1) – (6y + 3) when x = - 2 and y = 3.
2 * -2 - 1 = -5
6 * 3 + 3 = 21
-5 - 21 = -26
(2x - 1) - (6y + 3) = -26
25. Simplify the expression. Show all steps of work as you follow the order of
operations.
- 4(3
3
– 2
4
)
3^3 = 27
2^4 = 16
27 - 16 = 11
-4*11 = -44