Tennessee Christian
Preparatory School
Summer Math
Entering Algebra 1
Upper School
2017
“Whatever you do, put your whole heart into it, as into work done
for God…”
Colossians 3:23
Dear Parents,
One of the greatest impacts on the future academic success of a
child lies in the continued repetitive review of reading and
math facts. God created an orderly world, one in which His
immutability is evident to students of math.
Here at TCPS we want our students, your children, to keep
those skills alive over the summer. We want your child to be so
exposed to basics, and we want the basics to be easy.
Every year, math teachers in our nation have to review for
almost 2 months; constant exposure reduces the need for
review and allows a class to add new information almost
immediately.
We want our students to be competitive in math, to be sure of
their knowledge and skills, and to be receptive to new
instruction. The completion of this math packet is one step in
preparing our students.
This packet is not meant to be devoured in one sitting; it
should be worked on a little bit each day, slowly reviewing
skills and acquiring a new one or two as the summer
progresses. As a result, our math classes will be able to run
faster and with increased fluidity. Feel free to help your child,
to google concepts, and to have them work together. And
maybe, through an appreciation of this review, students will be
able to reflect upon God’s creation in a new way.
-
Brian Stockton, Assistant Principal
Summer Math Guidelines
1.
The packet will be graded for accuracy as well as effort.
2. All work should be completed in pencil.
3. All work should be completed on the scratch pages in this
packet.
4. As much as possible, you should show your work on all
problems.
5.
Answers should be recorded in the appropriate answer block
for each question.
6. The completed packet will be due on August 15th, (first full
day of school).
1.
The hour hand of a clock turns 30° in 60 minutes. How many
1
degrees will the hour hand turn in 2 hours?
2
2.
A 15% tip on $14.95 lunch bill is about
3.
What is the cost of a 4-mile taxi ride if the charge is $2.50 to start
plus $2.80 per mile?
4.
During the game the pitcher threw 54 strikes and 36 balls. What
was the balls-to-strikes ratio?
5.
The price of 2.6 pounds of oranges at 70¢ per pound is
6.
At $15 per square foot, the cost of installing flooring in a room with
these dimensions is
7.
How much does a worker who is paid $24 per hour earn in 3
2
hours?
1
Refer to the triangle for questions 8 and 9.
8.
The perimeter of the triangle is
9.
The area of the triangle is
10. The area of a triangle with vertices at (−3, −2), (3, −2), and (1, 2) is
11. If 40% of the students were boys, then what fraction were girls?
12. Convert
1
12
to a decimal equivalent.
13. Express 250,000 in scientific notation.
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13.
14. Triangle ABC is transformed to triangle A’B’C’ by what
transformation?
15. The product of 106 and 103 is
16. Solve for t:
17.
1
18.
1.2 − 0.36
3
+
1
2
0.06
∙
1
4
𝑡+4
5
=6
equals
equals
19. 10 + 2 + 3 ∙ 4 − 5 equals
20.
𝑥 2 ∙𝑥 5
𝑥3
equals
21. If 𝑎 = 4, 𝑏 = 10, and 𝑐 = 6, then 𝑏 2 − 4𝑎𝑐 equals
22. Factor the expression: 𝑤𝑥 + 𝑤𝑦
23. Write the prime factorization of one million.
24. Solve for x: 3.3 = 3𝑥 + 0.3
25. Which point is the greatest distance from the origin?
26. A quarterback completed 18 of 30 passes. The percent of passes the
quarterback completed was
27. The trip from Omaha to Salt Lake City along Interstate 80 is about
1516 kilometers. At 90 km per hour, the trip would take about how
many hours?
28. How much is a 20% down payment on a $22,900 car?
29. The vertices of ∆𝐴𝐵𝐶 are at 𝐴(−3, 2), 𝐵(−3, 5), and 𝐶(−1, 3). If
∆𝐴𝐵𝐶 is reflected across the x-axis, what are the coordinates of
vertex 𝐴′ , 𝐵′ , and 𝐶′?
30. The team won 12 of its 20 games. The team’s won-lost ratio is
31. Maria draws one marble from a bag containing 5 red, 3 green, and 4
yellow marbles. What is the probability that she draws a yellow
marble?
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28.
29.
30.
31.
32. A terrarium that is 20 inches long, 10 inches wide, and 12 inches
deep. What is its volume?
33. A gallon of exterior paint covers 300 𝑓𝑡 2 . How many gallons of
paint are needed to paint the outside of a building that is 10 feet
high and has a perimeter of 179 𝑓𝑡 2 ?
34. With a full 12-gallon tank of fuel, Dillon’s car can travel about 420
miles. At that rate, about how far can Dillon’s car travel on 5
gallons of fuel?
35. Use a unit multiplier to convert 6.5 gallons to quarts.
36. The two triangles are similar. Which pair of parts do not
correspond?
37. The area of the figure is
38. A hose is coiled into circular loops about 30 inches in diameter.
What is the length of each loop?
39. A circular target is 19 inches in diameter. What is its area?
40. If
16
6
=
𝑛
, then n equals
1.2
41. If 5𝑥 − 𝑥 − 7 = 29, the x equals
42.
7.5 × 108
5
× 104 equals
43. (4 × 10−8 )(1.2 × 10−6 ) equals
44.
(−6) + (−4) − (−2)
(−1)(−2)
equals
45. 5𝑥 + 2(𝑥 − 3) + 4 equals
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45.
46. The area of the parallelogram is
47. A spinner was divided into three sectors of different sizes and
labeled A, B, and C. Britton spun the spinner a number of times
and recorded the following results: A – 24 times, B – 15 times, C –
21 times. Based on these results, what is the probability that the
spinner will stop in sector B on the next spin?
48. Figure ABCD is a parallelogram. What is the measure of ∠𝐷?
For questions 49 and 50, refer to this graph.
49. What is the slope of the graphed line?
50. What is the y-intercept of the graphed line?
51. An architect draws house plans for a client using the scale 1 inch
equals 4 feet. How long should the architect draw a wall that will be
22 feet long?
52. The product of 5 × 105 and 6 × 106 is
53. The price of a $28.00 item plus 7.5% sales tax is
54. If a coin is flipped five times, what is the probability of getting
heads all five times?
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54.
55. What is the lateral surface of the triangular prism?
56. A bag of marbles contains four red, three blue, two yellow, and one
green marble. If two marbles are drawn from the bag without
replacement, what is the probability that both marbles are red?
57. The height of this pyramid with a square base is 5 feet. What is its
volume?
58. Which equation is a rule for this sequence? 0, 3, 8, 15, …
59. Write the intersection of sets A and B if Set A = {2, 4, 6, 8, 10} and
Set B = {1, 2, 3, 4, 5}.
60. Which x and y pair of numbers is a solution to both of these
𝑥+𝑦=8
equations? {
𝑦−𝑥 =4
61. What is the area of the trapezoid?
62. The vertices of paralellogram ABCD are 𝐴(6, 3), 𝐵(0, 3), 𝐶(−2, −1),
and 𝐷(4, −1). What is the area of the parallelogram?
63. If paralellogram ABCD in question 62 above is dilated by a scale
factor of 3 from the origin, what are the coordinates of the image
point C’?
7
64. Round to the nearest percent.
9
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64.
65. 5𝑥(3𝑥 − 2) equals
66. If the area of a square is 36 units2, what is the length of its
diagonal?
67. If 0.04 + 0.2𝑥 = 0.06 , then x equals
68. Solve for n:
1.2
36
=
0.3
𝑛
69. 𝑥 −3 𝑦 2 𝑥𝑦 0 equals
70. 2√6 ∙ 3√3 equals
71. Which of these equations indicates a proportional relationship
between x and y?
72. Solve for w: 𝑉 = 𝑙𝑤ℎ
73. Solve the inequality: 2 − 𝑥 < 3
74. A softball backstop that is 10 feet high casts an 8-foot shadow at the
same time a light pole casts a 20-foot shadow. About how tall is the
flagpole?
75. (−3) + (−2)(4) − (−5) equals
76. 520 ÷ 25 =
77. 40.6 + 27.84 + 12 =
78. 3.8 − (2 − 0.18) =
79. 0.14 × 0.15 =
80. 0.14 ÷ 70 =
1
1
1
2
6
3
82. 5
1
− 3 =
83. 3
3
81. 2 + 3 + 2 =
6
4
3
4
1
∙ 3 =
3
5
1
6
2
84. 5 ÷ 2 =
85. Reduce
24𝑥 2 𝑦
40𝑥𝑦 2
86. Which digit in 50.143 has the same place value as the 7 in 6.8792?
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67.
68.
69.
70.
71.
72.
73.
74.
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80.
81.
82.
83.
84.
85.
86.
87. (8 × 103 )(4 × 104 )
88. One inch equals 2.54 centimeters. One foot equals how many
centimeters?
89. The formula 𝐹 = 1.8𝐶 + 32 may be used to convert temperatures in
℃(𝐶) to ℉(𝐹). 30℃ equals how many ℉?
90. Which of these is NOT equivalent to 4%
A.
91.
24 ∙26
22
0.04
B.
4
C.
100
1
D.
25
2
50
E. None Correct
=
92. √52 − 32 =
93. Write ten and two hundredths in standard form.
5
2
94. Estimate the product of 9 and 11 by first rounding each mixed
8
5
number to the nearest whole number.
95. Arrange the following numbers from least to greatest: 0.1, −1, 1, 0
96. What number solves this proportion?
2.4
𝑚
=
3
4.5
97. The team’s win-loss ratio was 5 to 3. If the team played 120 games
without a tie, how many games did the team win?
98. The average of Bianca’s first three test scores was 90. The average
of her next two test scores was 95. What was Bianca’s average of
Bianca’s first five test scores?
99. Sam’s first six scores were 90, 80, 90, 80, 80, and 100. What is the
median of these scores?
100. One white marble, two blue marbles, and three red marbles were in
a bag. One marble was drawn from the bag and then put back.
Then another marble was drawn. What is the probability that a
white marble was drawn both times?
101. Dixon deposited $2000.00 in an account that paid 5% interest
compounded annually. How much interest will the account earn in
two years?
102. Greg drove 386 miles and used 20 gallons of gas. His car averaged
how many miles per gallon?
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102.
103. At a 25%-off sale, a shirt cost $36.00. What was the regular price of
the shirt?
104. Janice correctly answered 21 of the 24 questions. What percent of
the questions did she answer correctly?
105. Jaime ran the first 2000 meters in 6 minutes. At that rate, how
long would it take Jaime to run 5000 meters?
106. Which of these quadrilaterals appears to be a trapezoid?
107. If ∠𝑥 measures 140°, then what is the measure of ∠𝑦?
108. What is the perimeter of this figure? All angles are right angles.
109. An arch in the form of a semicircle was over a 40-inch-wide
doorway. Find the length of the arch to the nearest inch.
110. What is the total surface area of a cube with a side length that
measures 3 inches?
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110.
111. The diameter of a circle is 12 inches. What is the area of a 90°
sector of the circle? Use 3.14 for 𝜋.
112. What is the volume of this triangular prism?
113. These two triangles are similar. Find x.
114. In rectangle QRST, QR is 30 mm and RS is 40 mm. How long is
segment QS?
115. In this figure, line m is parallel to line n and the measure of ∠𝑎 =
105°. What is the measure of ∠𝑔?
116. (−6) − (−7)(−4) =
117. If 𝑎 = 3, 𝑏 = 4, and 𝑐 = −2, the 𝑏 2 − 4𝑎𝑐 equals
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117.
118. (−2)3 − (−2)2 =
119. Write the prime factorization of 500.
120. 3(𝑥 − 3) =
121. If 3.6𝑛 − 0.18 = 7.02, what does n equal?
122. Translate “Six less than twice a number” into an mathematical
statement.
123.
(2𝑥𝑦)(4𝑥 2 𝑦)
8𝑥 2 𝑦
=
124. Solve and graph the inequality 2𝑥 − 1 < 5.
125. This line represents what equation?
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Math Department Contacts:
Brian Stockton (Assistant Principal)
[email protected]
Andrew Kuhn (Math Instructor)
[email protected]
Vision: Tennessee Christian Preparatory School will serve students and
families by providing a quality college preparatory education from a Biblical
worldview.
Mission: Tennessee Christian Preparatory School provides a quality college
preparatory education from a Biblical worldview and equips students for
tomorrow's challenges by educating the mind and the soul.
TENNESSEE CHRISTIAN PREPARATORY SCHOOL
4995 N. Lee Hwy
Cleveland, TN 37312
www.tcpsk12.org
423.559.8939