Tennessee Christian
Preparatory School
Summer Math
Upper School
2012
Hebrews 13:8, “Jesus Christ is the same yesterday, today, and forever.”
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
the math skills and concepts that it will be easy to build upon the
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 (see grade level requirements) 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.
-Audri Wood, Upper School Principal
Table of Contents
Summer Math Guidelines
Grade Level Instructions:
Entering Sixth Grade
Entering Seventh Grade
Entering Eighth Grade
Entering Ninth Grade
Entering Tenth Grade
Entering Eleventh Grade
Entering Twelfth Grade
Math Sections:
Section 1
Section 2
Section 3
Section 4
Section 5
Answer Sheets:
Section 1
Section 2
Section 3
Section 4
Summer Math Guidelines
You will need:
3-prong pocketed folder
Loose-leaf paper
Pencil
1.
The packet will be graded for accuracy as well as effort.
2. You must show your work on all problems. Do NOT simply
write your answers on the answer sheet.
3. All work should be completed in pencil.
4. Work should be neatly organized on loose-leaf paper. Your
work will be collected when you turn in the packet.
5. Write the section and concept at the top of each page.
6. Problems should be numbered down the left side of the page.
7.
Answers should be circled.
8. Answers should be recorded on the correct answer sheet.
9. Read the instructions for your specific grade to ensure that
you are working the correct section or sections.
10. The completed packet and your work will be due the first full
day of school.
Entering Sixth Grade
Students who will be entering the sixth grade should:
1.
Complete Section 1 of the packet.
2. Know multiplication facts through the 15’s.
Entering Seventh Grade
Students who will be entering the seventh grade should:
1.
Complete Section 1 of the packet.
2. Review multiplication facts through the 15’s.
Entering Eighth Grade
Students who will be entering the eighth grade should:
1.
Complete Section 1 and Section 2 of the packet.
2. Review multiplication facts through the 15’s.
Entering Ninth Grade
Students who will be entering the ninth grade should:
1.
Complete Section 1, Section 2, and Section 3 of the packet.
Entering Tenth Grade
Students who will be entering the tenth grade should:
1.
Complete Section 1, Section 2, Section 3 and Section 4 of the
packet.
Entering Eleventh Grade
Students who will be entering the eleventh grade should:
1.
Complete Section 1, Section 2, Section 3 and Section 4 of the
packet.
Entering Twelfth Grade
Students who will be entering the twelfth grade should:
1.
Complete Section 1, Section 2, Section 3, Section 4, and
Section 5 of the packet.
2. Please note that Section 5 does not have an answer sheet. As
with previous sections you will neatly organize your work on
loose-leaf paper. Be sure to circle your answers.
Section 1
Concept: Numbers and Operations
1.
Which digit is in the millions place in 123,456,789?
2.
Use words to write 21,350,608.
3.
Use digits to write four billion, five hundred twenty million.
4.
Arrange these numbers from least to greatest: 0, -1, 2, -3
5.
Which is greater:
6.
Calculate:
7.
Calculate:
8.
Calculate:
9.
Calculate:
10. Calculate:
11. Calculate:
12. Calculate:
13. Calculate:
14. Calculate:
15. Calculate:
16. Calculate:
17. Calculate:
18. Calculate:
19. Calculate:
20. Calculate:
21. Calculate:
22. Calculate:
23. Calculate:
24. Find the greatest common factor (GCF): 10 and 15
25. Find the greatest common factor (GCF): 18 and 24
26. Find the least common multiple (LCM): 6 and 8
27. Find the least common multiple (LCM): 3 and 5
28. Write the prime factors of 72, using exponents.
29. Write the prime factors of 99, using exponents.
30. Write the prime factors of 56, using exponents.
31. Calculate:
32. Calculate:
33. Calculate:
34. Calculate:
35. Calculate:
36. Calculate:
37. Calculate:
38. Calculate:
39. Calculate:
40. Calculate:
41. Calculate:
42. Calculate:
43. Calculate:
44. Calculate:
45. Calculate:
Section 1
Concept: Algebra
1.
What number is of 60?
2.
What number is
3.
Convert to a decimal:
4.
Convert to a decimal: 2
5.
Convert to a decimal:
6.
Convert to a percent:
of 80?
7.
Convert to a percent:
8.
Convert to a percent:
9.
Convert to a fraction: 0.25
10. Convert to a fraction: 0.6
11. Convert to a fraction: 0.9
12. Solve:
13. Solve:
14. The ratio of salamanders to frogs was 5 to 7. If there were
20 salamanders, how many frogs were there?
15. If 3 sacks of concrete will make 12 square feet of sidewalk,
predict how many sacks of concrete are needed to make 40
square feet of sidewalk?
16. The ratio of boys to girls in the cafeteria was 6 to 5. If there
were 60 girls, how many boys were there?
17. Determine the missing number in the table:
X
3
5
6
10
Y
1
3
4
18. Determine the missing number in the table:
X
3X + 1
3
10
6
19
8
19. Find the next term in the sequence: 1, 3, 9, 27, _____,…
20. Find the next term in the sequence: 5, 10, 15, 20, _____,…
21. Solve:
22. Solve:
23. Solve:
24. Solve:
25. Solve:
26. Solve:
Section 1
Concept: Geometry
1.
Draw and label a line segment.
2.
Draw and label a ray.
3.
Draw and label an acute angle.
4.
Draw and label an obtuse angle.
5.
Draw and label a right angle.
6.
Draw a pair of parallel lines.
7.
Draw a pair of perpendicular lines.
8.
Draw a pair of intersecting lines.
9.
The complement of a 60° angle is an angle that measures
how many degrees?
10. The supplement of a 60° angle is an angle that measures how
many degrees?
11. Draw an acute triangle.
12. Draw an obtuse triangle.
13. Draw a right triangle.
14. Draw a pentagon.
15. Draw a parallelogram.
16. Draw a trapezoid.
17. Draw cube.
18. Draw a cylinder.
19. How many sides does a hexagon have?
Use the following graph for the next four questions.
20. What are the coordinates of point a?
21. What are the coordinates of point d?
22. Which point has the coordinates
23. Which point has the coordinates
24. Which point has the coordinates
Section 1
Concept: Measurement
1.
Abraham Lincoln was born in 1809 and died in 1865. How
many years did he live?
2.
A half gallon of milk is how many pints of milk?
3.
Which has the greater capacity, a 12-ounce can or a 1-pint
container?
4.
What fraction of a gallon is equal to a quart?
5.
What is the perimeter of an equilateral triangle with sides of
3 inches?
6.
What is the perimeter of a square with 4 inch sides?
7.
What is the circumference of a circle with a diameter of 10
inches?
8.
What is the area of right triangle with sides of 3, 4, and 5
inches?
9.
What is the area of a square with 4 inch sides?
10. What is the area of a circle with a diameter of 10 inches?
Section 1
Concept: Data Analysis and Probability
Use the line plot below to answer questions 1-4.
1.
What is the mean price of story books?
2.
What is the median of the prices of story books?
3.
What is the mode of the prices of story books?
4.
What is the range of the prices of story books?
5.
A number cube is rolled. What is the probability that a
number less than five is rolled?
6.
A number cube is rolled and a coin is flipped. What is the
probability of rolling a one and tossing a Heads?
Use the following for questions 7 and 8. A bag contains 5 red
marbles, 4 yellow marbles, and 3 green marbles.
7.
What is the probability of drawing a yellow marble?
8.
What is the probability of not drawing a red marble?
Section 2
Concept: Numbers and Operations
1.
Use words to write 364,278,501.
2.
Arrange these numbers in order from least to greatest:
3.
Use digits to write twenty-five million, two hundred six
thousand, and forty.
4.
Calculate:
5.
Calculate:
6.
Calculate:
7.
Calculate:
8.
Write the prime factors of 10,500 using exponents.
9.
Write in scientific notation: 25,000
10. Write in scientific notation:
11. Write in standard notation:
12. Find the product:
13. Find the product:
14. Calculate:
15. Calculate:
16. Calculate:
17. Calculate:
18. Calculate:
19. Calculate:
Section 2
Concept: Algebra
1.
Convert to a decimal:
2.
Convert to a fraction: 0.85
3.
Express as a percent:
4.
Solve:
5.
In one northern city, the average snowfall after four months
was 7 inches. What must the average snowfall be for the
next two months in order to have a six-month average of 12
inches?
6.
Find the next term in the sequence: 1, 9, 81, 729, _____,…
7.
Solve:
8.
Solve:
9.
Calculate:
, if
and
10. Write an equation that represents the following data:
Number of Tables
(x)
1
2
3
4
Number of Chairs
(y)
4
8
12
16
11. Graph on a number line:
12. Graph on a number line:
Section 2
Concept: Geometry
1.
The complement of a 37° angle is an angle that measures
how many degrees?
2.
The supplement of a 99° angle is an angle that measures how
many degrees?
Use the following diagram for the next four questions.
3.
Name four pairs of corresponding angles.
4.
Name two pairs of alternate interior angles.
5.
Name two pairs of alternate exterior angles.
6.
Name four pairs of opposite angles.
7.
Find the missing length in the right triangle below.
8.
Find the missing length in the right triangle below.
9.
Draw a rectangular prism.
10. Draw a triangular prism.
11. The edge of a cube is 5cm. What is the cube’s surface area?
12. How many faces does a cube have?
13. How many edges does a cube have?
14. How many vertices does a cube have?
15. Write the following equation in slope-intercept form:
16. Using the slope and intercept, graph
Section 2
Concept: Measurement
1.
Convert 9 yards per second to feet per second.
2.
Convert 60 beats per second to beats per hour.
3.
Convert 22 feet per second to miles per hour.
4.
Calculate the perimeter of the shape below.
5.
Calculate the perimeter of a regular hexagon with a side
length of 8mm.
6.
Calculate the area of the triangle below.
7.
Calculate the area of the trapezoid below.
8.
Calculate the area of the geometric figure below.
Section 2
Concept: Data Analysis and Probability
Use the pie chart below to answer questions 1-4.
9.
Altogether, how many hours are included in this graph?
10. What fraction of Ayisha’s day is spent at school?
11. What fraction of Ayisha’s day is spent somewhere other than
at home or at school?
12. What fraction of Ayisha’s day is spent at home?
Use the following information to answer questions 4-8: Five
volunteers collected bottles to be recycled. The number they
collected were 242, 236, 248, 258, and 236.
13. What was the average number of bottles collected?
14. What is the median of the number of bottles collected?
15. What is the mode of the number of bottles collected?
16. What is the range of the number of bottles collected?
Section 3
Concept: Numbers and Operations
1.
Calculate:
2.
Calculate:
3.
Calculate:
4.
Calculate:
5.
Calculate:
6.
Write the product in scientific notation:
7.
Write the quotient in scientific notation :
8.
Collect like terms:
9.
Find the quotient:
10. Find the product:
11. Add the trinomials:
12. Add the trinomials:
13. Find the product:
14. Find the product:
15. Simplify:
16. Simplify:
17. Simplify:
18. Simplify:
and
and
Section 3
Concept: Algebra
1.
The ratio of football players to soccer players was 5 to 7. If
the total number of players was 48, how many were football
players?
2.
Convert to a decimal:
3.
Simplify:
4.
If 8 cows eat 200 pounds of hay a day, how many pounds of
hay would 20 cows eat?
5.
A $15 item on sale for $12 is marked down what percent?
6.
Find the 7th term in this sequence: 1, 4, 9, 16, …
7.
What are the first four terms of the sequence generated by
the formula:
8.
Find the tenth term in the sequence generated by the
formula:
9.
Solve:
10. Calculate: 2.7
11. Solve:
12. Solve:
, if
and
Section 3
Concept: Geometry
Use the following diagram for the next three questions.
1.
Name two pairs of vertical angles.
2.
Name four pairs of supplementary angles.
3.
If
, then what are the measures of angles 2, 3,
and 4?
Use the following diagram for questions 4 and 5.
4.
Find the slope of line
5.
Find the slope of line
6.
If the dimensions of a cube are increased by 100%, by what
percent is the volume increased?
7.
A right triangle has legs of lengths 4cm and 8cm. How long
is the hypotenuse?
8.
A right triangle has legs of lengths
cm and 2cm. How
long is the hypotenuse?
9.
Graph the function
and label the y-intercept.
10. Find the x- and y-intercepts of
. Graph the
equation and label the intercepts.
11. Jill is thinking of two numbers. The sum of the numbers is
5. If the lesser number is subtracted from the greater number
the result is 7. Graph this system of equations to find the
two numbers.
Section 3
Concept: Measurement
1.
A semicircular window has a radius of 36 inches. What is its area?
2.
Calculate the area of the sector of the circle below.
3.
A cube has edges 8cm long. Find the total surface area of
the cube.
4.
A cube has edges 8cm long. Find the volume of the cube.
5.
Find the surface of the triangular prism shown below.
6.
The bases of a trapezoid are 12cm and 18cm. The height is
8cm. Find the area.
Section 3
Concept: Data Analysis and Probability
Use the following information to answer questions 4-8
A popular TV show receive these ratings over its season:
16.0
15.2
15.3
15.5
15.7
15.1
14.8
15.6
15.0
14.6
14.4
15.8
15.3
14.7
14.2
15.7
1.
What is the mean TV rating?
2.
What is the median of the TV ratings?
3.
What is the mode of the TV ratings?
4.
What is the range of the TV ratings?
5.
Create a line plot displaying the data.
6.
Create a histogram displaying the data.
Section 4
Section 5
Section 1
Concept: Numbers and Operations
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Section 1
Concept: Algebra
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Section 1
Concept: Geometry
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Section 1
Concept: Measurement
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Section 1
Concept: Data Analysis and Probability
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Section 2
Concept: Numbers and Operations
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Section 2
Concept: Algebra
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Section 2
Concept: Geometry
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2
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Section 2
Concept: Measurement
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Section 2
Concept: Data Analysis and Probability
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Section 3
Concept: Numbers and Operations
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Section 3
Concept: Algebra
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Section 3
Concept: Geometry
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2
10
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10
15
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10
15
8
2
6
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2
8
10
5
8
2
6
4
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2
8
10
5
2
4
6
8
Section 3
Concept: Measurement
1.
2.
3.
4.
5.
6.
Section 3
Concept: Data Analysis and Probability
1.
2.
3.
5.
6.
4.
Section 4
Math Department Contacts:
Brian Stockton
[email protected]
Audri Wood (Principal)
[email protected]
Vision: Tennessee Christian Preparatory School will serve students and
families by providing a quality college preparatory education from a
Christian worldview.
Mission: Tennessee Christian Preparatory School provides a quality college
preparatory education from a Christian 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