rising 8th grade summer math packet -...
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1 Rising 8th Grade Math Summer Review Packet
Rising 8th Grade Summer Math Packet
I appreciate the time you are taking to review and practice your math skills this summer.
This packet includes a review of seventh grade skills considered to be a prerequisite to
the eighth grade Algebra course.
Completion of the first half of this packet is mandatory for all 8th grade
students enrolled at Cornerstone Christian Academy who will be taking Algebra
in the fall.
You should complete this packet without the use of a calculator and show all steps
used to arrive at your final answer.
It is recommended to start this packet in the middle of July and to spread it out
over several days. It is not intended to do all in one sitting.
During the first week of school, you will turn in your completed review packet and
take a diagnostic test. Please keep in mind while you are working on this review
packet that you will not be allowed to use a calculator during the assessment in
August.
The first five days in this packet will count as your first homework grade in math.
If the entire packet (all 10 days) is completed, your lowest first semester test
grade will be bumped to an A.
We look forward to seeing you at school in August!
Math Team
Name:___________________________________________________
2 Rising 8th Grade Math Summer Review Packet
HELPFUL HINTS:
When adding and subtracting whole numbers or decimals, line up the place values.
When adding or subtracting fractions, get a common denominator.
When multiplying or dividing mixed numbers, put them into improper fractions first.
When dividing fractions, do not forget to change the sign to multiplication and make
the second fraction its reciprocal.
Factors are numbers that can be evenly divided into a number…the factors of 6 are 1,
2, 3, and 6.
Multiples are the product of a number and any other number…the first few multiples of
5 are 0, 5, 10, 15, etc.
To change a fraction into a decimal, divide the numerator by the denominator.
To change a decimal to a fraction, put the number over the place value of the last digit
and reduce.
To change a fraction or decimal into a percent, multiply by 100.
To change a percent into a fraction or decimal, divide by 100.
For percent problems, use the proportion
.
NO CALCULATORS ARE TO BE USED!
3 Rising 8th Grade Math Summer Review Packet
1) Simplify 24 _____________________________
2) >, <, or =. 3-2 _____ (-3)2 _____________________________
3) 3.583 x 104 = __________ _____________________________
4) Write
as a percent. _____________________________
5) Convert 300 minutes to hours. _____________________________
6) Find the perimeter of a hexagon with side length 7cm. _____________________________
7) Find √ . _____________________________
8) What is of 120? _____________________________
9) 5 is 25% of what number? _____________________________
10) A rectangular package is 6 in. high, 3 in. wide,
and 2 in. deep. What is the volume of the
package if the width is doubled? _____________________________
Day 1 - Mandatory
4 Rising 8th Grade Math Summer Review Packet
Complete the table.
Fraction Decimal Percent
1) a) b) 2.5%
2) a) 1.07 b)
3)
a) b)
Solve for the variable.
4)
6)
5)
7)
8) Order from least to greatest. _____________________________
7.4, -15.1, 16.03, -16.3, 7.39 , 0
9) Express 2.9 x 10-3 in standard notation. _____________________________
10) Find the perimeter and area of the shape below. _____________________________
Day 2 - Mandatory
5 in.
6.3 in. 2.5 in.
4.1 in.
X
7.5 in.
5 Rising 8th Grade Math Summer Review Packet
1) Simplify 4 – (8) ● (2) + 5 _____________________________
2) Find the angle complementary to 43°. _____________________________
3) Simplify using exponents
·
·
·
. _____________________________
4) Evaluate _____________________________
5) Write 324,000,000 in scientific notation. _____________________________
6) Find the volume of a cube with side length 3cm. _____________________________
7) Compare using <, >, or =. 112 ______ 120 _____________________________
8) 2 is what percent of 40? _____________________________
9) What is 12.5% of 80? _____________________________
Simplify.
10) 11)
12)
Day 3 - Mandatory
6 Rising 8th Grade Math Summer Review Packet
1) Solve . _____________________________
2) Write 10,000 as a base ten. _____________________________
3) Write 0.001 as a base ten. _____________________________
4) If Ryan makes $325 a week, how much will he make in a year? _____________________________
5) Find a surface area of a sphere that has radius 5m.
Use 3.14 for . Recall that _____________________________
6) What is the percent increase from 25 to 30? _____________________________
7) What angle is supplementary to 83°? _____________________________
8) _____________________________
9) Convert. 20 meters/min. = ___?___ cm/min. _____________________________
10) Find the perimeter and area of the triangle. _____________________________
11) If you paid $15 for a t-shirt that was marked
down 20%, what was the original price of the shirt? ____________________________
12) Solve the inequality . _____________________________ Hint: don’t forget something happens to the inequality sign when you divide by an integer!)
Day 4 - Mandatory
4 cm
3 cm
x cm
Recall the Pythagorean Theorem .
7 Rising 8th Grade Math Summer Review Packet
Solve the problem below. Write a justification explaining your answer and solution on the next
page. Use complete sentences. (Note: for this problem only, you may use a calculator. However,
you will still need to explain how you solved the problem.)
Sharon is wrapping a present that is 2 inches, by 10 inches, by 13 inches.
a. How many square inches of wrapping paper will she need to cover the entire box?
(Think surface area.)
b. Now add 10 square inches to your surface area on part a. so that she will have some
wrapping paper left over.
c. If a craft store is selling wrapping paper for $0.38 per square inch, how much would it
cost Sharon to wrap her present? (use the number from part b.)
d. If there is a tax on the wrapping paper, what will the total cost of Sharon’s purchase
be?
Day 5 - Mandatory
8 Rising 8th Grade Math Summer Review Packet
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Wrapping Presents SOLUTION JUSTIFICATION
9 Rising 8th Grade Math Summer Review Packet
1) Solve.
_____________________________
2) Simplify . _____________________________
3) 5.36 x 104 = ? _____________________________
4) What is the circumference in terms of
of a circle with radius 2.4 cm? ______________________________
5)
______________________________
6) 5 is 60% of what number? _____________________________
7) What is 10% of 540? _____________________________
8) Simplify. 2 – 2x + 6x +10 _____________________________
9) If a bakery can produce 132 donuts in an hour, how
many donuts can they produce in a 8-hour work day? _____________________________
10) A group of fisherman on a charter boat have the
following ages: 89, 49, 52, 49, 79, 39. What is the mode? _____________________________
Day 6 - Optional
10 Rising 8th Grade Math Summer Review Packet
1) Simplify -16 _____________________________
2) Compare using > or <. -6.05 ________ -6.14 _____________________________
3) Simplify (-4)-2 _____________________________
4) Convert
to a mixed number. _____________________________
5) If you can paint one box in 2/3 of an hour, how long do 5 boxes take? _____________________________
6) Find all the square roots of 225. _____________________________
7) Simplify 9-(-12) ·(-6) + 10 _____________________________
8) Rachel has a collection of 40 stuffed animals.
of the animals are bears and are dogs. How many
bears and dogs does she have? _____________________________
9) A camp cook purchased 2
lb of hamburger,
6
lb of chicken, and 1
lb of pork. How many
total pounds of meat did he purchase? _____________________________
10) Find the volume of the cylinder in terms of . _____________________________
Recall that .
Day 7 - Optional
11 Rising 8th Grade Math Summer Review Packet
1) Simplify 42 · 43 _____________________________
2) Compare using >, >, or =.
_______
_____________________________
3) 55% of 100 is what number? _____________________________
4) Write the expression, “ less than 2 times x” _____________________________
5) Solve. x + x + x + 2 = 20 _____________________________
6) Sol e x _____________________________
7) George bought a skateboard that was 60% off
the original price. If the original price was $90,
how much was the discount? _____________________________
8) The shadow of a 20 ft. tall building was 15 ft. next
to the building stands a tree that had a 7.5 ft. shadow.
How tall is the tree? _____________________________
9) You left a 20% tip on a $75 bill at J.Alexanders.
How much did you pay in all? _____________________________
10) Mrs. Ray sold 96 pounds of shrimp.
of it was sold
at $5.60 per pound and the rest at $4.70 per pound.
How much money did she receive altogether? _____________________________
11) A map has a scale of 3cm : 18km. If Riverside and
Smithville are 54 km apart then they are how far
apart on the map? _____________________________
Day 8 - Optional
12 Rising 8th Grade Math Summer Review Packet
1) List all of the factors of 49. _____________________________
2) 12 – 32 = ? _____________________________
3)
_____________________________
4) Reduce
to simplest terms. _____________________________
5)
_____________________________
6) Solve. – _____________________________
7) Simplify. _____________________________
8) 30 is 5% of what number? _____________________________
9) Find the measure of an angle whose
complement is two times the measure of the angle. _____________________________
10) A 12 ft tall tent standing next to a cardboard box casts a
9ft shadow. If the cardboard box casts a shadow that is
6ft long then how tall is it? _____________________________
Day 9 - Optional
13 Rising 8th Grade Math Summer Review Packet
Solve the problem below. Write a justification explaining your answer and solution on the next
page. Use complete sentences.
Carlos and Leroy are starting their own gym and selling memberships. Carlos says that they will
make more profit by charging an initial $110 sign-up fee then charging $15 a month. Whereas Leroy
says that they will make more profit by charging an initial $20 sign-up fee and then charging $25 a
month.
a. Who’s plan will generate more income after 3 months of membership? 6 months? 1 year? 2
years?
b. Will there ever be a month where both plans are the exact same price?
c. In your explanation, include your strategy method you used. Did you use a table, graph,
chart, guess and check?
Day 10 - Optional
14 Rising 8th Grade Math Summer Review Packet
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Owning a Gym SOLUTION JUSTIFICATION