rising 8th grade summer math packet -...

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1 Rising 8 th 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 8 th 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:___________________________________________________

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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