7th grade math 1st semester review ch -...

7th Grade Math 1st Semester Review Ch.1

Multiple Choice

Identify the choice that best completes the statement or answers the question.

____ 1. Simplify the expression 45 + 16 2 4 – 6.

a. 24.5 c. 47

b. 13.25 d. 29

____ 2. Simplify the expression .

a. –12 c. 100

b. 76 d. 64

____ 3. Pablo earns money by caring for turtles while people are on vacation. Pablo earns $25 per week per pet.

The table shows the number of turtles cared for per week during July. Simplify the expression

to find out how much Pablo earned for the month of July.

Week Pets

Week 1 4

Week 2 2

Week 3 2

Week 4 2

a. $35 c. $450

b. $250 d. $154

____ 4. In an online media store, downloaded songs cost $3 each and books cost $9 each. Taji paid $7 in sales tax

when he purchased 15 songs and 3 books. Write and simplify an expression to show how much Taji spent on

everything, including sales tax.

a. ; $37 c. ; $151

b. ; $223 d. ; $79

____ 5. Tell which property is represented.

a. Associative Property c. Distributive Property

b. Commutative Property d. Identity Property

____ 6. Simplify the expression. Justify each step. Complete the justification.

= ?

= ?

= Add.

=

a. Commutative Property; Identity Property

b. Commutative Property; Associative Property

c. Associative Property; Commutative Property

d. Identity Property; Associative Property

____ 7. Use the Distributive Property to find .

a. 846 c. 534

b. 774 d. 666

____ 8. Evaluate n + 13 for n = 24.

a. 11 c. 312

b. 37 d. 24n + 13

____ 9. Evaluate 7y – 2 for y = 9.

a. 49 c. 9y – 2

b. 61 d. 77

____ 10. Evaluate for y = 6 and z = 3.

a.

c. 95

b. 61

2 d. 29

____ 11. Write the phrase as an algebraic expression.

4 times the sum of a number and 20

a. c.

b. 20 + y d. 4y – 20y

____ 12. A fence has a total of 650 planks. Violeta paints n planks each day. Write an algebraic expression for how

many days it will take Violeta to finish painting the fence.

a.

c. 650n

b.

d. 650 – n

____ 13. It takes 78 days to create a custom motorcycle. Write an algebraic expression to describe the number of days

it takes to create n custom motorcycles. How many days will it take to create 6 custom motorcycles?

a. ; 84 days c. ; 468 days

b. ; 546 days d. ; 13 days

____ 14. Identify like terms in the list: .

a. ;

b. ; ;

c. ; ;

d. ; ;

____ 15. Simplify . Justify your steps using the Commutative, Associative, and Distributive

Properties when necessary.

a. c. b. d.

____ 16. Write an expression for the perimeter of the trapezoid. Then, simplify the expression.

2a 2a

x

y a. ; c. ;

b. ; d. ;

____ 17. Jaime makes t dollars per hour installing computers. The table shows the number of hours he worked each

week in July. Write and simplify an expression for the amount of money Jaime earned in July. Evaluate the

expression for .

Hours Jaime Worked

Week Hours

1 19.0

2 19.5

3 17.5

4 23.0

a. ; ;

b. ; ;

c. ; ;

d. ; ;


Answer Section

MULTIPLE CHOICE

1. C

2. D

3. B

4. D

5. D

6. B

7. B

8. B

9. B

10. D

11. C

12. A

13. C

14. B

15. B

16. A

17. C


Multiple Choice


____ 1. Graph the integer 4 and its opposite on a number line.

a.

0 2 4 6 8 100–2–4–6–8–10

c.

0 2 4 6 8 100–2–4–6–8–10

b.

0 2 4 6 8 100–2–4–6–8–10

d.

0 2 4 6 8 100–2–4–6–8–10

____ 2. Compare –2 _?__ 4. Write < or >.

0 1 2 3 4 5 60–1–2–3–4–5–6

a. < b. >

____ 3. Use a number line to order the integers 3, –7, 7, –9, 6, and 0 from least to greatest.

a.

0 2 4 6 8 100–2–4–6–8–10

3,

–7, 7, –9, 6, 0

c.

0 2 4 6 8 100–2–4–6–8–10

–9,

–7, 0, 3, 6, 7

b.

0 2 4 6 8 100–2–4–6–8–10

–9,

–7, 0, 3, 6, 7

d.

0 2 4 6 8 100–2–4–6–8–10

7,

6, 3, 0, –7, –9

____ 4. Find the absolute value.

|–3|

a. 3 c. 0

b. –3 d. 9

____ 5. The four best scores from an amateur golf tournament sponsored by a local golf club are given in the table.

Since the lowest score wins, which golfer won the tournament?

Player Score

Mr. Benitez 2

Mr. Hill –3

Mr. Williams –8

Mr. Hayashi 8

a. Mr. Hayashi c. Mr. Hill

b. Mr. Benitez d. Mr. Williams

____ 6. The table shows the change in four companies’ stock prices at the end of a day’s trading. Which company’s

stock lost the most?

Company Change in Price

King –5

Farley 1

Allendale 5

Tellers –3

a. Farley c. King

b. Tellers d. Allendale

____ 7. Find the sum –37 + (–25).

a. –12 c. 62

b. 12 d. –62

____ 8. Evaluate for –46 and 34.

a. –12 c. –80

b. 80 d. 12

____ 9. The income from the Spanish Club’s bake sale was $240. Expenses for the sale totaled $40. Use integer

addition to find the total profit or loss from the bake sale.

a. profit of $280 c. profit of $240

b. profit of $200 d. loss of $40

____ 10. Find the difference 10 (–25).

a. 35 c. –35

b. 15 d. –15

____ 11. Evaluate for –13 and –50.

a. 37 c. 63

b. –63 d. –37

____ 12. The highest temperature recorded in the town of Westgate this summer was °F. Last winter, the lowest

temperature recorded was –1 °F. Find the difference between these extremes.

a. –101 °F c. –99 °F

b. 101 °F d. 99 °F

____ 13. Find the product 2(–9).

a. 7 c. –7

b. 18 d. –18

____ 14. Find the product 6 • (–9).

a. 3 c. 54

b. –54 d. –3

____ 15. Find the quotient 130 2.

a. 128 c. 132

b. –65 d. 65

____ 16. Miguel spends $35 a day for 4 days. He earns $21 a day for 5 days. Does Miguel end up with more or less

money than he started with? By how much?

a. Miguel ends up with $35 more than he started with.

b. Miguel ends up with $35 less than he started with.

c. Miguel ends up with $91 more than he started with.

d. Miguel ends up with $91 less than he started with.

____ 17. Solve the equation h – (–22) = 11. Check your answer.

a. h = 11 c. h = 33

b. h = –33 d. h = –11

____ 18. Solve the equation = –9. Check your answer.

a. f = 18 c. f = –18

b. f = –7 d. f = –11

____ 19. This year, a construction company had expenses of $850 million, which was $75 million more than the

expenses from last year. How much were last year’s expenses?

a. $775 million c. $925 million

b. $850 million d. $75 million

____ 20. Write the fraction as a decimal. If necessary, round your answer to the nearest hundredth.

a. 0.55 c. 22.12

b. 1.83 d. 2.03

____ 21. Write the fraction as a decimal. If necessary, round your answer to the nearest hundredth.

a. 0.28 c. 0.5

b. 0.18 d. 0.09

____ 22. Write the decimal 0.51 as a fraction in simplest form.

a. 1

2 c. 1

51

100

b. 1

51 d. 51

100

____ 23. Write the decimal 1.71 as a mixed number in simplest form.

a. 71

100 c. 1

71

100

b. 17

10 d. 1

71

____ 24. During a review game, Mr. Pai’s class correctly answered 69 questions on the first try. If there were 72

questions in the game, at what rate were questions answered correctly on the first try? Express your answer as

a decimal. Round to the nearest hundredth.

a. 0.958 c. 0.042

b. 1.043 d. 0.096

____ 25. Write as a decimal.

a. 3.16 c. 4.16 b. 2.05 d. 3.05

____ 26. Compare the fractions . Write < or >.

a. < b. >

____ 27. Compare the decimals 0.22 __?_ 0.79. Write < or >.

a. < b. >

____ 28. Order –0.985, –0.95, 3

4 from least to greatest.

a. –0.95, –0.985, 3

4 c. 3

4, –0.95, –0.985

b. –0.985, 3

4, –0.95 d. –0.985, –0.95,

3

4


Answer Section

MULTIPLE CHOICE

1. A

2. A

3. C

4. A

5. D

6. C

7. D

8. A

9. B

10. A

11. A

12. B

13. D

14. B

15. D

16. B

17. D

18. C

19. A

20. B

21. B

22. D

23. C

24. A

25. A

26. A

27. A

28. D


Multiple Choice


____ 1. Add. Estimate to check whether the answer is reasonable.

31.9 + 6.9

a. 38.7 c. 3.88

b. 3.87 d. 38.8

____ 2. Subtract. Estimate to check whether the answer is reasonable.

91.4 87.7

a. 3.71 c. 179.1

b. 179 d. 3.7

____ 3. Mr. Romito is a bus driver. He drove the Maple Hills Senior Citizen Group on a 2-day motor trip through

upstate New York. On the first day, he drove 433.4 miles. On the second day, he drove 347.9 miles. How

many more miles did he drive the first day than the second day?

a. 8.55 miles c. 85.4 miles

b. 855 miles d. 85.5 miles

____ 4. Two pounds of corned beef cost $14.91, and a package of cabbage cost $3.34. What is the total cost of the

corned beef and the cabbage?

a. $18.35 c. $1.83

b. $18.25 d. $182.50

____ 5. Multiply.

–4.46 • 11

a. –49.06 c. –48.96

b. –4.906 d. –4.896

____ 6. Multiply. Estimate to check whether the answer is reasonable.

6.1 • (–15.8)

a. –96.38 c. –96.28

b. –9.628 d. –9.638

____ 7. The average yearly rainfall in Lakeview is 21.55 inches. What is the total amount of rainfall in inches in

Lakeview in 5.75 years?

a. 12.39125 inches c. 1,239.125 inches

b. 27.3 inches d. 123.9125 inches

____ 8. Divide.

48.18 (–21.9)

a. –0.22 c. 22

b. –2.2 d. 2.2

____ 9. Divide. Estimate to check whether the answer is reasonable.

76 (–3.8)

a. –2 c. –20

b. 200 d. 20

____ 10. Mr. and Mrs. Nozaki are moving from Riverside to Prarieton. The distance from their old house to their new

house is 1128.85 miles. If their car gets 21.1 miles per gallon, how many gallons of gas will they need for the

trip?

a. 54.5 gallons c. 53.4 gallons

b. 5.35 gallons d. 53.5 gallons

____ 11. Kristi had $7.00 when she went to the store. When she got back, she had $2.39. How much did she spend?

a. $4.43 c. $9.39

b. $6.76 d. $4.61

____ 12. Add. Express your answer in simplest form.

a. 1

3 c. 1

6

b. 1

3 d. 2

3

____ 13. Add. Express your answer in simplest form.

a. 11

56 c. 7

15

b. 53

56 d. 53

16

____ 14. Two carpenters are building a fence. After 5 minutes, one carpenter is finished of the way and the other is

finished of the way. How much of the way ahead of the second carpenter is the first carpenter?

a. 25

14 of the way c. 25

56 of the way

b. 13

28 of the way d. 39

56 of the way

____ 15. There are two bookcases against a wall. If one takes up 5

9 of the wall and the other takes up

1

5 of the wall,

how much of the wall is covered by bookcases?

a. 17

9 of the wall c. 34

45 of the wall

b. 3

7 of the wall d. 11

15 of the wall

____ 16. Multiply. Express your answer in simplest form.

–3 • 1

4

a. 1

12 c. 12

b. 12 d. 3

4

____ 17. Multiply. Express your answer in simplest form. 7

9 •

1

2

a. 7

18 c. 7

3

b. 14

9 d. 7

54

____ 18. Multiply. Express your answer in simplest form.

32

7 •

5

8

a. 56

115 c. 5

9

35

b. 23

56 d. 35

184

____ 19. In 2001, bus fare on the Metropolitan Bus Line was $4.00. In 1975, the fare was 1

2 the fare in 2001. What

was the fare in 1975?

a. $1.46 c. $8.00

b. $2.00 d. $7.42

____ 20. A computer processor costs $96.00. It is expected that in 8 months the processor will cost 3

4 its current price.

How much will it cost in 8 months?

a. $72.14 c. $128.00

b. $72.00 d. $127.34

____ 21. Marcus hikes at a rate of 2 miles per hour. If he hikes for 6 hours, how many miles will he hike?

a. 12 miles c. 122

3 miles

b. 14 miles d. 8 miles

____ 22. Divide. Express your answer in simplest form. 3

10 ÷

13

14

a. 21

65 c. 140

39

b. 65

21 d. 39

140

____ 23. Divide. Express your answer in simplest form.

17

11 ÷ 2

1

2

a. 36

55 c. 4

1

11

b. 119

36 d. 11

45

____ 24. How many 3

8-foot pieces of wood can you cut from a board that is 1

7

8 feet long?

a. 45

64 pieces of wood c. 1

5 pieces of wood

b. 3 pieces of wood d. 5 pieces of wood

____ 25. In a fish tank, 1

2 of the fish have a red stripe on them. If 10 of the fish have red stripes, how many total fish

are in the tank?

a. 25 fish c. 24 fish

b. 22 fish d. 20 fish

____ 26. On one day, the temperature at dawn in Chattanooga, Tennessee is 211

4 °C. During the day, it warms up 6

2

7

°C. What is the new temperature?

a. 118

11 °C c. 14

27

28 °C

b. 271

2 °C d. 27

15

28 °C


Answer Section

MULTIPLE CHOICE

1. D

2. D

3. D

4. B

5. A

6. A

7. D

8. B

9. C

10. D

11. D

12. D

13. B

14. C

15. C

16. D

17. A

18. B

19. B

20. B

21. C

22. A

23. A

24. D

25. D

26. D

7th Graede Math 1st Semester Review Ch.4

Multiple Choice


____ 1. You can get 640 calories from eating 8 apples. How many calories can you get from eating 1 apple?

a. 80 calories per apple c. 82 calories per apple

b. 83 calories per apple d. 81 calories per apple

____ 2. Ignacio is going on vacation. He needs to drive 579 miles in 8 hours. What is his average speed in miles per

hour?

a. 63 miles per hour c. 67 miles per hour

b. 65 miles per hour d. 69 miles per hour

____ 3. Tony and Tiffany collect semi-precious stones. At the Rockhound Hut, Tiffany paid $38 for 9 pounds of

snowflake obsidian. At The Solid Rock Shop, Tony paid $19 for 3 pounds of the same type of stone. Who

made the better buy?

a. Tony b. Tiffany

____ 4. Tina and Noly wanted to see whose car gets better gas mileage, so they each drove 210 miles and recorded

how much gas they used. Use the bar graph to find how many miles per gallon each person’s car gets. Round

your answers to the nearest tenth.

Am

ou

nt

of

Gas

Use

d (

ga

l)

Tina's car Noly's car

12

20

3

6

9

12

15

18

21

a. Tina’s car: 17.5 mi/gal. Noly’s car: 10.5 mi/gal.

b. Tina’s car: 19.5 mi/gal. Noly’s car: 12.5 mi/gal.

c. Tina’s car: 175 mi/gal. Noly’s car: 105 mi/gal.

d. Tina’s car: 12.5 mi/gal. Noly’s car: 19.5 mi/gal.

____ 5. Determine whether the ratios are proportional.

a. not proportional b. proportional

____ 6. Determine whether the ratios and are proportional.

a. proportional b. not proportional

____ 7. Determine whether the ratios are proportional.

a. proportional b. not proportional

____ 8. Marie rode her bike 325 kilometers in 20 hours last month. Tamara rode her bike 255 kilometers in 15 hours

last month. Are these speed rates proportional? Explain.

a. No; Marie’s rate is 16.25 km/h and Tamara’s rate is 17 km/h.

b. Yes; to find both speed rates, you need to divide the distance by the time.

c. No; Marie’s distance and time are greater than Tamara’s distance and time.

d. Yes; Marie’s and Tamara’s rates are almost the same.

____ 9. Solve the proportion .

a. r = 528 c. r = 10

b. r = 4.09 d. r = 8.8

____ 10. The Anderson family is preparing for a family reunion. They think they will need 22 juice boxes for every 6

children who attend. How many juice boxes will they need if they are expecting 12 children?

a. 22 juice boxes c. 44 juice boxes

b. 264 juice boxes d. 132 juice boxes

____ 11. Tell whether and similar. The measures of the corresponding angles are equal.

A

BC

15

12

20

X

YZ

5

4

7

a. similar b. not similar

____ 12. Tell whether parallelogram ABCD and parallelogram WXYZ are similar. The measures of the corresponding

angles are equal, and the opposite sides are equal.

12

8

A B

CD

9

6

W X

YZ

a. not similar b. similar

____ 13. Tell whether trapezoid ABCD and trapezoid WXYZ are similar. The measures of the corresponding angles are

equal.

18

14

22

14

A B

CD

9

7

11

7

W X

YZ

a. not similar b. similar

____ 14. Tell whether the rectangles are similar. If so, write the similarity ratio and a similarity statement. The

measures of the corresponding angles are equal, and the opposite sides are equal.

6

9M N

OP

10

15R S

TU

a. similarity ratio:

rectangle MNOP ~ rectangle RSTU

b. The rectangles are not similar.

c. similarity ratio:


d. similarity ratio:


____ 15. . Find XY.

A

BC

16.517

X

YZ

8.5 ?

a. s = 8 c. s = 8.25

b. s = 33 d. s = 8.76

____ 16. The front of Jane’s house is similar in shape to the front of Spot’s doghouse. The base of the doghouse is 5

feet and the height is 6 feet. If the height of Jane’s house is 30 feet, what is the length of its base? If necessary,

round your answer to the nearest tenth.

Jane30

base = x

Spot

5

6

a. 30 ft c. 36 ft

b. 25 ft d. 29 ft

____ 17. Juan sees a maple tree and a pine tree in the forest. He knows that the pine tree is 20.68 feet tall. On a sunny

day, the shadow of the pine is 4.2 feet long while the maple’s shadow is 20.02 feet long. Estimate the height

of the maple tree.

a. about 63 feet c. about 100 feet

b. about 97 feet d. about 80 feet

____ 18. A model airplane is built to a scale of 1 in.:12 ft. If the model plane is 11 inches long, find the length of the

actual plane. Round your answer to the nearest foot.

a. 1584 feet c. 13 feet

b. 132 feet d. 11 feet

____ 19. Identify the scale factor if the length of a model train engine is 36 inches and the length of the engine itself is

24 feet.

a. 3 c. 288 to 1

b. 3

2 d. 1

8

____ 20. In an investigation, Detective Tracy discovered a photograph that showed his number one suspect at the scene

of the crime. To get a better look, he enlarged the picture by a scale factor of . If the original photo

measured 4 inches by 6 inches, what were the dimensions of the enlargement?

a. 40 inches by 60 inches c. 14 inches by 16 inches

b. 20 inches by 60 inches d. 40 inches by 30 inches

____ 21. Lisa and Susan are driving to college together. They look at a map to find out how far they have to drive. On

the map, Lisa measures the distance to be 3.5 inches. How many miles do they have to drive if the map scale

is 1 in. = 50 mi?

a. 162

3 miles c. 225 miles

b. 175 miles d. 3

50 mile

7th Graede Math 1st Semester Review Ch.4

Answer Section

MULTIPLE CHOICE

1. A

2. B

3. B

4. A

5. A

6. A

7. B

8. A

9. D

10. C

11. B

12. B

13. B

14. A

15. C

16. B

17. D

18. B

19. D

20. A

21. B


Multiple Choice


____ 1. Identify the quadrant that contains the point (3, 6).

10–10 x

10

–10

y

a. Quadrant III c. Quadrant II

b. Quadrant IV d. Quadrant I

____ 2. Identify the quadrant that contains the point (9, 0).

10–10 x

10

–10

y

a. between Quadrants II and III c. between Quadrants I and II

b. between Quadrants I and IV d. between Quadrants III and IV

____ 3. Plot the point (–6, 0) on a coordinate plane.

a.

5–5–10 x

5

10

–5

–10

y

c.

5–5–10 x

5

10

–5

–10

y

b.

5–5–10 x

5

10

–5

–10

y

d.

5–5–10 x

5

10

–5

–10

y

____ 4. Give the coordinates of the point.

5 10–5–10 x

5

10

–5

–10

y

a. (4, –4) c. (–4, 4)

b. (–4, –4) d. (4, 4)

____ 5. The coordinates of three vertices of a rectangle are , , and . Find the coordinates of

the fourth vertex D.

a. c.

b. d.

____ 6. Kathy rented a bicycle. In the first half hour, she rode the bike for 2 miles. Then, she stopped and rested for a

half hour. In the next two hours, she increased her speed and rode as fast as she can to race with another

bicyclist for 12 miles. She stopped by a water fountain to get a drink of water and rested for another half hour.

Finally, she rode the bike back to the rental site to return the bike in the last hours. Sketch a graph to

show the distance that Kathy rode the bike compared to time. Use the graph to find the total distance traveled.

a.

Time (h)

Dis

tan

ce f

rom

Ren

tal S

ite

(mi)

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

2

4

6

8

10

12

14

16

Kathy traveled a total of 14 miles.

c.

Time (h)

Dis

tan

ce f

rom

Ren

tal S

ite

(mi)

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

2

4

6

8

10

12

14

16


b.

Time (h)

Dis

tan

ce f

rom

Ren

tal S

ite

(mi)

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

2

4

6

8

10

12

14

16


d.

Time (h)

Dis

tan

ce f

rom

Ren

tal S

ite

(mi)

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

2

4

6

8

10

12

14

16


____ 7. Tell whether the slope is positive or negative. Then, find the slope.

(2, 4) (5, 2)

2 4 6 8–2–4–6–8 x

2

4

6

8

–2

–4

–6

–8

y

a. positive; 2

3 c. negative;

2

3

b. positive; 2

5 d. negative;

3

2

____ 8. Use the slope of 2 and the point (–6, –3) to graph the line.

a.

3 6 9 12 15–3–6–9–12–15 x

3

6

9

12

15

–3

–6

–9

–12

–15

y

c.

3 6 9 12 15–3–6–9–12–15 x

3

6

9

12

15

–3

–6

–9

–12

–15

y

b.

3 6 9 12 15–3–6–9–12–15 x

3

6

9

12

15

–3

–6

–9

–12

–15

y

d.

3 6 9 12 15–3–6–9–12–15 x

3

6

9

12

15

–3

–6

–9

–12

–15

y

____ 9. Tell whether the graph shows a constant or variable rate of change.

4 8–4–8 x

4

8

–4

–8

y

a. variable rate of change b. constant rate of change


Answer Section

MULTIPLE CHOICE

1. D

2. B

3. C

4. A

5. B

6. B

7. C

8. A

9. B

7th grade math 1st semester review ch -...

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