2017-2018 7 grade math final comprehensive · case 7th grade math do not reproduce page 6 go to the...

2017-2018

7th Grade Math

Final Comprehensive (Selected Response)

Chattanooga Girls Leadership Academy Tennessee

Published by TE21, Inc. January 2018

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CALCULATOR INACTIVE

The items in this test are based on the Tennessee Academic Standards for Mathematics.

DIRECTIONS FOR THE CALCULATOR INACTIVE SECTION OF THE TEST: Calculators may not be used during this test. Read each problem carefully. Choose the best answer from the choices given. Fractions in some answer choices may have been

simplified. Check each answer choice to see if this has been done.

Diagrams used in the test may not be drawn to scale. Stop when you see the words “STOP. END OF

CALCULATOR INACTIVE SECTION.” When you have completed the calculator inactive

questions, read and follow the directions at the end of this section of the test.



1. Which equation demonstrates a correct product of two rational numbers?

A - 2

3 ×

1

5 =

2

15

B 2

3 × -

1

5 =

−2

−15

C −2

3 ×

1

−5 = -

2

15

D - 2

3 × -

1

5 =

2

15

2. What is -7.13 + (-4.2 + 10.6) simplified?

A -21.93

B -13.53

C -0.73

D 7.67

3. The table shows the cost of a taxi ride after a certain number of minutes.

Minutes Cost

3 $2.25

6 $4.50

9 $6.75

What is the cost of a 1-minute taxi ride?

A $0.75

B $1.25

C $1.75

D $2.25



4. What is 𝟔

𝟏𝟏 written as a decimal?

A 0.54

B 0.54̅̅̅̅

C 1.83

D 1.83̅

5. A chef uses 𝟏

𝟐 cup of tomatoes for every

𝟏

𝟖 cup of onions to make salsa. How many

cups of onions will the chef need for 1 cup of tomatoes?

A 1

16 cup of onions

B 1

4 cup of onions

C 4 cups of onions

D 16 cups of onions

6. Which expression has the greatest value?

A -2 ⋅ -2 ÷ 1

2

B -2 ⋅ - 1

2 ÷ 2

C -2 ⋅ 1

2 ÷

1

2

D -2 ⋅ 2 ÷ 2



7. A middle school is selling candy bars to raise money for new calculators. The graph

shows the number of candy bars sold, x, and the amount of money collected, y.

Which equation represents this relationship?

A y = 0.5x

B y = 1.25x

C y = 2.5x

D y = 5x

8. A dieter loses a total of 24 pounds over 6 months. The dieter uses the expression

−𝟐𝟒

𝟔 to represent the average weight loss each month.

Which expressions are equivalent to the expression the dieter uses? Select ALL that apply.

A 24

−6

B 24

6

C - 24

6

D 6

−24

E 6

24



9. Last month, an investor’s stock portfolio was worth $46,950. The value of the stock

portfolio fell by $2,388.50 each week for 4 weeks. What is the value of the stock portfolio at the end of the 4 weeks?

A $56,504

B $44,562

C $37,396

D $9,554

10. Tiffany has 4.1 GB of data to use in one 4-week billing cycle on her cell phone. Any

unused data will roll over to the next cycle. The table shows how much data Tiffany uses each week before her next billing cycle.

Week Data Usage (in GB)

1 0.8

2 1.3

3 0.9

4 1.1

How much data does Tiffany have left to roll over to the next billing cycle at the end of the four weeks?

A 0 GB of data

B 0.8 GB of data

C 3 GB of data

D 3.3 GB of data

11. It takes a biker 𝟏

𝟑 hour to ride

𝟖

𝟑 miles. What is the biker’s rate, in miles per hour?

A 1

8 mile per hour

B 8

9 mile per hour

C 6 miles per hour

D 8 miles per hour



12. Four tables are shown.

Table 1 Table 2 Table 3 Table 4

x y 0 0

2 1

4 1.5

6 2

x y 2 3

3 4.5

4 6

5 7.5

x y 0 5

2 7

4 9

6 11

x y 2 4

3 9

4 16

5 25

Which table represents a proportional relationship? A Table 1

B Table 2

C Table 3

D Table 4

13. Castor goes deep-sea diving. He starts at sea level and dives 6𝟏

𝟒 feet every minute for

2𝟏

𝟐 minutes. After 2

𝟏

𝟐 minutes of diving, Castor’s speed slows down to 4

𝟏

𝟖 feet every

minute.

If Castor continues to dive 4𝟏

𝟖 feet every minute for 3 minutes, what is his depth at

the end of the last 3 minutes?

A 157

8 feet below sea level

B 20 feet below sea level

C 28 feet below sea level

D 291

16 feet below sea level

14. A scuba diver is at an elevation of 53 feet below sea level. A hiker is at an elevation of

228 feet above sea level.

What is the difference in elevation between the scuba diver and the hiker?

A -281 feet

B -175 feet

C 175 feet

D 281 feet



15. The table shows the number of jumping jacks a student completes in a certain number

of seconds.

Time (in seconds) Jumping Jacks

4 5

8 10

12 15

16 20

If the pattern continues, which statement about the student’s constant of proportionality with regard to the number of jumping jacks per second and per minute is true?

A The student completes 11

4 jumping jacks per second and 37

1

2 jumping jacks per minute.

B The student completes 11

4 jumping jacks per second and 75 jumping jacks per minute.

C The student completes 4

5 jumping jack per second and 24 jumping jacks per minute.

D The student completes 4

5 jumping jack per second and 48 jumping jacks per minute.

END OF CALCULATOR INACTIVE SECTION

DIRECTIONS: Look back over your answers for the calculator inactive

questions. You will not be able to go back and work on these questions once you are given a calculator.

Raise your hand to let your teacher know you are ready to begin the calculator active questions.

Do not begin work on the calculator active test questions until your teacher has given you a calculator.

When your teacher has given you a calculator, GO TO THE NEXT PAGE, and BEGIN the calculator active questions.

Stop when you see the words “STOP. END OF SELECTED RESPONSE.”



16. Consider the expression.

5(x + 2) – 7(x + 2) Which choice simplifies the expression correctly ? A 12x + 24

B 12x – 4

C -2x + 24

D -2x – 4

17. Bailey and Marcus buy a dog that weighs 18 pounds. The dog gains 2𝟑

𝟒 pounds each

year. The dog now weighs 34𝟏

𝟐 pounds.

How many years ago did Bailey and Marcus buy the dog?

A 4 years

B 5 years

C 6 years

D 7 years

18. Kelly purchases merchandise online. She pays a total of $c for the merchandise

including the shipping and handling. The shipping and handling are 40% of Kelly’s total cost. The expression c (1 – 0.4) represents the cost of the merchandise.

Which is an equivalent expression for the cost of the merchandise?

A c (0.4)

B c (0.6)

C c (1.4)

D c (1.6)



19. Which expression is equivalent to 5(x + 𝟒

𝟓 ) −

𝟏

𝟒 (12x − 52)?

A 2x − 11

B 2x − 9

C 2x + 17

D 2x + 25

Use the information given to answer questions 20-21. Student X rolls a fair number cube numbered from 1-6. Student Y tosses a coin 30 times. The table shows the results for Student Y.

Heads Tails

12 18

Part A 20. Based on the table, what is the relative frequency of Student Y ’s coin landing on tails?

A 18%

B 40%

C 60%

D 82%

Part B 21. If Student X rolls the number cube 120 times, approximately how many times should

the number cube land on 5?

A 60 times

B 54 times

C 24 times

D 20 times



22. Which graph displays the solution to the inequality -6x − 72 > 24 correctly ?

A

B

C

D

23. Consider the diagram.

What is the value of n ? A 46

B 38

C 27

D 20



24. A student expresses the dimensions of a rectangle in terms of m and n. The table

shows the dimensions.

Length 4(m + 2n )

Width 6(m + n )

Which expression represents the perimeter of the student’s rectangle? A 10m + 3n B 10m + 14n C 20m + 6n D 20m + 28n

25. Nathan eats 2,000 calories per day. His food intake is based on different categories

within the food pyramid. Fruits and vegetables make up 33% of Nathan’s daily intake,

dairy products are 𝟑

𝟐𝟎 of his daily intake, and non-dairy products make up 12%.

How many calories does Nathan have left to enjoy in another food category?

A 1,200 calories

B 1,000 calories

C 800 calories

D 660 calories

26. Craig and Madison spend d dollars on dinner and then tip the server 18%. Which

expressions represent the total cost of Craig and Madison’s dinner? Select ALL that apply.

A 0.82d

B 1.18d

C d + 0.18

D d + 0.18d

E d + 1.18



27. Mr. and Mrs. Barnes budget to spend $350 on a coat, shoes, and a television at a

department store. The table shows how much Mr. and Mrs. Barnes would spend if they buy all the items.

Item Amount Spent

coat 55% off of $180

shoes 𝟏

𝟐 off of $150

television $240

Which statement about Mr. and Mrs. Barnes’s budget is true?

A Mr. and Mrs. Barnes are over their budget by $46.

B Mr. and Mrs. Barnes are over their budget by $64.

C Mr. and Mrs. Barnes are under their budget by $46.

D Mr. and Mrs. Barnes are under their budget by $64.

28. A gymnast competes in eight gymnastic meets during the year and records the scores

for each meet.

8.4, 3.1, 8.2, 2.3, 9.0, 8.5, 8.6, 3.1

Which statement about the comparison of the mean and median scores is true?

A The mean score is higher than the median, which indicates the gymnast had a few meets scoring higher than 6.4, negatively affecting the mean.

B The mean score is higher than the median, which indicates the gymnast had a few meets scoring higher than 8.3, negatively affecting the median.

C The mean score is lower than the median, which indicates the gymnast had a few meets scoring lower than 6.4, negatively affecting the mean.

D The mean score is lower than the median, which indicates the gymnast had a few meets scoring lower than 8.3, negatively affecting the median.



29. Eleanor is randomly choosing a pair of socks from her dresser. She has 6 pairs of

white socks, 8 pairs of black socks, and 14 pairs of gray socks.

Which statement is true?

A Eleanor has an unlikely chance of choosing a pair of gray socks.

B Eleanor has a likely chance of choosing a pair of white socks.

C Eleanor has a likely chance of choosing a pair of black socks.

D Eleanor has neither an unlikely nor likely chance of choosing a pair of gray socks.

30. Jonathan was 45 inches tall when he started kindergarten. He grew an average of 2.5 inches every year. Jonathan is now 62.5 inches tall.

Which equation can be used to find how many years ago Jonathan started kindergarten, and how many years ago was it?

A (45 + 62.5) ÷ 2.5 = x 7 years

B 2.5x + 45 = 62.5 7 years

C (45 + 62.5) ÷ 2.5 = x 43 years

D 2.5x + 45 = 62.5 43 years

31. A basketball player scores p points each quarter for each of the four quarters of the

regular game and then scores 5 points in overtime. Which expression represents the total number of points the basketball player scores during all four quarters and overtime?

A 4(p + 5) B 4p + 5 C 5(p + 4) D 5p + 4



32. A cashier’s weekly pay increases from $80 to $100. What is the percent increase in the

cashier’s weekly pay?

A 40%

B 25%

C 20%

D 10%

Use the information given to answer questions 33-34.

Celine and Diego are both playing a game. The table shows their scores, in points, at the end of each round of the game.

Round Celine Diego

1 12.8 8.2

2 5.9 15.1

3 19.3 1.7

4 16.1 4.9

5 7.4 13.6

Part A

33. What is the difference between Celine’s and Diego’s average scores?

A 3.6 points

B 4.6 points

C 18 points

D 21 points

Part B

34. Which statement is true?

A Celine’s scores have a greater range value than Diego’s scores, while Diego’s scores have a greater interquartile range value than Celine’s scores.

B Diego’s scores have a greater range value than Celine’s scores, while Celine’s scores have a greater interquartile range value than Diego’s scores.

C Celine’s scores and Diego’s scores have the exact same range values but different interquartile range values.

D Celine’s scores and Diego’s scores have the exact same range and the exact same interquartile range values.



35. A student draws triangle EFG. The table shows the measurements of each angle of the

triangle.

Angle Measurement

∠EFG 90o

∠FGE 45o

∠GEF 45o


A Triangle EFG is not a unique triangle because the side lengths are not given, so the angle measurements can form many different triangles.

B Triangle EFG is not a unique triangle because the three angle measurements do not add up to 360o, so they cannot form a triangle.

C Triangle EFG is a unique triangle because the angle measurements indicate triangle EFG is a unique, isosceles triangle.

D Triangle EFG is a unique triangle because the three angle measurements add up to 180o, which can make only one, unique triangle.

36. A chef makes a fruit salad using pears and mangos. Pears and mangos each cost

$2.25 per fruit. The chef buys x pears and y mangos. Which two expressions represent the chef’s cost of making the fruit salad?

A 2.25xy B 2.25 + xy C 2.25(x + y ) D 2.25x + y E 2.25x + 2.25y



37. The dimensions of a rectangular prism are shown in the table.

Length 10 in.

Width 12 in.

Height 16 in.

What is the surface area of the rectangular prism? A 3,840 in.2

B 1,920 in.2

C 944 in.2

D 472 in.2

38. Jaden and Monica go to the mall.

Jaden brings $120, and Monica brings $144. Jaden spends 80% of his money.

Monica spends 𝟑

𝟒 of her money.

Which statement is true? A Jaden spends $12 more than Monica because Jaden spends $36, and Monica spends $24. B Jaden spends $12 more than Monica because Jaden spends $108, and Monica spends $96. C Monica spends $12 more than Jaden because Monica spends $36, and Jaden spends $24. D Monica spends $12 more than Jaden because Monica spends $108, and Jaden spends $96.

39. A rectangle has a width, w, equal to 6 less than the length, 𝓵. Which expressions

represent ways to find the perimeter of the rectangle? Select ALL that apply.

A 4ℓ + 12

B 4ℓ − 12

C 2(ℓ − 6) + 2ℓ

D 2(6 − ℓ) + 2ℓ

E 12 + 2ℓ + 2ℓ



40. The distance on a map between two locations is 2.25 inches. If 1 inch = 24 miles,

what is the actual distance between the two locations?

A 54 miles

B 48 miles

C 26.25 miles

D 10.67̅ miles

41. Mr. Smith places 10 cards labeled 1, 5, 8, 9, 11, 19, 21, 23, 28, and 30 in a bowl. He

will randomly select one card from the bowl without looking.

What is the probability that Mr. Smith will select a card with a two-digit number?

A 1

8

B 2

5

C 3

5

D 3

2

42. Joy and Tyler conduct a survey on the favorite video games of all middle school-aged

students. Which population sample produces the most valid results for the survey?

A surveying all 7th grade boys

B surveying every 5th student who walks into school in the morning

C surveying every girl on the volleyball team

D surveying every other student in the eighth grade lunch line

43. The temperature in a town starts at -6° Celsius at 7:00 a.m. and rises 3° Celsius every

hour. Which inequality shows the number of hours, x, past 7:00 a.m. it will take for the temperature to be more than 3° Celsius?

A x < 3

B x > 3

C x < 1

D x > 1



44. A carpenter inscribes a circle within a square. The carpenter shades in the area of the

square outside of the circle. The circumference of the circle is 50.24 inches.

What is the approximate area of the shaded part of the carpenter’s figure? (Use 3.14 as an approximation of pi.) A 55.04 square inches

B 96.78 square inches

C 152.32 square inches

D 200.96 square inches

45. The tables show the ages of a random sample of female and male teachers at a school.

Ages of Female Teachers

32 47 25

38 29 33

52 41 40

Ages of Male Teachers

29 60 42

37 32 51

44 47 49

Which statements are true? Select ALL that apply.

A On average, female teachers at the school are older than male teachers.

B The average age of male teachers at the school is 6 years older than the average age of female teachers.

C The maximum age of male teachers at the school is 3 years older than the maximum age of female teachers.

D The median ages of female and male teachers at the school are the same.

E The minimum age of female teachers at the school is 4 years younger than the minimum age of male teachers.



46. Two random samples of students are asked which types of music they prefer. The

table shows the results.

Student Sample Country Pop Rap Total

#1 16 53 31 100

#2 9 67 24 100

According to the survey, which statement is true?

A The majority of the students prefer to listen to pop music.

B The majority of the students prefer to listen to rap music.

C From both samples combined, 55% of the students prefer to listen to rap music.

D From both samples combined, 25% of the students prefer to listen to country music.

47. Kendrick and Perla spend a total of $92 at an amusement park. They spend $28 on

parking and lunch combined, and the rest on two admission tickets.

How much does each admission ticket cost?

A $18.00

B $32.00

C $36.00

D $64.00

48. Nancy and Fabian’s dinner bill at a restaurant is $28 before tax. The tax on their meal is 2.5%.

How much is Nancy and Fabian’s final bill after tax is added?

A $21.00

B $27.30

C $28.70

D $35.00


Page 20 STOP. END OF SELECTED RESPONSE.

49. A lifeguard earns $12 per hour working during the summer. The lifeguard works a

total of 52 hours and spends 80% of the money earned on a video game system.


A The lifeguard has about $500 left after earning $624 and spending about $125 of that on the video game system.

B The lifeguard has about $500 left after earning $624 and spending about $499 of that on the video game system.

C The lifeguard has about $125 left after earning $624 and spending about $125 of that on the video game system.

D The lifeguard has about $125 left after earning $624 and spending about $499 of that on the video game system.

50. A student simplifies an expression as -12z – 72 correctly. Which expression could the

student have simplified?

A -6(2z + 12) B -4(3z – 68) C 6(-2z – 72) D 12(-z + 6)

2017-2018 7 grade math final comprehensive · case 7th grade math do not reproduce page 6 go to the...

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