7th Grade Semester Final (Practice Test)

Math 7 – Second Semester Final – Practice Test

Name__________________________________________ Period______ Date____________ Part 1 – Learning Target 5: I can solve and explain formulas involving volume of geometric solids. 1. Which label would be appropriate for a volume measurement? A. ft² C. in2 B. m³ D. cm 2. What is the volume of the sphere shown below? Use 3.14 for π. A. ≈ 418.66 cm³ B. ≈ 4,186.66 cm³ C. ≈ 12,560 cm³ D. ≈ 34,464.63 cm³ 3. Cindy has a cylindrical water bottle. The water bottle is 8 inches tall and has a 2 inch radius. Approximately how much water can the water bottle hold? Use 3.14 for π.

A. 16 in³ C. 100 in³ B. 50 in³ D. 85 in³ 4. What is the volume of the cone shown below? Use 3.14 for π. A. ≈ 32 m³ B. ≈ 54 m³ C. ≈ 75 m³ D. ≈ 133 m³

5. The area of the base of a trapezoidal pyramid is 30 ft². The pyramid is 13.6 feet tall. What is the volume of the pyramid?

A. 68 ft3 C. 304 ft3 B. 136 ft3 D. 480 ft3 6. The perimeter of the base of a square pyramid is 10 yd. The height of the pyramid is 18 yd. What is the volume of the pyramid?

A. 40 yd3 C. 120 yd3 B. 60 yd3 D. 150 yd3

7. A rectangular prism measures 7 cm by 6.5 cm by 13.2 cm. What is the volume of the prism? A. 65.2 cm³ C. 600.6 cm³ B. 384.5 cm³ D. 818.8 cm³ 8. A cylindrical water barrel is 4 feet tall. It has a 1.5-foot radius. What is the volume of the barrel? Use 3.14 for π. A. 28.26 ft3 C. 49.3 ft3 B. 31.4 ft3 D. 78.5 ft3 9. The base of a square pyramid has sides that are 6 centimeters long. The volume of the pyramid is 144 cubic centimeters. What is the height of the pyramid? A. 10 cm C. 12 cm B. 11 cm D. 15 cm

10 cm m

6.8 m 8 m

4 m

7th Grade Semester Final (Practice Test)

10. Volume can be measured in “______ meters”? A. square C. regular B. cubic D. triangular 11. A cylinder has been removed from a cube. What is the remaining volume of the solid? Use 3.14 for π. A. 21.86 cm³ B. 87.92 cm³ C. 343 cm³ D. 255.08 cm³ 12. A rectangular prism is 6 cm long, 4 cm wide and 9 cm tall. What is the volume of the prism? A. 24 cm3 B. 54 cm3 C. 216 cm3 D. 320 cm3 13. Most of the volume formulas contain “h”. What does the “h” stand for? A. Base length B. Height C. Area of the Base D. Perimeter of the Base 14. What is the volume of the composite solid? A. 256 cm3 B. 320 cm3 C. 482 cm3 D. 510 cm3

15. If the volume of the cylinder below is 100.48 cm³, what is the height? Use 3.14 for π. A. 0.5 cm B. 1 cm C. 1.5 cm D. 2 cm 16. When solving a problem like #11, which is the general strategy? A. Find the volume of each solid and add them together. B. Find the volume of the rectangular prism and then subtract off the volume of the cylinder. C. Find the volume of each solid and multiply them. D. Find the surface area of each solid and subtract them. 17. What is the volume of this solid? A. 72 yd³ B. 48 yd³ C. 288 yd³ D. 144 yd³ 18. A cylinder has a volume of 90 cubic centimeters. What is the volume of a cone with a congruent base and height to the cylinder? A. 180 cm3 C. 45 cm3 B. 270 cm3 D. 30 cm3

7 cm

7 cm

7 cm

2 cm

5 cm

9 cm

4 cm

10 cm

h

4 cm

4 yd

6 yd

12 yd

7th Grade Semester Final (Practice Test)

19. What is the volume of this solid? A. 287.66 cm³ B. 352.4 cm³ C. 125.37 cm³ D. 408.23 cm³

20. Jim has a cylindrical above ground pool in his back yard. The radius of the pool is 8 feet. The pool is 3.5 feet tall. When the pool if half full, how much water does it hold? Use 3.14 for π. A. 87.92 ft3 C. 43.96 ft3 B. 351.68 ft3 D. 703.36 ft3

Part 2 – Learning Target 6: I can solve problems applying scale factor to geometric figures or scale drawings. 21. What is the value of x in the proportion

!!"= !

! ?

A. 8.3 C. 16.8 B. 10.7 D. 18.5 22. ΔMAT is similar to ΔRUG. Which side of ΔRUG corresponds to AM in ΔMAT? A. RU B. UG C. UR D. RG 23. Inessa ran 5 laps in 12 minutes. How long would it take her to run 15 laps at this pace? A. 36 minutes C. 24 minutes B. 26 !

! minutes D. 33 !

! minutes

24. Trevor bought 8 packages of cake mix for $22.00. How much would 13 packages of cake mix cost? A. $30.00 C. $36.25 B. $35.75 D. $37.50

25. What is the value for y in the similar figures? A. 6.5 B. 7 C. 7.5 D. 8 26. Mia ran 12 laps in 10 minutes. How many laps did Mia run in 1 minute? A. 1.3 laps per min C. 1.4 laps per min B. 1.2 laps per min D. 0.83 laps per min 27. What is the scale factor for the similar figures? A. 2 : 3 B. 1 : 2 C. 3 : 4 D. 4 : 5 28. A map scale is 1 inch : 6 kilometers. If two cities are 48 kilometers apart in real life, how far apart are they on the map? A. 10 inches C. 8 inches B. 12 inches D. 1 inch

18

24

32 10

24 y

R

U

G

M

A

T

3.8 cm

The area of the base is 75.7 cm2.

7th Grade Semester Final (Practice Test)

29. Two similar triangles have a scale factor of 2 : 3. The smaller triangle has a perimeter of 18 inches. What is the perimeter of the larger triangle? A. 18 inches C. 27 inches B. 21 inches D. 36 inches Use the figure below for questions 30-32. 30. What is the scale factor? A. 4 : 3 C. 7 : 4 B. 7 : 3 D. 3 : 4 31. What is the ratio of the perimeters? A. 4 : 3 C. 7 : 4 B. 7 : 3 D. 3 : 4 32. What is the ratio of the areas? A. 16 : 9 C. 25 : 9 B. 25 : 16 D. 49 : 9 33. A wildlife ranger caught and tagged 108 rabbits in a forest and then released them back into the wild. Later, he caught 405 rabbits, and of those, 45 had tags. Approximately how many rabbits are in the forest? A. 972 C. 12 B. 169 D. 1000

34. A map has a scale of 1 inch : 8 miles. If two cities are 8 inches apart on the map, how far apart are they in real life? A. 8 miles C. 48 miles B. 16 miles D. 64 miles 35. Victor wanted to know the height of a tree at his friend’s house. On Saturday morning, he measured the shadow of the tree along the ground to be 21 feet long. At the same time, he measured his own shadow to be 3 feet long. Victor is 6 feet tall. Find the height of the tree. A. 10.5 feet C. 86 feet B. 42 feet D. 39 feet 36. What is the value for x in the similar figures? A. 15 B. 21 C. 22 D. 23 37. A blue print of a house has a scale of 1 inch : 3 feet. Find the actual length of a wall that is 9 inches on the blue print? A. 9 feet C. 27 feet B. 18 feet D. 36 feet 38. Two squares are similar. The smaller one has a side length of 3 and the larger has a side length of 4. What is the ratio of their areas? A. 3 : 4 C. 4 : 3 B. 6 : 8 D. 9 : 16

42 cm

18 cm

24 8

5 x

7th Grade Semester Final (Practice Test)

39. Two similar triangles have a scale factor of 2 : 3. The smaller triangle has a perimeter of 16 inches. What is the perimeter of the larger triangle? A. 17 inches C. 21 inches B. 24 inches D. 27 inches

40. A model car has a scale of !

!". The length

of the frame on the model is 8 inches. How long is the frame (in feet) on the real car? A. 144 C. 12 B. 2.25 D. 15

Part 3 – Learning Target 7: I can understand and use proportions to solve percent problems.

41. What is 45% as a decimal? A. 0.4 C. 0.85 B. 0.45 D. 0.9 42. Corey hit 5 homeruns at batting practice out of 20 pitches thrown. What is the ratio of homeruns Corey hit to the total pitches thrown? A. !

! C. !

!

B.  !! D. !

!

43. Which number is the smallest? A. !

! C. 0.44

B. !! D. 42%

44. The Central Park fish pond has several different varieties of fish. If 34% of the fish are Koi and the pond has 550 total fish, how many fish are Koi? A. 156 C. 195 B. 187 D. 203

45. What is 70% of 140? A. 75 C. 98 B. 104 D. 89 46. Lydia wants to buy a new computer that has an original price $800. It is on sale for 15% off. How much would her discount be? A. $15 C. $120 B. $60 D. $680 47. A car salesman earns a 5% commission on his car sales. If the salesman sells a car for $24,000, how much does he make? A. $800 C. $1,200 B. $1,000 D. $1,400 48. Andrew decides to treat his friends to dinner. The bill for their meals is $54.60. Andrew wants to leave a 20% tip. How much money should he leave as a tip for the waiter? A. $10.92 C. $12.37 B. $11.08 D. $13.75

7th Grade Semester Final (Practice Test)

49. If Stephanie invests $4,000 at an annual rate of 5.5%, how much money will she have in her account at the end of the year? A. $4,550 C. $4,250 B. $4,050 D. $4,220 50. What is the value of !

! written as a

percent? A. 15% C. 55% B. 30% D. 60% 51. Lia bought a new jacket. The original price of the jacket was $48 but it was on sale for 15% off. How much did Lia pay for the jacket after the discount? A. $7.20 C. $40.80 B. $33.00 D. $42.20 52. A landlord decides to raise the rent on one of his properties. Currently he is charging $1,000 per month for rent. He plans to raise the rent 5%. What is the new monthly rental rate? A. $1,005 C. $1,500 B. $1,050 D. $1,025 53. Last year, 15 dogs entered the local dog show. This year, 20 entered. What is the percent increase? A. 20% C. 33 !

!%

B. 25% D. 75%

54. Seventy-five of the 120 songs on Joey’s iPod are Rap songs. What percent of his songs are Rap songs? A. 50.4% C. 66.6% B. 55.8% D. 62.5% 55. What is 0.5% of 44? A. 0.22 C. 0.11 B. 2.2 D. 22 56. Bulk pretzels are $1.45 per pound at Winco. Jill wants to know how much 2.5 pounds would cost. Which proportion would help solve this problem? A. $".!"

!  !"#$%= $  !

!.!  !"#$%&

B. !  !"#$%$".!"

= $  !!.!  !"#$%&

C. !  !"#$%$".!"

= !.!  !"#$%&$  !

D. Both A & C

57. Andre’s car gets 32 miles per gallon of gas. Andre wants to travel 300 miles and wants to know how many gallons of gas he will need. Which proportion would help him solve this problem? A. !"  !"#$%

!  !"#!"#= !  !"##$%&

!""  !"#$%

B. !"  !"#$%!  !"##$%

= !""  !"#$%!  !"##$%&

C. !  !"##$%!"  !"#$%

= !""  !"#$%!  !"##$%&

D. Both A & C

7th Grade Semester Final (Practice Test)

58. 18 is what percent of 45? A. 25% C. 40% B. 35% D. 45% 59. What is 30% of 60? A. 18 C. 24 B. 20 D. 30

60. Six is 3% of what number? A. 0.18 C. 18 B. 2 D. 200

Part 4 – Learning Target 8: I can summarize and compare data displays and make inferences about populations using random samples.

Use the data set below to answer questions 61-64.

25, 28, 32, 32, 37, 41, 43, 55, 58 61. What is the mean of the data set above? A. 39 C. 38 B. 41 D. 43 62. What is the median of the data set above? A. 32 C. 41 B. 37 D. 34.5 63. What is the mode of the data set? A. 25 C. 58 B. 43 D. 32 64. What is the range of the data set? A. 25 C. 58 B. 33 D. 58

65. Which measure of center best represents the following data set? 29, 29, 32, 33, 34, 37, 59 A. the mean C. the median B. the mode D. the range 66. What are the mean, median and mode of the following data set?

27, 31, 33, 33, 35, 45

A. Mean = 32, Median = 32, Mode = 33 B. Mean = 33, Median = 32, Mode = 27 C. Mean = 34, Median = 33, Mode = 33 D. Mean = 35, Median = 33, Mode = 45 67. What is the mode of the following data set?

10, 11, 11, 11, 17, 21, 24, 24, 30

A. 11 C. 24 B. 17 D. 11 and 24

7th Grade Semester Final (Practice Test)

Use the histogram below to answer questions 68 and 69.

68. How many values are less than 18 in this histogram? A. 5 C. 7 B. 6 D. 8 69. What is the ratio of values less than 21 to total values? A. 3 : 13 B. 3 : 10 C. 8 : 13 D. 1 : 2 70. Which stems would be best to use to display the following data set?

608, 653, 716, 737, 756, 778, 789, 902, 935

A. 60-93 B. 6, 7, 8, 9 C. 6, 7, 9 D. 1-10

The stem-and-leaf plot shows some of the point totals of students on the latest quiz. Use the information to answer questions 71 and 72. 71. How many students scored above 20 points on this quiz? A. 5 C. 7 B. 6 D. 8 72. If 30 students took this test, about how many would you expect to have scored at least 20 points? A. 13 C. 20 B. 15 D. 24 73. Michael’s goal is to score an average of 18 points per game in his five basketball games. In his first four games, he scored 12, 18, 15, and 20 points. At least how many points will he need in his fifth game to reach his goal? A. 22 C. 19 B. 25 D. 23

0 8 1 2 7 2 3 3 5 8 3 4 5

Key: 2 | 5 = 25

7th Grade Semester Final (Practice Test)

The box-and-whisker plot shows the ages of registered drivers in a city. Use the data to answer questions 74 and 75. 74. What was the median age of drivers in this city? A. 36 years old C. 38 years old B. 28 years old D. 52 years old 75. If 100 random drivers were asked their age, what percent would you expect to be 52 or older? A. 25% C. 75% B. 50% D. 20% 76. What are the missing numbers in the data set? Assume the numbers are in order. 23, 24, ___, 29, 33, ___

Range = 15 Mean = 29 A. 29, 37 C. 25, 48 B. 28, 36 D. 27, 38

77. What is the five-number summary of the following data set?

16, 19, 22, 23, 25, 27, 30, 35, 44, 45, 47

A. 19 ~ 23 ~ 27 ~ 44 ~ 45 B. 16 ~ 22.5 ~ 27 ~ 40 ~ 47 C. 16 ~ 22 ~ 27 ~ 44 ~ 47 D. 19 ~ 22 ~ 27 ~ 40 ~ 45

78. Consider the following data set: 39, 44, 45, 48, 51

A new number, 8, is included in the data set. How will that affect the mean and median of the data set? A. The mean and median will increase the same amount B. The median will change more than the mean C. Neither the mean nor the median will change D. The mean will change more than the median 79. Candace collected data about the number of hours students spend watching TV each week. She determined the five-number summary to be:

1.5 ~ 9 ~ 13 ~ 16.5 ~ 22

What percent of students watched TV for at least 13 hours per week? A. 10% C. 50% B. 25% D. 75% 80. Use the given information to find the missing numbers in the following ordered data set. 13, ___, 22, 25, 28, 29, ___

Range = 22 IQR = 12

A. 22, 25 C. 17, 35 B. 18, 35 D. 17, 37

7th Grade Semester Final (Practice Test)

Circle Formulas

Circumference 𝑪 = 𝟐𝝅𝒓 = 𝒅𝝅

Circle Area 𝑨 = 𝝅𝒓𝟐

Area Formulas Rectangle Area

𝑨 = 𝒍𝒘 Parallelogram Area

𝑨 = 𝒃𝒉 Triangle Area

𝑨 =𝟏𝟐𝒃𝒉 Trapezoid Area

𝑨 =𝟏𝟐𝒉(𝒃𝟏 + 𝒃𝟐)

Volume Formulas Prism Volume

𝑽 = 𝑩𝒉 Cylinder Volume 𝑽 = 𝑩𝒉 = 𝝅𝒓𝟐𝒉

Pyramid Volume

𝑽 =𝟏𝟑𝑩𝒉 =

𝑩𝒉𝟑 Cone Volume

𝑽 =𝑩𝒉𝟑=𝝅𝒓𝟐𝒉𝟑

Sphere Volume

𝑽 =𝟒𝟑𝝅𝒓𝟑 =

𝟒𝝅𝒓𝟑

𝟑