Part VI Review: ACT Math Study Guide

This set mixes all four Part VI chapters together with no chapter labels. Twenty questions test recognition across the full Integrating Essential Skills Part. No calculator is required, though Desmos or a handheld may still help on a few.

Question 1

Find 35% of 220.

A. 77
B. 66
C. 88
D. 55

Question 2

A value rises from 45 to 63. Find the percent increase.

F. 40%
G. 18%
H. 28%
J. 35%

Question 3

A train travels 315 miles in 6 hours. Find its unit rate in miles per hour.

A. 315
B. 52.5
C. 6
D. 45

Question 4

A rate rises from 8% to 13%. By how many percentage points did it increase?

F. 62.5
G. 5%
H. 8
J. 5

Question 5

Solve the proportion 7/12 = x/60.

A. 35
B. 30
C. 40
D. 25

Question 6

Convert 6 yards to inches.

F. 18
G. 72
H. 6
J. 216

Question 7

Convert 5 square yards to square feet.

A. 15
B. 5
C. 135
D. 45

Question 8

Convert 2 cubic yards to cubic feet.

F. 6
G. 18
H. 54
J. 162

Question 9

Convert 72 miles per hour to feet per second.

A. 72
B. 105.6
C. 96
D. 120

Question 10

Convert 3.75 hours to minutes.

F. 200
G. 210
H. 225
J. 220

Question 11

Four numbers have an average of 16. Three of them are 12, 18, and 22. Find the fourth.

A. 16
B. 18
C. 14
D. 12

Question 12

A grade is weighted 3 credit hours at 3.5 and 5 credit hours at 2.8. Find the weighted average, rounded to four decimal places.

F. 3.0625
G. 3.15
H. 3.25
J. 2.95

Question 13

A trip covers 90 miles at 45 miles per hour, then 90 miles at 60 miles per hour. Find the average speed for the whole trip, rounded to the nearest hundredth.

A. 45
B. 60
C. 51.43
D. 52.5

Question 14

A grade is 60% Exam 1 and 40% Exam 2. A student scores 72 on Exam 1 and 88 on Exam 2. Find the weighted average.

F. 78.4
G. 80
H. 76
J. 82

Question 15

Five numbers have an average of 20. Four of them are 15, 18, 22, and 25. Find the fifth.

A. 20
B. 25
C. 18
D. 15

Question 16

A $70 item is increased 25%, then decreased 20% from the new price. Find the final price.

F. $66.50
G. $70
H. $73.50
J. $56

Question 17

A runner holds a pace of 7 minutes per mile for 4.5 miles. Find the total time in minutes.

A. 24.5
B. 28
C. 31.5
D. 35

Question 18

Four exams average 85. A fifth exam score of 97 is added. Find the new average of all five exams.

F. 91
G. 87.4
H. 85
J. 89.5

Question 19

A recipe for 6 servings needs 3 cups of flour. Scaled to 15 servings, how many tablespoons of flour are needed? (1 cup = 16 tablespoons)

A. 7.5
B. 120
C. 16
D. 90

Question 20

A store marks up its cost by 35% to set a retail price, then discounts 15% from that retail price. If the original cost was $100, find the final price.

F. $100
G. $114.75
H. $120
J. $135

▸ Answers and Explanations

Show the answers and explanations

1: A. 0.35×220=77. Choice B comes from an arithmetic slip while computing 0.35×220.

2: F. (63−45)÷45×100=40%. Choice G reports the raw increase (18) instead of converting it to a percent of the original value.

3: B. 315÷6=52.5. Choice A reports the total miles without dividing by the number of hours.

4: J. A percentage point difference is the raw subtraction: 13−8=5. Choice F computes the percent increase relative to the original value instead of the raw percentage-point difference.

5: A. Cross-multiply: 12x=7(60)=420, so x=35. Choice B comes from a cross-multiplication slip instead of 12x=420.

6: J. 6 yards × 36 inches/yard = 216 inches. Choice F uses the yards-to-feet conversion factor (3) instead of the yards-to-inches factor (36).

7: D. 1 square yard=9 square feet; 5×9=45. Choice A uses the linear conversion factor (3) instead of squaring it for a square-unit conversion.

8: H. 1 cubic yard=27 cubic feet; 2×27=54. Choice F uses the linear conversion factor (3) instead of cubing it for a cubic-unit conversion.

9: B. 72×5,280÷3,600=105.6 feet per second. Choice A reports the original value in miles per hour, forgetting to convert to feet per second.

10: H. 3.75×60=225 minutes. Choice F comes from an arithmetic slip while multiplying 3.75 by 60.

11: D. Total = 16×4=64; 64−(12+18+22)=12. Choice A reports the given average itself instead of solving for the missing value.

12: F. (3×3.5+5×2.8)÷8=(10.5+14)÷8=3.0625. Choice G computes the simple average of the two GPAs instead of the weighted average by credit hours.

13: C. Time: 90/45=2 hr and 90/60=1.5 hr; average speed=180/3.5≈51.43. Choice A reports only the first leg's speed instead of computing the average for the whole trip.

14: F. 0.60(72)+0.40(88)=43.2+35.2=78.4. Choice G computes the simple average of the two exam scores instead of the weighted average.

15: A. Total=20×5=100; 100−(15+18+22+25)=20. Choice B comes from an arithmetic slip while recovering the total or subtracting the known values.

16: G. After the increase: 70×1.25=87.50; after the decrease: 87.50×0.80=70. Choice F comes from an arithmetic slip in the two-step chain.

17: C. 7×4.5=31.5 minutes. Choice A comes from an arithmetic slip while multiplying the pace by the distance.

18: G. Total of the first four: 85×4=340; new total: 340+97=437; new average: 437÷5=87.4. Choice F comes from an arithmetic slip while recomputing the average with the new score.

19: B. Scaled flour: 3×(15/6)=7.5 cups; converted to tablespoons: 7.5×16=120. Choice A stops after scaling the recipe, forgetting to complete the unit conversion to tablespoons.

20: G. Retail: 100×1.35=135; after the discount: 135×0.85=$114.75. Choice F reports the original cost, forgetting to apply either the markup or the discount.

Part VI Review

▸ Answers and Explanations

PART VII · EXECUTION