Drill 1 · Math · Integrating Essential Skills
ACT Math: Integrating Essential Skills (Drill 1) is a Math practice drill covering Integrating Essential Skills. It contains 5 original questions created by Brian Stewart, a Barron's test prep author with over 20 years of tutoring experience.
Integrating Essential Skills questions require you to apply mathematical concepts to real-world contexts. This drill covers percents, unit rates, percent change, multi-step rate problems, and proportional reasoning.
Question 1. A store is having a 35% off sale. A jacket originally costs $120. What is the sale price of the jacket?
Explanation: Discount amount = 35% × $120 = 0.35 × 120 = $42. Sale price = $120 − $42 = $78. Alternatively, the sale price is 65% of the original: 0.65 × $120 = $78. Choice A is the discount amount itself ($42), not the sale price. Choice C results from computing 30% off instead of 35%: 0.70 × $120 = $84 ≈ $85. Choice D results from adding the discount rather than subtracting it: $120 + $35 = $155.
Question 2. A car travels 351 miles on 13 gallons of gas. At the same rate, how many miles can the car travel on a full tank of 20 gallons?
Explanation: Unit rate = 351 ÷ 13 = 27 miles per gallon. Miles on 20 gallons = 27 × 20 = 540. Choice A results from computing 25 mpg × 20 = 500, using an incorrect unit rate of 25. Choice B results from computing 26 × 20 = 520, rounding the unit rate down to 26. Choice D results from computing 28 × 20 = 560, rounding the unit rate up to 28.
Question 3. A town's population was 24,000 in 2010. By 2020, the population had grown to 30,000. What was the percent increase in population from 2010 to 2020?
Explanation: Percent increase = (change ÷ original) × 100 = (6,000 ÷ 24,000) × 100 = 0.25 × 100 = 25%. Choice A results from dividing the change by the new population instead of the original: 6,000 ÷ 30,000 = 20%. Choice C results from dividing the change by 100,000 or confusing the populations: 6,000 ÷ 100,000 = 6%. Choice D results from computing the ratio of the original to the change and expressing as a percent: 24,000 ÷ 30,000 × 100 ≈ 80%.
Question 4. Maya drives from City A to City B, a distance of 240 miles, at an average speed of 60 mph. She then drives from City B to City C, a distance of 150 miles, at an average speed of 50 mph. What is Maya's average speed, in mph, for the entire trip?
Explanation: Average speed = total distance ÷ total time. Total distance = 240 + 150 = 390 miles. Time A to B = 240 ÷ 60 = 4 hours. Time B to C = 150 ÷ 50 = 3 hours. Total time = 4 + 3 = 7 hours. Average speed = 390 ÷ 7 ≈ 55.7 ≈ 55 mph (to the nearest whole number). Choice A is correct. Choice B results from computing (390) ÷ (4 + 3 − 0.5) = 390 ÷ 6.5 ≈ 60... or rounding 390/7 up to 56. Choice C results from computing (60 + 50) ÷ 2 × some adjustment ≈ 57, incorrectly averaging the two speeds directly. Choice D results from a small arithmetic error in total time, using 7.2 hours: 390 ÷ 7.2 ≈ 54.
Question 5. A recipe that makes 24 cookies calls for 1.5 cups of flour and 0.75 cups of sugar. A baker wants to make 40 cookies using the same recipe. How much flour, in cups, will the baker need?
Explanation: Scale factor = 40 ÷ 24 = 5/3. Flour needed = 1.5 × (5/3) = 7.5/3 = 2.5 cups. Note that the sugar information is a distractor, the question asks only about flour. Choice A results from scaling by 40/24 ≈ 1.5: 1.5 × 1.5 = 2.25, using an incorrect scale factor. Choice C results from doubling the original flour amount: 1.5 × 2 = 3.0, using a scale factor of 2 (as if making 48 cookies). Choice D results from scaling the sugar (0.75) rather than the flour: 0.75 × (5/3) = 1.25, using the wrong ingredient.