ACT Science Practice Test: Interpolation and Extrapolation
- Interpolation and Extrapolation
- 10 questions
- 10 minutes
This test has two original passages, each followed by five questions that ask you to predict a value the table does not show. Find the pattern first: a steady change per step allows a straight-line estimate, while a change that shrinks or grows from step to step needs more care.
Tap an option to mark your answer. You can change your mind, or tap the same option again to leave the question blank. The correct answers and explanations appear when you finish the test.Tap an option to answer; tap it again to leave the question blank.
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Question 1
Passage I
Students measured the speed of sound in dry air at several air temperatures. Table 1 shows their results, rounded to the nearest meter per second (m/s).
Table 1 Air temperature (°C) Speed of sound (m/s) 0 331 10 337 20 343 30 349 40 355 Based on Table 1, the speed of sound at 25°C is closest to:
Correct answer: C
25°C is halfway between 20°C and 30°C, so the speed is about halfway between 343 and 349 m/s, or 346 m/s. The choice 343 m/s is the value at 20°C.
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Question 2
Passage I (see above):
If the trend in Table 1 continues, the speed of sound at 60°C would be closest to:
Correct answer: B
The speed rises 6 m/s for every 10°C, so from 355 m/s at 40°C it would reach 361 at 50°C and 367 at 60°C. The choice 361 m/s stops at 50°C.
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Question 3
Passage I (see above):
Based on Table 1, at approximately what air temperature would the speed of sound be 352 m/s?
Correct answer: D
352 m/s is halfway between 349 m/s (30°C) and 355 m/s (40°C), so the temperature is about 35°C. The choice 30°C gives 349 m/s.
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Question 4
Passage I (see above):
If the pattern in Table 1 also holds below 0°C, the speed of sound at −10°C would be closest to:
Correct answer: B
Going 10°C colder lowers the speed by 6 m/s, so 331 − 6 = 325 m/s. The choice 337 m/s adds 6 instead of subtracting, which is the value at +10°C.
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Question 5
Passage I (see above):
Which statement best describes the relationship shown in Table 1?
Correct answer: A
Each 10°C step in Table 1 raises the speed by exactly 6 m/s (331, 337, 343, …). A change of 6 m/s per single degree would be ten times too large.
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Question 6
Passage II
The amount of oxygen gas that can dissolve in fresh water depends on the water temperature. Table 2 lists the maximum dissolved oxygen, in milligrams per liter (mg/L), for water in contact with air at sea level.
Table 2 Water temperature (°C) Maximum dissolved oxygen (mg/L) 0 14.6 10 11.3 20 9.1 30 7.6 40 6.4 Based on Table 2, the maximum dissolved oxygen at 15°C is closest to:
Correct answer: C
15°C lies halfway between 10°C (11.3 mg/L) and 20°C (9.1 mg/L), so the value is about (11.3 + 9.1) ÷ 2 = 10.2 mg/L. Only this choice falls between the two table values.
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Question 7
Passage II (see above):
According to Table 2, the maximum dissolved oxygen in water at 25°C would be:
Correct answer: B
Because the values fall steadily as temperature rises, 25°C must lie between the values for 20°C (9.1) and 30°C (7.6). The range 9.1-11.3 belongs to temperatures from 10°C to 20°C.
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Question 8
Passage II (see above):
If the trend in Table 2 continues, the maximum dissolved oxygen at 50°C would most likely be:
Correct answer: A
The value keeps falling, but each 10°C drop is smaller than the one before (3.3, 2.2, 1.5, 1.2), so the next drop should be a little less than 1.2 mg/L. That places the value just above 5.0 mg/L; a drop to 2-3 mg/L would require a much larger decrease.
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Question 9
Passage II (see above):
A certain fish species needs water with at least 8.0 mg/L of dissolved oxygen. Assume the water holds the maximum amount of oxygen shown in Table 2.
At which of the following temperatures would the water meet the fish's need?
Correct answer: A
At 25°C the value is about halfway between 9.1 and 7.6, roughly 8.3 mg/L, which is above 8.0. At 30°C the table shows only 7.6 mg/L, and warmer water holds even less.
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Question 10
Passage II (see above):
Which statement best describes how the values in Table 2 change as the temperature increases?
Correct answer: D
The drops are 3.3, 2.2, 1.5 and 1.2 mg/L, so the values fall more slowly as the water warms. Because the steps are not equal, a straight-line pattern does not fit.
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