Interpolation and Extrapolation on the ACT® Science Test
Read time: 4 minutes Last updated: September 23rd, 2024
Introduction
The ACT® Science Test often asks you to extend or modify experiments. This type of question is pretty straightforward. You'll use the numbers given to predict what another trial would look like. Let's look at how it works.
How to Answer These Questions
Here's an example of what you might see on the ACT® Science Test:
| Marble Type | Angle (degrees) | Maximum Velocity (m/s) by Track Length | ||
|---|---|---|---|---|
| 10 inches | 15 inches | 30 inches | ||
| A | 15 | 0.8 | 1.0 | 1.4 |
| A | 20 | 1.0 | 1.2 | 1.7 |
| B | 15 | 0.9 | 1.1 | 1.5 |
| B | 20 | 1.1 | 1.3 | 1.8 |
| C | 15 | 1.0 | 1.2 | 1.6 |
| C | 20 | 1.2 | 1.4 | 1.9 |
| D | 15 | 1.1 | 1.3 | 1.7 |
| D | 20 | 1.3 | 1.5 | 2.0 |
Question 1:
If the students did another trial with Marble A on a 17.5 degree angle on a 10" track, what would the max velocity likely be in m/s?
- A) 0.6
- B) 0.7
- C) 0.8
- D) 0.9
Click for the Answer and Explanation
Correct Answer: D) 0.9 m/s
Explanation:
To solve this, look at the given values for Marble A. We don't have data for 17.5 degrees, but we know it's between 15 and 20 degrees. For a 10" track, we see:
- 15 degrees = 0.8 m/s
- 20 degrees = 1.0 m/s
Since 17.5 is halfway between 15 and 20, we can guess the velocity would be halfway between 0.8 and 1.0. Therefore, 0.9 m/s is the most likely answer.
Question 2:
If the students added a trial for Marble D at a 25 degree angle on the 30" track, what would the max velocity likely be in m/s?
- A) 1.9
- B) 2.1
- C) 2.3
- D) 3.5
Click for the Answer and Explanation
Correct Answer: C) 2.3 m/s
Explanation:
We solve this similarly. Look at what we know about Marble D on the 30" track:
- 15 degrees = 1.7 m/s
- 20 degrees = 2.0 m/s
From 15 to 20 degrees (a 5-degree increase), the velocity goes up by 0.3 m/s. If we assume this change is constant, another 5-degree increase should add another 0.3 m/s. Therefore, 2.3 m/s is the most likely answer as it follows this pattern.
Dealing with Graphs
Sometimes, the ACT® Science asks you to pick a graph that represents the data. Let's look at an example:
Question 3:
Which graph shows the values for Marble C on a 20 degree angle slope?
Click for the Answer and Explanation
Correct Answer: Graph B
Explanation:
To answer this, you'd look at the data for Marble C at 20 degrees: 1.2, 1.4, and 1.9 m/s. Then, you'd eliminate graphs that don't match this pattern:
- Graph A starts high, then goes low. That's not right.
- Graph B starts low and gradually gets higher. This could work.
- Graph C starts very low, gets high, then goes back down. That's wrong.
- Graph D starts low, gets middle-high, then shoots up. The jumps are too big.
B is the best choice because it shows a gradual increase, matching our data.
Wrapping It Up
The main thing to remember is how to reason out what a new trial would look like. You don't need to know fancy terms - just understand how to work with the values you're given. If you can do that, you'll do well on these questions.