Data Representation
Data Representation
The three Data Representation passages tend to be the most straightforward passages on the Science Reasoning Test. Each Data Representation passage begins with a written introduction. Read this introduction for a general idea of the passage, but don’t labor over it. The charts in Data Representation are the focus of the passage’s questions. Use diagrams such as the one below to clarify the often confusing terminology in the introduction and to see graphic representations of the terminology.
The Sample Passage
If left at rest, a spring will hang at its equilibrium position. If a mass (M) is attached to that spring, the spring will grow in length by a distance known as its displacement (x). A larger mass will create a larger displacement than a small mass.
The force (F), in newtons (N), required to return the spring to its equilibrium position is the negative product of the displacement (x) and a spring constant (k), where the negative indicates the direction, not the value, of the force. The spring constant measures the elasticity of a spring: if a spring has a high k, the spring cannot be stretched easily; if a spring has a low k, it can be stretched more easily.
Various masses were attached to two springs with different spring constants, and the force was measured in each of these trials. The energy used (J) returning the spring to its equilibrium position, or Potential Energy (PE), was also measured.
Table 1
Trial Spring Constant, k Displacement, x (m) Force on spring, F (N) Potential Energy, PE (J) Mass, M (g)
1 5 1 5 2.5
2 5 5 25 62.5
3 5 10 50 250
4 10 1 10 5
5 10 5 50 125
6 10 10 100 500
Strategy for Reading the Passage
Since the Data Representation passage is fairly straightforward, you don’t necessarily need to employ specific reading strategies. But there are a couple of tips you should keep in mind when going through the passage.
We suggest that you begin by skimming the introduction to the passage. Since the introductions to passages on the Science Reasoning Test are usually full of confusing scientific terminology, you should not spend time struggling to understand everything the introduction says. Rather, use the introduction to get a general idea of what the subsequent chart illustrates. Also, consider circling key terms in the introduction to make referring back to the passage easier.
When you get to the chart (our Data Representation example has only one chart, but you will sometimes come across two), you should glance over it to make sure that you know what’s being measured and that, in general, you feel comfortable finding information in the chart. Save detailed exploration of the chart for when you answer specific questions.
The Questions
Each Data Representation passage is accompanied by five questions. These questions fall into one of four categories, and we’ll show you how to handle all four below. All of the following questions refer to the sample passage above.
Read the Chart
Read the Chart questions test your ability to locate and understand the information presented in the charts provided in the passage. The answers to these questions are usually explicitly stated within the charts. Here’s an example of a Read the Chart question:
Which of the following statements about displacement and the force on the spring is consistent with the data in Table 1?
A. The force on the spring increases as displacement increases.
B. The force on the spring decreases as displacement increases.
C. The force on the spring does not change as displacement increases.
D. The force on the spring increases then decreases as displacement increases.
Answering this question is a simple matter of reading the chart. The question explicitly tells you to look at two numbers—the displacement of the spring and the force on the spring—and identify their relationship. All of the answer choices deal with what happens when the displacement increases, so you know that your goal is to see what happens to the force on the spring. Trials 1–3 and Trials 4–6 both show displacement increasing from 1 meter to 5 meters to 10 meters. Your next step should be to check out the corresponding numbers in the Force column. In Trial 1 (a displacement of 1 meter), the force is equal to 5 newtons; in Trial 2 (a displacement of 5 meters), the force is equal to 25 newtons; in Trial 3 (a displacement of 10 meters), the force is equal to 50 newtons. These numbers seem to indicate that force increases with displacement. Now check whether the statement holds true in Trials 4–6. In Trials 4–6, the force rises from 10 newtons to 50 newtons to 100 newtons; in other words, it increases as displacement increases. You’ve just successfully formulated an answer to the question (“when displacement increases, force increases”), so you can complete the last step of matching your answer with the test’s. The correct answer is A.
Use the Chart
To answer Use the Chart questions, you must use information from the given chart or charts to decipher additional information. For instance,
According to the information provided in the introduction and Table 1, which of the following is the largest mass?
The question tells you to refer to both the introduction and Table 1. In the introduction, there are two sentences that will help you solve this question. The first sentence is “A larger mass will create a larger displacement than a small mass.” This sentence indicates that you should look at the amount of displacement to gauge the relative size of the masses. But if you look only at the displacement, you’re probably wondering how to choose between and which both indicate a displacement of 10 meters. To solve this problem, look to the crucial sentence found later in the passage: “The spring constant measures the elasticity of a spring: if a spring has a high k, the spring cannot be stretched easily; if a spring has a low k, it can be stretched more easily.” This sentence points to the difference between the two springs being tested (one with k = 5 and the other with k = 10). If the spring with k = 10 is the tougher to stretch of the two, you can assume that it requires a heavier mass to stretch the tough spring 10 meters than it does to stretch the weaker spring 10 meters. So the heaviest mass (and the correct answer) is D.
Now try this Use the Chart question:
If Trial 2 were repeated with a spring with k = 15, the displacement of the spring would be:
A. less than 5.
B. 5.
C. greater than 5.
D. indeterminable from the given information.
This question resembles the last one in a key way: both questions require you understand the sentence, “The spring constant measures the elasticity of a spring; if a spring has a high k, the spring cannot be stretched easily; if a spring has a low k, it can be stretched more easily.” This sentence tells you that replacing the spring in Trial 2 with a spring that’s tougher to pull will result in a smaller displacement of the spring (if the mass pulling on it remains the same). When k = 5, Trial 2 produces a displacement of 5 meters, so with a larger k (k = 15) and the same mass, the displacement must be less than 5 meters. Choice A is correct.
Handle Graphs
These questions will generally ask you to transform the data given in the charts into graphic form. If you are unfamiliar with how to graph data and the differences between linear and exponential functions, you should review this information. Briefly, straight lines indicate linear functions, while curved lines represent exponential functions. Straight horizontal lines indicate that the variable remains constant. For example,
Which of the following graphs best represents the change in potential energy with increasing displacement for Trials 1–3 ?
When answering such questions, you should look first at the axes of the graphs. In this question, each of the graphs represents displacement on the x-axis, or horizontal axis, while potential energy is represented on the y-axis, or vertical axis. As you move right on the x-axis and up on the y-axis, numerical values increase.
To answer this question, you should first examine the relationship between potential energy and displacement according to Table 1. From the chart, you can see that potential energy rises as displacement increases. Because you’re looking for a rise in potential energy, you can eliminate choices A and B, since choice A shows potential energy decreasing with an increase in displacement, and choice B shows potential energy remaining constant. Now you’ve narrowed down your choices to C and D. The key difference between the graphs of these two choices is that C shows potential energy rising exponentially and D shows it rising linearly. In other words, the potential energy represented in C does not increase in direct proportion to displacement; instead, each incremental increase in displacement leads to an ever larger jump in potential energy. From Table 1, you can determine that C’s depiction of potential energy is correct because the numbers do not rise in a steady manner (as the numbers for force do).
Take the Next Step
Take the Next Step questions present you with a stated goal that can be achieved through experimentation and tests. Your object is to choose the answer that would best achieve that goal. You will not see these questions as frequently on the Data Representation passages as you will on Research Summaries; in fact, you may not see any of these questions on Data Representation passages, but you should still be prepared to answer them. Here’s an example:
What would be the best method of determining how the spring constant affects displacement?
A. Reproduce Trials 1–6 but use only springs with spring constant k = 5.
B. Reproduce Trials 1–3.
C. Reproduce Trials 4–6.
D. Reproduce Trials 1–6 but change the masses in Trials 4–6 to , , and , respectively.
First, you should make sure you understand the goal stated in the question. This particular question wants you to measure how displacement changes when you have different spring constants. Although this question may seem difficult, it is actually fairly simple because it can be answered through process of elimination. If you don’t know the answer on your own, just look through the answer choices to see which one makes sense. You know that the goal calls for testing with different spring constants, so you can eliminate choices A, B, and C because they all call for the use of just one spring constant. Wasn’t that pretty simple? You can double check that you’re right by asking yourself whether D makes sense. Choice D uses two spring constants (k = 5 and k = 10), and it proposes that you use the same masses with the second spring that you used with the first. This proposal makes a lot of sense because the only variable will be the spring constant—you won’t need to take mass into account in the comparison. So D is the correct answer to this problem.
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