Domain: Problem-Solving and Data Analysis | Skill: Two-variable data: models and scatterplots | Difficulty: Easy

Mastering SAT Scatterplots & Models: Easy Strategies & Practice

Ever looked at a graph and felt like you were supposed to see a story? That’s exactly what the SAT tests in its Problem-Solving and Data Analysis section. Questions about scatterplots and models are all about understanding the relationship between two sets of information—like time vs. temperature, or hours studied vs. test scores. The good news is that at the ‘Easy’ difficulty level, these questions are some of the most straightforward on the test. Mastering them is a fantastic way to build your confidence and secure foundational points. This guide will give you the simple strategies and practice you need to turn these questions into an easy win.

Typical Question Formats

On the SAT, questions about two-variable data can be presented in a few common ways. Here’s a quick breakdown of what to expect.

Typical Format	What It Tests	Quick Strategy
A word problem describing growth or decay (e.g., “A bacteria culture increases by…”)	Your ability to identify a linear vs. an exponential model from a description.	Look for keywords. “Constant amount” = linear. “Constant percent/factor” = exponential.
A scatterplot with a question about the relationship (e.g., “A researcher studies the relationship between…”)	Your ability to interpret the overall trend of the data points.	Mentally (or lightly) draw a line of best fit. Does it go up or down? Is it a straight line or a curve?
A given linear equation representing a real-world scenario (e.g., “A bakery uses the equation…”)	Your ability to connect the parts of an equation (slope, y-intercept) to the context.	Identify the slope as the “rate of change” and the y-intercept as the “starting amount” or “initial value.”
A table of values with a question about the relationship.	Your ability to determine the function type from a set of data points.	Check the change in y-values. Is there a constant difference (linear) or a constant ratio (exponential)?

Real SAT-Style Example

Let’s look at a typical ‘Easy’ question you might encounter on the SAT. This type focuses on identifying the correct model from a description.

Question: A population of bacteria increases by 50 bacteria every hour, starting with 100 bacteria. Which type of function best models the relationship between the bacteria population size \( P \) and time \( t \)?

A) Increasing exponential

B) Increasing linear ✅

C) Decreasing exponential

D) Decreasing linear

Step-by-Step Strategy for Easy Models Questions

For word problems that ask you to choose a model type, follow these simple steps to get to the right answer every time.

1. Identify the Key Information: Read the problem carefully and pull out the two variables being compared, the starting value, and how the value changes over time.
2. Scan for Keywords: Look for specific words or phrases that describe the change. The most important distinction is between a constant amount and a constant percentage or factor.
3. Determine the Function Type (Linear vs. Exponential):

• If the value changes by a constant amount (e.g., “adds 50 each hour,” “loses $10 per month”), it’s a linear function.
• If the value changes by a constant percentage or factor (e.g., “grows by 15%,” “doubles,” “is cut in half”), it’s an exponential function.

4. Determine the Direction (Increasing vs. Decreasing): Does the problem state that the value is growing, increasing, adding, or rising? Or is it shrinking, decreasing, losing, or falling? This tells you the direction.
5. Select the Best Match: Combine your findings from steps 3 and 4 to choose the answer that perfectly describes the model (e.g., “Increasing Linear”).

Applying the Strategy to Our Example

Now, let’s use our 5-step strategy to break down the example question.

Step 1 Applied: Identify the Key Information

We read the problem: “A population of bacteria increases by 50 bacteria every hour, starting with 100 bacteria.”

• Variables: Population size \( P \) and time \( t \).
• Starting Value: 100 bacteria.
• Change: Increases by 50 bacteria every hour.

Step 2 Applied: Scan for Keywords

The key phrase is “increases by 50 bacteria every hour.”

Step 3 Applied: Determine the Function Type

The phrase “increases by 50” signifies a change by a constant amount. It’s not a percentage or a multiplier. Therefore, the function must be linear.

Step 4 Applied: Determine the Direction

The word “increases” clearly tells us the function is increasing.

Step 5 Applied: Select the Best Match

Combining our findings, we are looking for an Increasing Linear model. This matches option B perfectly.

Ready to Try It on Real Questions?

Now that you understand the strategy, it’s time to practice with authentic SAT questions! Head to mytestprep.ai and follow these steps:

1. Login using your account or signup on mytestprep.ai
2. Click on Practice Sessions once you are on the dashboard. You will see the link on the left side navigation menu of the dashboard
3. Click on Create New Session
4. Start with Co-Pilot Mode on with hints and explanations—it’s like having a personal coach who explains exactly why each answer is right or wrong
5. Select Math as your subject
6. Select Problem-Solving and Data Analysis, Two-variable data: models and scatterplots and Easy Difficulty
7. Start practicing. Happy Practicing!

Key Takeaways

To ace these ‘Easy’ SAT questions, remember these core ideas:

• A change by a constant amount (e.g., +5, -10) means the model is Linear.
• A change by a constant factor or percentage (e.g., x2, +10%) means the model is Exponential.
• Pay close attention to keywords: “initial,” “starting,” “rate,” “per,” “percent,” “doubles.”
• For scatterplots, a quick sketch of a line of best fit can instantly reveal the trend (positive/negative) and model type (linear/curved).