Homework · Medium + Hard · Two-variable data

Models and Scatterplots

Eight original SAT and PSAT problems, grouped by model type. Start with nonlinear models, then practice lines of best fit and prediction error.

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01 · Main focus

Nonlinear Models

Quadratic shape, exponential growth, and comparing model behavior.
Nonlinear model

A. Choosing a quadratic model

Original SAT Question Bank problem · e821a26d

Hard
Original SAT nuclear energy scatterplot and quadratic model choices
Work from the same problem below.Use the guiding questions first, then submit the final SAT answer.
1Guiding step 1 of 3

What model type matches a graph that increases and then decreases with one turning point?

2Guiding step 2 of 3

The parabola opens downward. What must be true about the coefficient of x²?

3Guiding step 3 of 3

Estimate the y-intercept of a reasonable model from the graph.

4Final SAT answer

Which equation best models the data?

Nonlinear model

B. Exponential growth versus linear growth

Original SAT Question Bank problem · af142f8d

Hard
Work from the same problem below.Use the guiding questions first, then submit the final SAT answer.
5Guiding step 1 of 3

Which pair correctly classifies the two account models?

6Guiding step 2 of 3

How many dollars does Account A earn during the first year?

7Guiding step 3 of 3

After the first year, what happens to Account A's yearly earnings?

8Final SAT answer

Which statement about the investments is true?

02 · New practice

Linear Models

Move from reading a rate to building and evaluating a model, then finish with a short review.
Linear model

C. Slope from a line of best fit

Original SAT Question Bank problem · 9d95e7ad · new

Hard
Original SAT sandwich protein and fat scatterplot problem
Work from the same problem below.Use the guiding questions first, then submit the final SAT answer.
9Guiding step

Using approximately (20, 33) and (40, 63), calculate the slope.

10Final SAT answer

What is the predicted increase in total fat for every 1-gram increase in total protein?

Linear model

D. Average rate of change from two data points

Original SAT Question Bank problem · 7b52985c

Hard
Original SAT bird flight-time scatterplot problem
Work from the same problem below.Use the guiding questions first, then submit the final SAT answer.
11Guiding step

Which two ordered pairs represent January 13 and January 15?

12Final SAT answer

Find the average rate of change in hours per day.

Linear model

E. Choosing an equation from a line of best fit

Original PSAT/NMSQT & PSAT 10 Question Bank problem · 4313e24f · new

Hard
Original PSAT railroad museum visitors scatterplot with a line of best fit
Work from the same problem below.Use the guiding questions first, then submit the final SAT answer.
13Guiding step

Estimate the y-intercept of the line of best fit.

14Final PSAT answer

Which equation could represent the line of best fit?

Linear model

F. Medium checkpoint: measuring prediction error

Original PSAT/NMSQT & PSAT 10 Question Bank problem · de590716 · new

Medium
Original PSAT scatterplot asking for the difference between an actual and predicted value
Work from the same problem below.Use the guiding questions first, then submit the final SAT answer.
15Guiding step

At x = 1, what y-value does the line of best fit predict?

16Final PSAT answer

The actual point has y = 12. What is the difference between the actual and predicted values?

Linear model

G. Estimating a line from a cluster of points

Original SAT Question Bank problem · 79137c1b · new

Hard
Original SAT scatterplot of house size and sale price with four model choices
Work from the same problem below.Use the guiding questions first, then submit the final SAT answer.
17Guiding step

Using about (1, 200) and (2.5, 350), estimate the slope.

18Final SAT answer

Which equation could be a line of best fit for the data?

Linear model

H. Final review: scaling a slope

Original SAT Question Bank problem · d0430601 · new

Hard
Original SAT scatterplot of beach visitors versus temperature
Work from the same problem below.Use the guiding questions first, then submit the final SAT answer.
19Guiding step

A slope of 57 means how many additional visitors are predicted for a 1°C increase?

20Final SAT answer

How many additional visitors are predicted for a 5°C increase?