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SAT: Problem-Solving and Data Analysis - Two-variable data: Models and scatterplots

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Last updated 4 months ago
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Asemmisa {{asɛmmisaAhyɛnsode}}
1.

The scatterplot shows the relationship between two variables, $x$ and $y$. A line of best fit for the data is also shown. Which of the following is closest to the difference between the $y$-coordinate of the data point with $x = 1$ and the $y$-value predicted by the line of best fit at $x = 1$?

Scatterplot with line of best fit for variables x and y.

Asemmisa {{asɛmmisaAhyɛnsode}}
2.

Scatterplot of data points forming a U-shaped curve opening upward.

Of the following, which is the best model for the data in the scatterplot?

Asemmisa {{asɛmmisaAhyɛnsode}}
3.

Graph of the temperature of a cup of coffee over time after being removed from a heat source

In an experiment, a heated cup of coffee is removed from a heat source, and the cup of coffee is then left in a room that is kept at a constant temperature. The graph above shows the temperature, in degrees Fahrenheit ($^\circ\text{F}$), of the coffee immediately after being removed from the heat source and at 10-minute intervals thereafter. During which of the following 10-minute intervals does the temperature of the coffee decrease at the greatest average rate?

The scatterplot shows the relationship between two variables, $x$ and $y$. A line of best fit is also shown.

1
Asemmisa {{asɛmmisaAhyɛnsode}}
4.

Which of the following equations best represents the line of best fit shown?

Asemmisa {{asɛmmisaAhyɛnsode}}
5.

Scatterplot and line of best fit showing temperature versus elevation for locations in the Lake Tahoe Basin.

The scatterplot above shows the high temperature on a certain day and the elevation of 8 different locations in the Lake Tahoe Basin. A line of best fit for the data is also shown. What temperature is predicted by the line of best fit for a location in the Lake Tahoe Basin with an elevation of 8,500 feet?

Asemmisa {{asɛmmisaAhyɛnsode}}
6.

The scatterplot shows the relationship between two variables, $x$ and $y$. An equation for the exponential model shown can be written as $y = a(b)^x$, where $a$ and $b$ are positive constants. Which of the following is closest to the value of $b$?

The line graph shows the percent of cars for sale at a used car lot on a given day by model year.

1
Asemmisa {{asɛmmisaAhyɛnsode}}
7.

For what model year is the percent of cars for sale the smallest?

The scatterplot shows the relationship between two variables, $x$ and $y$.

1
Asemmisa {{asɛmmisaAhyɛnsode}}
8.

Which of the following graphs shows the most appropriate model for the data?

Asemmisa {{asɛmmisaAhyɛnsode}}
9.

In the given scatterplot, a line of best fit for the data is shown.

Which of the following is closest to the slope of this line of best fit?

Asemmisa {{asɛmmisaAhyɛnsode}}
10.

The scatterplot shows the relationship between two variables, $x$ and $y$, for data set E. A line of best fit is shown. Data set F is created by multiplying the $y$-coordinate of each data point from data set E by $3.9$. Which of the following could be an equation of a line of best fit for data set F?

Asemmisa {{asɛmmisaAhyɛnsode}}
11.

Which of the following is true about the values of $2^x$ and $2x+2$ for $x > 0$?

Asemmisa {{asɛmmisaAhyɛnsode}}
12.

The scatterplot shows the relationship between two variables, $x$ and $y$. A line of best fit is also shown.

Which of the following is closest to the slope of the line of best fit shown?

Asemmisa {{asɛmmisaAhyɛnsode}}
13.

Scatterplot of minimum wage versus years since 1940 with line of best fit

The scatterplot above shows the federal-mandated minimum wage every 10 years between 1940 and 2010. A line of best fit is shown, and its equation is

y = 0.096x - 0.488

What does the line of best fit predict about the increase in the minimum wage over the 70-year period?

Asemmisa {{asɛmmisaAhyɛnsode}}
14.

Line graph of number of graduates who enrolled in college within 24 months by graduating class year from 2001 to 2007

The line graph shows the number of graduates from the classes of 2001 through 2007 at a certain school who enrolled in college within 24 months of graduation. Of the following, which class had the fewest graduates who enrolled in college within 24 months of graduation?

Asemmisa {{asɛmmisaAhyɛnsode}}
15.

Graph of Theresa's running speed versus time in minutes.

Theresa ran on a treadmill for thirty minutes, and her time and speed are shown on the graph above. According to the graph, which of the following statements is NOT true concerning Theresa’s run?

The scatterplot shows the relationship between two variables, $x$ and $y$. A line of best fit for the data is also shown.

1
Asemmisa {{asɛmmisaAhyɛnsode}}
16.

At $x = 25.5$, which of the following is closest to the $y$-value predicted by the line of best fit?

Asemmisa {{asɛmmisaAhyɛnsode}}
17.

An inspector begins a day of work with a large sample of shirts that need to be checked for defects. The inspector works at a constant rate throughout the morning. What type of model is best to model the number of shirts remaining to be checked for defects at any given time throughout the morning?

The scatterplot shows the relationship between two variables, $x$ and $y$. A line of best fit is also shown.

1
Asemmisa {{asɛmmisaAhyɛnsode}}
18.

Which of the following equations best represents the line of best fit shown?

Asemmisa {{asɛmmisaAhyɛnsode}}
19.

ID: 7fd284ac

Scatterplot titled 'Income and Percent of Total Expenses Spent on Programs for Ten Charities in 2011' with a line of best fit.

The scatterplot above shows data for ten charities along with the line of best fit. For the charity with the greatest percent of total expenses spent on programs, which of the following is closest to the difference of the actual percent and the percent predicted by the line of best fit?

The scatterplot shows the relationship between two variables, $x$ and $y$. A line of best fit for the data is also shown.

1
Asemmisa {{asɛmmisaAhyɛnsode}}
20.

For how many of the 10 data points is the actual $y$-value greater than the $y$-value predicted by the line of best fit?

Asemmisa {{asɛmmisaAhyɛnsode}}
21.

Scatterplot of ice cream sales versus temperature with a line of best fit

The scatterplot above shows a company's ice cream sales $d$, in dollars, and the high temperature $t$, in degrees Celsius (°C), on 12 different days. A line of best fit for the data is also shown. Which of the following could be an equation of the line of best fit?

Asemmisa {{asɛmmisaAhyɛnsode}}
22.

The line graph shows the probability of snow, as a percent, at a certain location for each day during a four-day period. According to the line graph, for which day during this four-day period is the probability of snow 30%?

Asemmisa {{asɛmmisaAhyɛnsode}}
23.

Scatterplot of long jump distance versus high jump height

Each dot in the scatterplot above represents the height $x$, in feet, in the high jump, and the distance $y$, in feet, in the long jump, made by each student in a group of twenty students. The graph of which of the following equations is a line that most closely fits the data?

Asemmisa {{asɛmmisaAhyɛnsode}}
24.

Scatterplot titled Density of Grape Juice showing density in kilograms per cubic meter versus concentration percentage.

The densities of different concentrations of grape juice are shown in the scatterplot above. According to the trend shown by the data, which of the following is closest to the predicted density, in kilograms per cubic meter ($\text{kg/m}^3$), for grape juice with a concentration of 60%?

Asemmisa {{asɛmmisaAhyɛnsode}}
25.

Line graph titled 'Number of 3-D Movies Released by Year' showing years 2003 to 2011 and corresponding numbers of movies released.

According to the line graph above, between which two consecutive years was there the greatest change in the number of 3-D movies released?

The scatterplot shows the relationship between two variables, $x$ and $y$.

1
Asemmisa {{asɛmmisaAhyɛnsode}}
26.

Which equation is the most appropriate linear model for this relationship?

Asemmisa {{asɛmmisaAhyɛnsode}}
27.

Scatterplot titled Railroad Museum Visitors showing annual visitors versus years since 1968 with a line of best fit

The scatterplot above shows the number of visitors to a railroad museum in Pennsylvania each year from 1968 to 1980, where $t$ is the number of years since 1968 and $n$ is the number of visitors. A line of best fit is also shown. Which of the following could be an equation of the line of best fit shown?

Asemmisa {{asɛmmisaAhyɛnsode}}
28.

Twelve data points are shown in the scatterplot. A line of best fit for the data is also shown. At $x = 1,200$, which of the following is closest to the y-value predicted by the line of best fit?

Asemmisa {{asɛmmisaAhyɛnsode}}
29.

The scatterplot shows the relationship between two variables, $x$ and $y$. A line of best fit is also shown.

Which of the following equations best represents the line of best fit shown?

Asemmisa {{asɛmmisaAhyɛnsode}}
30.

An airplane descends from an altitude of 9,500 feet to 5,000 feet at a constant rate of 400 feet per minute. What type of function best models the relationship between the descending airplane’s altitude and time?

Asemmisa {{asɛmmisaAhyɛnsode}}
31.

Scatterplot of points decreasing from about (0,6) to (5,1)

Which of the following could be an equation for a line of best fit for the data in the scatterplot?

Asemmisa {{asɛmmisaAhyɛnsode}}
32.

Graph titled Braking Distance versus Speed showing braking distance in feet versus speed in miles per hour

The graph above shows the relationship between the speed of a particular car, in miles per hour, and its corresponding braking distance, in feet. Approximately how many feet greater will the car’s braking distance be when the car is traveling at 50 miles per hour than when the car is traveling at 30 miles per hour?

Asemmisa {{asɛmmisaAhyɛnsode}}
33.

In which of the following tables is the relationship between the values of $x$ and their corresponding $y$-values nonlinear?

A.

Table A with x: 1, 2, 3, 4 and y: 8, 11, 14, 17

B.

Table B with x: 1, 2, 3, 4 and y: 4, 8, 12, 16

C.

Table C with x: 1, 2, 3, 4 and y: 8, 13, 18, 23

D.

Table D with x: 1, 2, 3, 4 and y: 6, 12, 24, 48

Asemmisa {{asɛmmisaAhyɛnsode}}
34.

In the given scatterplot, a line of best fit for the data is shown.

Which of the following is closest to the slope of the line of best fit shown?

The line graph shows the estimated number of chipmunks in a state park on April 1 of each year from 1989 to 1999.

1
Asemmisa {{asɛmmisaAhyɛnsode}}
35.

Based on the line graph, in which year was the estimated number of chipmunks in the state park the greatest?

Asemmisa {{asɛmmisaAhyɛnsode}}
36.

The graph of function $f$ is shown, where $y = f(x)$.Graph of a straight line increasing from left to right on a coordinate grid labeled x and y.

Which of the following describes function $f$?

The scatterplot below shows the amount of electric energy generated, in millions of megawatt-hours, by nuclear sources over a 10-year period.

Scatterplot of electric energy generated by nuclear sources over 10 years

1
Asemmisa {{asɛmmisaAhyɛnsode}}
37.

Of the following equations, which best models the data in the scatterplot?

Asemmisa {{asɛmmisaAhyɛnsode}}
38.

ID: 9eb896c5

Scatterplot of data points increasing from left to right.

Which of the following could be the equation for a line of best fit for the data shown in the scatterplot above?

The scatterplot shows the temperature $y$, in $^{\circ}\text{F}$, recorded by a meteorologist at various times $x$, in days since June 1.

1
Asemmisa {{asɛmmisaAhyɛnsode}}
39.

During which of the following time periods did the greatest increase in recorded temperature take place?

A study was done to determine a new car’s stopping distance when it was traveling at different speeds. The study was done on a dry road with good surface conditions. The results are shown below, along with the graph of a quadratic function that models the data.

Graph titled Vehicle Stopping Distance showing stopping distance in feet versus speed in miles per hour.

1
Asemmisa {{asɛmmisaAhyɛnsode}}
40.

According to the model, which of the following is the best estimate for the stopping distance, in feet, if the vehicle was traveling 55 miles per hour?

Asemmisa {{asɛmmisaAhyɛnsode}}
41.

Scatterplot of points decreasing from near (0,10) to near (5,1) with x-axis from 0 to 10 and y-axis from 0 to 10

Which of the following equations is the most appropriate linear model for the data shown in the scatterplot?

Asemmisa {{asɛmmisaAhyɛnsode}}
42.

In the given scatterplot, a line of best fit for the data is shown.

Which of the following is closest to the slope of the line of best fit shown?

Asemmisa {{asɛmmisaAhyɛnsode}}
43.

Scatterplot of temperature versus elevation with line of best fit.

The scatterplot above shows the high temperature on a certain day and the elevation of 8 different locations in the Lake Tahoe Basin. A line of best fit for the data is also shown. Which of the following statements best describes the association between the elevation and the temperature of locations in the Lake Tahoe Basin?

Asemmisa {{asɛmmisaAhyɛnsode}}
44.

The table shows selected values from function $f$.

Which of the following is the best description of function $f$?

Asemmisa {{asɛmmisaAhyɛnsode}}
45.

The scatterplot below shows the size $x$ and the sale price $y$ of 25 houses for sale in Town H. Which of the following could be an equation for a line of best fit for the data?

Scatterplot of size and sale price of houses in Town H

Asemmisa {{asɛmmisaAhyɛnsode}}
46.

The scatterplot shows the relationship between two variables, $x$ and $y$. A line of best fit for the data is also shown.

At $x = 32$, which of the following is closest to the y-value predicted by the line of best fit?

Asemmisa {{asɛmmisaAhyɛnsode}}
47.

For $x > 0$, the function $f$ is defined as follows: $f(x)$ equals 201% of $x$.
Which of the following could describe this function?

Asemmisa {{asɛmmisaAhyɛnsode}}
48.

Two investments were made as shown in the table above. The interest in Account A is compounded once per year. Which of the following is true about the investments?

The scatterplot shows the temperature, in degrees Fahrenheit (°F), and the distance above sea level, in feet, measured at 6 locations on Mount Jefferson. A line of best fit is also shown.

1
Asemmisa {{asɛmmisaAhyɛnsode}}
49.

At a distance of 4,000 feet above sea level, what is the temperature, in °F, predicted by the line of best fit?

Asemmisa {{asɛmmisaAhyɛnsode}}
50.

The scatterplot shows the relationship between two variables, $x$ and $y$.

Which of the following equations is the most appropriate linear model for the data shown?

Asemmisa {{asɛmmisaAhyɛnsode}}
51.

The scatterplot shows the relationship between two variables, $x$ and $y$. A line of best fit is also shown.

Which of the following is closest to the slope of this line of best fit?

Asemmisa {{asɛmmisaAhyɛnsode}}
52.

Scatterplot with line of best fit showing total protein versus total fat for eight sandwiches.

The scatterplot above shows the numbers of grams of both total protein and total fat for eight sandwiches on a restaurant menu. The line of best fit for the data is also shown. According to the line of best fit, which of the following is closest to the predicted increase in total fat, in grams, for every increase of $1$ gram in total protein?

Asemmisa {{asɛmmisaAhyɛnsode}}
53.

The scatterplot shows the relationship between $x$ and $y$. A line of best fit is also shown.

Which of the following is closest to the slope of the line of best fit shown?

Asemmisa {{asɛmmisaAhyɛnsode}}
54.

Each year, the value of an investment increases by 0.49% of its value the previous year. Which of the following functions best models how the value of the investment changes over time?

The scatterplot shows the relationship between the weight, in pounds, of each of 9 female gray wolves on April 30 and the number of offspring each gray wolf produced.

1
Asemmisa {{asɛmmisaAhyɛnsode}}
55.

How many offspring did the 50-pound gray wolf produce?

Asemmisa {{asɛmmisaAhyɛnsode}}
56.

Scatterplot showing distance and density of planetoids in the inner solar system, with a line of best fit.

The scatterplot above shows the densities of 7 planetoids, in grams per cubic centimeter, with respect to their average distances from the Sun in astronomical units (AU). The line of best fit is also shown. An astronomer has discovered a new planetoid about 1.2 AU from the Sun. According to the line of best fit, which of the following best approximates the density of the planetoid, in grams per cubic centimeter?