Digital SAT Math: Two-variable data: models and scatterplots Practice Questions

SAT MAth Practice questions – all topics

Problem-solving and Data Analysis Weightage: 15% Questions: 5-7
- Ratios, rates, proportional relationships, and units
- Percentages
- One-variable data: distributions and measures of centre and spread
- Two-variable data: models and scatterplots
- Probability and conditional probability
- Inference from sample statistics and margin of error
- Evaluating statistical claims: observational studies and Experiments

SAT MAth and English – full syllabus practice tests

[Calc] Question Easy

The number of southern white rhinos was 3,800 in 1984 . Due to conservation methods over time, the number of southern white rhinos increased to 20,405 by 2012 . The scatterplot shows the relationship between time, in number of years since 1984, and the number of southern white rhinos. A line of best fit for the data is also shown.

What is the best approximation for the ratio of southern white rhinos in 1984 to southern white rhinos in 2012?
A) 1 to 3
B) 1 to 5
C) 1 to 20
D) 1 to 28

▶️Answer/Explanation

Ans:B

To determine the best approximation for the ratio of southern white rhinos in 1984 to the number of southern white rhinos in 2012, we need to use the given numbers for both years.

The number of southern white rhinos in 1984: $3,800$
The number of southern white rhinos in 2012: $20,405$

The ratio is calculated by dividing the number of rhinos in 1984 by the number of rhinos in 2012:

\[
\text{Ratio} = \frac{3,800}{20,405}
\]

To approximate this ratio, we can simplify it:

1. Divide both the numerator and the denominator by 1000 to make calculations easier:
\[
\frac{3,800}{20,405} \approx \frac{3.8}{20.405}
\]

2. Simplify the fraction by dividing both the numerator and the denominator by the numerator:
\[
\frac{3.8}{20.405} \approx \frac{3.8 \div 3.8}{20.405 \div 3.8} \approx \frac{1}{5.37}
\]

This approximate ratio $\frac{1}{5.37}$ is close to $\frac{1}{5}$.

Thus, the best approximation for the ratio of southern white rhinos in 1984 to the number in 2012 is: B) 1 to 5

[Calc] Question Easy

In the given scatterplot, a line of best fit for the data is shown. At $x=20$, approximately how much greater is the actual $y$-value than the $y$-value predicted by the line of best fit?
A) 3
B) 20
C) 75
D) 250

▶️Answer/Explanation

Ans:C

To determine how much greater the actual $ y $-value is than the $ y $-value predicted by the line of best fit at $ x = 20 $, you would follow these steps:

1. Identify the $ y $-value predicted by the line of best fit at $ x = 20 $.
2. Identify the actual $ y $-value at $ x = 20 $ from the scatterplot.
3. Calculate the difference between the actual $ y $-value and the predicted $ y $-value.

The $ y $-value predicted by the line of best fit at $ x = 20 $ is $250$

Actual $ y $-value at $ x = 20 $ from the scatter plot $=325$

Difference $= 325-250 \Rightarrow 75$

[Calc] Question Easy

A researcher measured the height of a poodle’s shoulders from the ground, in centimeters (cm), as it aged over 10 months. The scatterplot shows this relationship. A line of best fit for the data is also shown.

What is the height of the poodle’s shoulders, in $\mathrm{cm}$, predicted by the line of best fit when the poodle is 5 months old?
A) 18.7
B) 19.4
C) 20.7
D) 21.8

▶️Answer/Explanation

Ans:B

The height of the poodle’s shoulders, in $\mathrm{cm}$, predicted by the line of best fit when the poodle is 5 months old is between 19 to 20 so Option B is best choice.

[Calc] Question Easy

Eight data points are shown in the scatterplot. A line of best fit for the data is also shown. Which of the following is closest to the $y$-value predicted by the line of best fit for an $x$-value of 3,700 ?
A. 40
B. 33
C. 20
D. 14

▶️Answer/Explanation

Ans:B

To determine the $y$-value predicted by the line of best fit for an $x$-value of 3,700 , we need to interpret the graph and the line of best fit.
1. Locate $x=3,700$ on the horizontal axis.
2. Move vertically upwards from $x=3,700$ to intersect the line of best fit.
3. Check the value on the vertical axis at the point of intersection.

Following these steps:
1. On the horizontal axis ( $x$ ), locate the point at $x=3,700$.
2. From $x=3,700$, move vertically upwards to intersect the line of best fit.

– When $x=3,700$, the $y$-value would be greater then 30 and less then 36, which is 33 .

[Calc] Question Easy

The given function $C$ models the annual soybean use in China, in millions of metric tons, between 1995 and 2014, where $x$ is the number of years after 1995.
$
C(x)=4.3 x+19
$

Which graph represents the model?

▶️Answer/Explanation

Ans:A

Only the graph B and C is correct Match from model as it started from approx 19 which is value of y intercept

$
C(4)=4.3 \times 4 +19
$

$C(4)>35$ which is only in graph A , so A is correct

[Calc] Question Easy

Each data point on the scatterplot gives the height x, in inches. and weighty, in pounds, for a llama in a sample of 10 llamas. A line of best fit is also shown.

What is the range of the heights for the sample of 10 llamas?
A) 16 inches
B) 20 inches
C) 136 inches
D) 230 inches

▶️Answer/Explanation

A) 16 inches

To find the range of the heights for the sample of 10 llamas, I need to identify the minimum and maximum heights shown in the data.

Looking at the x-axis (Height in inches), the smallest value is around 60 inches and the largest value is around 76 inches.

Therefore, the range would be the largest value minus the smallest value:

Range = Maximum value – Minimum value = 76 inches – 60 inches = 16 inches

[Calc] Question Easy

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

What is an equation for the line of best fit shown ?
A) y=0.2x
B) y=4.9x
C) y= 0.2 + x
D) y=4.9 + x

▶️Answer/Explanation

B) y=4.9x

Since the best line fit graph is passing from origin so ,

The slope-intercept form of the equation of a line is: $y=m x$

The slope $m$ of the line passing through points $\left(x_1, y_1\right)$ and $\left(x_2, y_2\right)$ is given by:
\[
m=\frac{y_2-y_1}{x_2-x_1}
\]

Using the points $(6,30)$ and $(18,90)$ :
\[
m=\frac{90-30}{18-6}=\frac{60}{12}=5
\]

$y=5 x$

So option- B is best match.

[Calc] Question Easy

The scatterplot shows the relationship between two variables, x and y. A line of best fit for the data is also shown. For 𝑥 = 4, which of the following is closest to the y-value predicted by the line of best fit?
A. 10
B. 12
C. 14
D. 16

▶️Answer/Explanation

Ans: A

Locate $x=4$ on the Scatterplot: Find the point on the $\mathrm{x}$-axis where $x=4$.
Draw a Vertical Line to the Line of Best Fit: From $x=4$, draw a vertical line up (or down) to where it intersects with the line of best fit.
Determine the Corresponding $y$-Value: The $y$-coordinate of this intersection point is the predicted value for $y$ when $x=4$.

[Calc] Question Easy

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

Which of the following is an equation for the line of best fit?
A. 𝑦 = 𝑥
B. 𝑦 = 2𝑥
C. 𝑦 = 1 + 𝑥
D. 𝑦 = 2 + x

▶️Answer/Explanation

Ans: D

When x=0 the value of y intercept is 2 which only matches in Option- D

[Calc] Question Easy

The scatterplot shows the average price of a ticket to a certain theater for 12 select years from 1959 to 2014. An exponential model for the data is also shown. For which year is the predicted value of the average ticket price closest to $40 ?
A. 1959
B. 1974
C. 1992
D. 2014

▶️Answer/Explanation

Ans: C

[Calc] Question Easy

In Chicago in 1895, Frank Duryea won America’s first automobile race by driving 52.4 miles in 10 hours and 23 minutes. If he drove at a constant rate, the approximate distance he drove y, in miles, during the race could be modeled by y = 5x, where x is the time, in hours, after the start of the race.

Which graph best represents this relationship?

▶️Answer/Explanation

Only Option A and D are correct (as both are passing from origin) but in D 52.5 miles are covered less then 6 hours so D is wrong

Based on the given information about Frank Duryea’s race, where he drove 52.4 miles in 10 hours and 23 minutes (approximately 10.4 hours) at a constant rate, the graph that best represents the linear relationship between the distance traveled (y) in miles and the time elapsed (x) in hours is Graph A.

In Graph A, the line passes through the origin (0, 0) and has a positive slope, indicating a constant rate of change. The slope of the line appears to be close to 5, which aligns with the given equation y = 5x, where the distance traveled is approximately 5 times the number of hours elapsed.

Therefore, Graph A correctly models the distance traveled by Frank Duryea during the race based on the provided information.

[Calc] Question Easy

The graph shown models the relationship between the distance D, in kilometers, from Earth to the Moon and the time T, in millions of years after the present. Which of the following equations models this relationship?

A) D = −38T − 385,000

B) D = −38T + 385,000

C) D = 38T − 385,000

D) D = 38T + 385,000

▶️Answer/Explanation

D) D = 38T + 385,000

The graph shows a curved line representing the distance of an object from Earth plotted against time in millions of years after the present.

Regarding the slope, the curve appears to have an increasing positive slope, which means that as time increases, the distance from Earth also increases at an increasing rate. This suggests an accelerating motion or rate of change over time.

As for the intercept, the curve appears to start from the origin (0, less then 400,00), indicating that at time zero (the present), the distance from Earth is less then 400,00. This implies that the initial position of the object is at Earth’s location.

Based on the shape of the curve and the non-zero positive y-intercept between 300,000 and 400,000 units, the equation that best models the relationship between the distance D and time T (in millions of years after the present) is:

D) D = 38T + 385,000

This equation represents a linear relationship with a positive slope of 38 and a positive y-intercept of approximately 385,000 units, which aligns with the increasing curve and non-zero initial distance observed in the graph.

The positive slope of 38 indicates that the distance increases by 38 units for every 1 unit increase in time, which corresponds to the increasing rate of change seen in the curve.

[Calc] Question Easy

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?

A) y = −7 + 30x

B)y = 7 − 30x

C) y = 30 + 7x

D) y = 30 − 7x

▶️Answer/Explanation

D) y = 30 − 7x

The scatter plot shows a relatively strong negative linear relationship between x and y. As x increases, the y values decrease in an approximately straight line pattern.

Let’s examine each equation option:

A) y = -7 + 30x This has a positive slope of 30, which does not match the negative trend in the data. This option can be eliminated.

B) y = 7 – 30x This has a negative slope of -30, which could potentially fit the decreasing trend. The y-intercept of 7 not looks reasonable given the data points. This is a not equation.

C) y = 30 + 7x
This has a positive slope of 7, which does not match the negative relationship in the data. This option can be eliminated.

D) y = 30 – 7x This has a negative slope of -7, which directionally matches the decreasing trend. and, the y-intercept of 30 based on the data points. The option D) fits better visually.

[Calc] Question Easy

A museum built a scale model of the solar system throughout its city where 1 mile in the model represents an actual distance of 400,000,000 miles. The model of the Sun is x miles away from the model of Earth. Which expression represents the actual distance, in miles, between Earth and the Sun?

A)400,000,000x

B)1,000,000x

C)400x

D) $\frac{x}{400}$

▶️Answer/Explanation

A)400,000,000x

To find the actual distance between Earth and the Sun in the scale model, we use the given scale: 1 mile in the model represents an actual distance of $400,000,000$ miles.

If the model of the Sun is $x$ miles away from the model of Earth, then the actual distance is:
\[ \text{Actual distance} = x \times 400,000,000 \]

So, the expression representing the actual distance between Earth and the Sun is:
A) $400,000,000 x$

[No- Calc] Question Easy

At sea level, the boiling point of water is 212 degrees Fahrenheit $\left({ }^{\circ} \mathrm{F}\right)$. For every 500 -foot increase in elevation above sea level, the boiling point of water decreases by about $1^{\circ} \mathrm{F}$. Which equation models water’s boiling point $\mathrm{y}$, in ${ }^{\circ} \mathrm{F}$, in terms of $\mathrm{x}$, the elevation, in feet above sea level?
A) $-\frac{1}{500} x+212$
B) $-500 x+212$
C) $\frac{1}{500} x-212$
D) $500 x-212$

▶️Answer/Explanation

Ans:A

To model water’s boiling point ($y$) in terms of elevation ($x$), we need to consider that for every 500-foot increase in elevation above sea level, the boiling point of water decreases by about 1°F.

If $x$ represents the elevation in feet above sea level, and $y$ represents the boiling point of water in °F, we can use the slope-intercept form of a linear equation, $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Given that the boiling point decreases by 1°F for every 500-foot increase in elevation, the slope $m$ is $-\frac{1}{500}$ (negative because the boiling point decreases with increasing elevation).

At sea level ($x = 0$), the boiling point is 212°F, so the y-intercept $b$ is 212.

Therefore, the equation that models water’s boiling point in terms of elevation is:

\[ y = -\frac{1}{500}x + 212 \]

The correct answer is:

A) $-\frac{1}{500}x + 212$

[Calc] Question Easy

In a certain school district, 36 high school students were selected at random for a study on Internet use and offline reading habits. During October, each student reported the average amount of time, to the nearest half hour, spent reading offline on Saturdays and the average amount of time, to the nearest half hour, spent using the Internet on Saturdays. The scatterplot above shows the times recorded by the students. A line of best fit is also shown

According to the line of best fit, if a student spends an average of 1.25 hours reading offline on Saturdays, which of the following is the best estimate of time the student would be expected to spend using the Internet on Saturdays?

A)Between 3.5 and 4.0 hours

B)Between 3.0 and 3.5 hours

C)Between 2.5 and 3.0 hours

D)Between 2.0 and 2.5 hours

▶️Answer/Explanation

C)Between 2.5 and 3.0 hours
According to the scatter plot, if the students will spend an average of 1.25 hours reading offline on Saturdays, he/she would be expected to spend between 2.5 to 3.0 hours to spent on the internet on Saturday.

[Calc] Questions Easy

According to the model, what distance, in miles, had Haimi driven 3 hours after she started driving?
A) 20
B) 60
C) 120
D) 180

▶️Answer/Explanation

Ans: D

To find the distance $ d $ that Haimi drove 3 hours after she started driving, we use the given equation $ d = 60t $.

Given $ t = 3 $ hours:
\[ d = 60 \times 3 \]
\[ d = 180 \text{ miles} \]

Therefore, the distance Haimi had driven 3 hours after she started driving is:180

[Calc] Question Easy

At a certain location in the Columbia River, the velocity of the water flow at different depths was measured. The scatterplot shown gives 11 measurements of the velocity $\mathrm{v}$, in feet per second ( $\mathrm{ft} / \mathrm{s}$ ), of the water at various depths $\mathrm{d}$, in feet. A line of best fit for the data is also shown.

According to the line of best fit, what is the predicted velocity of the water flow, in feet per second, at a depth of 4 feet?

▶️Answer/Explanation

$1.2,6 / 5$

[Calc] Question Easy

Which of the following linear equations is the most appropriate model for the data shown in the scatterplot?
A) $y=6-x$
B) $y=6+x$
C) $y=-6-x$
D) $y=-6+x$

▶️Answer/Explanation

[Calc] Question Easy

The graph shown models the monthly revenue, in millions of dollars, for a particular marketing company from June 2009 through October 2010. According to the model, which of the following is closest to this company’s monthly revenue, in millions of dollars, for June 2009?
A) 8.5
B) 22.5
C) 62
D) 100

▶️Answer/Explanation

[Calc] Question Easy

Ten data points are in the scatterplot shown, along with a line of best fit. Which of the following best estimates the predicted value of $y$ when $x=6.5$ ?
A) 2
B) 8
C) 13
D) 16

▶️Answer/Explanation

Question

Data set X: 5.50, 5.50, 5.60, 5.65, 5.66
Data set Y: 4.00, 5.50, 5.50, 5.60, 5.65, 5.66

Data sets X and Y show the acidity, or pH, of rainwater samples from two different locations. Which statement about the mean pH of data set X and data set Y is true?3.9

The mean pH of data set X is greater than the mean pH of data set Y.
The mean pH of data set X is less than the mean pH of data set Y.
The mean pH of data set X is equal to the mean pH of data set Y.
There is not enough information to compare the mean pH of the two data sets.

▶️Answer/Explanation

Question

The graph above shows the Chen family’s water usage over 40 weeks. During which of the following periods was the family’s water usage above 750 gallons per week?

From week 5 through week 8
From week 13 through week 17
From week 22 through week 26
From week 33 through week 36
▶️Answer/Explanation
Ans: C

Questions

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

$y=3x+0.8$
$y=0.8x+3$
$y=-0.8x+3$
$y=-3x+0.8$
▶️Answer/Explanation
Ans: A

Questions

The scatterplot above shows the citrus production in millions of metric tons, in China from 2006 through 2014, Which of the following could be the slope of a line of best fit for these data?
A. 2.12
B. 5.25
C. 7.80
D. 10.29

▶️Answer/Explanation

Ans: A

Questions

The scatterplot above shows eight data points in the $x y$-plane. A line of best fit is also shown for the data. If each data point is shifted 3 units upward and a new line of best fit for the shifted points is drawn, how will the value of the $y$-intercept of the new line compare with that of the line shown?
A. It will increase.
B. It will decrease.
C. It will remain the same.
D. There-will no longer be a $y$-intercept.

▶️Answer/Explanation

Ans: A

Questions

A student walks $x$ kilometers $(\mathrm{km}$ ) along a straight path from point $P$ to point $Q$. Then the student walks $y \mathrm{~km}$ along a straight path from point $Q$ to point $R$. What is the total distance, $x+y$, in $\mathrm{km}$, that the student walks?
A. 2.0
B. 3.5
C. 5.5
D. 8.0

▶️Answer/Explanation

Ans: C

Questions

An initial investment of $\$ 1,000$ is made at a constant annual interest rate. The graphs above show the corresponding future value $v$, in dollars, of the investment for different annual interest rates, $r$, after 20 years. One graph shows the value when the interest is compounded daily, and the other graph shows the value when the interest is compounded annually. Which of the following statements is true?
A. As $r$ increases at a constant rate, $v$ increases more rapidly if interest is compounded annually rather than daily.
B. As $r$ increases at a constant rate, $v$ increases more rapidly if interest is compounded daily rather than annually.
C. As $r$ increases at a constant rate, the difference in interest compounded daily and interest compounded annually increases at a constant rate.
D. If $r=15 \%$ and interest is compounded annually, a $\$ 1,000$ investment will be worth $\$ 20,000$ after 20 years.

▶️Answer/Explanation

Ans: B

Question

For a particular cross-country skier, each point in the scatterplot gives the skier’s heart rate, in beats per minute (bpm), and the skier’s oxygen uptake, in liters per minute (L/min), as measured at various points on a cross-country ski course. A line of best fit is also shown.

When the skier’s heart rate was 85 bpm, which of the following is closest to the difference, in L/min, between the skier’s actual oxygen uptake and the oxygen uptake predicted by the line of best fit shown?

▶️Answer/Explanation

Questions

$P(t)=250+10 t$

The population of snow leopards in a certain area can be modeled by the function $P$ defined above, where $P(t)$ is the population $t$ years after 1990. Of the following, which is the best interpretation of the equation $P(30)=550$ ?
A. The snow leopard population in this area is predicted to be 30 in the year 2020 .
B. The snow leopard population in this area is predicted to be 30 in the year 2030 .
C. The snow leopard population in this area is predicted to be 550 in the year 2020 .
D. The snow leopard population in this area is predicted to be 550 in the year 2030 .

▶️Answer/Explanation

Ans: C

Questions

The Conowingo Reservoir had an original storage capacity of300,000 acre-feet at the end of 1928, the year in which it was built. Starting in 1929, sediment carried downstream by the Susquehanna River collected in the reservoir and began reducing the reservoir’s storage
capacity at the approximate rate of 1,700 acre-feet per year.

Which of the following could be a graph of the reservoir’s capacity $c$, in acre-feet, as a function of time $t$, in years, after 1928?

▶️Answer/Explanation
Ans: A

Questions

The scatterplot above shows the relationship between the amount of dietary cholesterol, in milligrams (mg), and the amount of total fat, in grams (g), in the 12 sandwiches offered by a certain restaurant. The line of best fit predicts the amount of total fat a sandwich has based on the amount of dietary cholesterol in the sandwich. How many grams of total fat are in the sandwich for which this prediction is the most accurate?

140
115
85
60

▶️Answer/Explanation

Ans: D

Questions

The scatterplot above shows the total number of home runs hit in major league baseball, in ten-year intervals, for selected years. The line of best fit for the data is also shown. Which of the following is closest to the difference between the actual number of home runs and the number predicted by the line of best fit in 2003?

250
500
750
850
▶️Answer/Explanation
Ans: C

Questions

The line graph above shows the average price of one metric ton of oranges, in dollars, for each of seven months in 2014.

Between which two consecutive months shown did the average price of one metric ton of oranges decrease the most?

March to April
May to June
June to July
July to August

▶️Answer/Explanation

Ans: C

Question

The temperature, in degrees Celsius (°C), of a hot object placed in a room is recorded every five minutes. The temperature of the object decreases rapidly at first, then decreases more slowly as the object’s temperature approaches the temperature of the room. Which of the following graphs could represent the temperature of this object over time?

▶️Answer/Explanation

Ans: A