## 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 ** ** Medium**

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.

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

A) \(-2,500\)

B) -650

C) 650

D) 2,500

**▶️Answer/Explanation**

**Ans:C**

The line of best fit is represented in the graph, and we will calculate its slope using two points on the line.

At \(x = 0\) (the year 1984), the number of rhinos is approximately \(3,800\).

At \(x = 28\) (28 years after 1984, which is 2012), the number of rhinos is approximately \(20,405\).

The slope \(m\) of the line is calculated as follows:

\[

m = \frac{\Delta y}{\Delta x} = \frac{y_2 – y_1}{x_2 – x_1}

\]

Using the chosen points \((0, 3800)\) and \((28, 20,405)\):

\[

m = \frac{20,405 – 3800}{28 – 0} = \frac{16200}{30} = 593

\]

Therefore, the slope is closest to:C) 650

**[Calc]**** ****Question*** *** medium**

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

$

According to the model, what is the best interpretation of 4.3 in this context?

A. Each year between 1995 and 2014, China used 4.3 million metric tons of soybeans.

B. Each year between 1995 and 2014, China’s annual use of soybeans increased by 4.3 million metric tons.

C. China used 4.3 million metric tons of soybeans in 1995.

D. China used a total of 4.3 million metric tons of soybeans between 1995 and 2014.

**▶️Answer/Explanation**

Ans:B

The given function \( C(x) = 4.3x + 19 \) models the annual soybean use in China, in millions of metric tons, where \( x \) is the number of years after 1995. To interpret the coefficient \( 4.3 \), let’s consider the structure of the linear function:

\[ C(x) = 4.3x + 19 \]

Here:

\( C(x) \) represents the annual soybean use in millions of metric tons.

\( x \) represents the number of years after 1995.

In a linear function of the form \( y = mx + b \):

\( m \) is the slope of the line.

\( b \) is the y-intercept.

The slope \( 4.3 \) indicates the rate of change of the annual soybean use per year. Specifically, it means that for each additional year after 1995, the annual soybean use in China increases by \( 4.3 \) million metric tons.

Therefore, the best interpretation of the coefficient \( 4.3 \) in this context is:

**The annual soybean use in China increases by 4.3 million metric tons each year after 1995.**

**[No calc]**** ****Question** ** **medium

𝑓(𝑡) = 0.17𝑡 + 2.54

The given function f models the annual worldwide production of avocados, in millions of metric tons, t years after 2000. According to the function, by how many millions of metric tons did the annual worldwide production of avocados increase from 2010 to 2011?

A. 0.17

B. 2.54

C. 2.71

D. 4.24

**▶️Answer/Explanation**

Ans: A

We need to find the difference in avocado production between 2010 and 2011, which corresponds to a difference of 1 year in \( t \). We’ll evaluate the function \( f(t) \) at \( t = 11 \) and \( t = 10 \), then find the difference.

\( f(11) = 0.17(11) + 2.54 = 1.87 + 2.54 = 4.41 \) million metric tons (2011)

\( f(10) = 0.17(10) + 2.54 = 1.7 + 2.54 = 4.24 \) million metric tons (2010)

Therefore, the increase from 2010 to 2011 is \( 4.41 – 4.24 = 0.17 \) million metric tons. So, the answer is A. \(0.17\).

**[Calc]**** ****Question**** ****Medium**

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.

Which of the following best approximates the equation for the line of best flt shown ?

A) y = -706 + 15.3x

B) y = -15.3 + 706x

C) y = 15.3 – 706x

D) y = 706 – 15.3x

**▶️Answer/Explanation**

A) y = -706 + 15.3x

From the scatter plot, we can observe that the line has a positive slope, indicating a direct relationship between height (x) and weight (y).

To approximate the slope, We can choose any two distinct points on the line and calculate the rise over the run (change in y over change in x).

Let’s use the points (60, around 200) and (70, around 360).

Rise = Change in $y = 360 – 200 = 160$ , Run = Change in $x = 70 – 60 = 10$

$Slope =\frac{ Rise}{Run} = \frac{160}{10} ≈ 16$

Using the point $(60, 200)$ and the calculated slope of $16$:

$200 ≈ 16(60) + b$

$200 ≈ 960 + b$

$b ≈ -760$

Therefore, the equation of the line can be approximated as:

$y ≈ 16x – 760$

**[Calc]**** ****Question** **Medium**

A procedure allows a researcher to determine the concentration of glucose \(y\), in micrograms per milliliter \((\mu \mathrm{g} / \mathrm{mL})\), in a soil sample by measuring the absorbance, \(x\), at a specific wavelength of light. The scatterplot shows this relationship for 5 soil samples.

Which equation is the most appropriate linear model for the data?

A) \(y=1.5+90 x\)

B) \(y=1.5+10 x\)

C) \(y=10+1.5 x\)

D) \(y=90+1.5 x\)

**▶️Answer/Explanation**

A

The slope \(m\) is given by:

\[

m=\frac{y_2-y_1}{x_2-x_1}

\]

Substitute the given points \(\left(x_1, y_1\right)=(0.09,9)\) and \(\left(x_2, y_2\right)=(0.19,18)\) :

\[

m=\frac{18-9}{0.19-0.09}=\frac{9}{0.10}=90

\]

Using the slope-intercept form \(y=m x+b\), we can substitute one of the points to solve for \(b\). Let’s use \((0.09,9)\) :

\[

\begin{aligned}

& 9=90 \cdot 0.09+b \\

& 9=8.1+b \\

& b=9-8.1 \\

& b=0.9

\end{aligned}

\]

The equation of the line is:

\[

y=90 x+0.9

\]

**[Calc]**** ****Question** ** ** **Medium**

For a sample of 13 red alder trees, an arborist measured each tree’s diameter, in centimeters \((\mathrm{cm})\), at a height of 1.4 meters. The arborist then counted the number of growth rings at this height. Each point in the scatterplot represents the diameter and number of rings for each tree. A line of best fit for these data is also shown.

A red alder tree will be selected at random from the sample. What is the probability that the selected tree will have a measured diameter that is greater than \(30 \mathrm{~cm}\) ?

A) \(\frac{1}{7}\)

B) \(\frac{6}{13}\)

C) \(\frac{7}{13}\)

D) \(\frac{6}{7}\)

**▶️Answer/Explanation**

Ans:C

Total number of trees in the sample: 13

Number of trees with a diameter greater than \(30 \text{ cm}\): 7

The probability is calculated as:

\[ \text{Probability} = \frac{\text{Number of trees with diameter > 30 cm}}{\text{Total number of trees}} = \frac{7}{13} \]

Therefore, the correct answer is:

\[ \boxed{\frac{7}{13}} \]

**[Calc]**** ****Question**** ** **Medium**

For a sample of 13 red alder trees, an arborist measured each tree’s diameter, in centimeters \((\mathrm{cm})\), at a height of 1.4 meters. The arborist then counted the number of growth rings at this height. Each point in the scatterplot represents the diameter and number of rings for each tree. A line of best fit for these data is also shown.

For how many of the trees in the sample is the number of growth rings greater than the number predicted by the line of best fit?

A) 3

B) 4

C) 6

D) 10

**▶️Answer/Explanation**

Ans:C

To determine how many of the trees in the sample have a number of growth rings greater than the number predicted by the line of best fit, we need to count the points on the scatterplot that lie above the line of best fit.

**[Calc]**** ****Question** ** ** **Medium**

The scatterplot shows 10 values from a data set. Which of the following equations is the most appropriate linear model for the data shown?

A) \(y=9+\frac{3}{10} x\)

B) \(y=9-\frac{3}{10} x\)

C) \(y=\frac{6}{5} x\)

D) \(y=\frac{3}{8} x\)

**▶️Answer/Explanation**

Ans:A

\[

m=\frac{y_2-y_1}{x_2-x_1}

\]

Given the points \((10,20)\) and \((50,25)\), we have:

\[

\begin{aligned}

& m=\frac{25-20}{50-10} \\

& m=\frac{5}{40} \\

& m=\frac{1}{8}

\end{aligned}

\]

\[

y-20=\frac{1}{8}(x-10)

\]

\[

\begin{aligned}

& y-20=\frac{1}{8} x-\frac{10}{8} \\

& y=\frac{1}{8} x+\frac{150}{8}

\end{aligned}

\]

**[Calc]**** ****Question** **Medium**

An observer counted the number of paddleboats on a lake each hour beginning at \(8 \mathrm{a} . \mathrm{m}\). The scatterplot shows these data.

How many paddleboats were counted on the lake at 2 p.m.?

**▶️Answer/Explanation**

7

**[Calc]**** ****Question** **Medium**

The scatterplot shows the relationship between two variables, \(x\) and \(y\). A line of best fit is also shown. For how many of the data points does the line of best fit predict a greater \(y\)-value than the actual \(y\)-value?

A) 11

B) 7

C) 4

D) 1

**▶️Answer/Explanation**

C

To determine how many data points the line of best fit predicts a greater y-value than the actual y-value, we need to count the number of points that lie below the line of best fit.

**[Calc]**** ****Question** **Medium**

The graph models the relationship between the area of a rain forest \(a\), in square miles, and the predicted number of flowering plant species, \(p\), found in that area. What equation represents this relationship?

A) \(p=200 a\)

B) \(p=375 a\)

C) \(p=500 a\)

D) \(p=750 a\)

**▶️Answer/Explanation**

B

Line is passing from origin so equation will be $y=mx$

To find the slope \( m \) of the line passing through the points \((40, 15000)\) and \((80, 30000)\), we use the slope formula:

\[ m = \frac{y_2 – y_1}{x_2 – x_1} \]

where \((x_1, y_1) = (40, 15000)\) and \((x_2, y_2) = (80, 30000)\).

Substitute the given points into the formula:

\[ m = \frac{30000 – 15000}{80 – 40} \]

\[ m = \frac{15000}{40} \]

\[ m = 375 \]

So, the slope \( m \) of the line passing through the points \((40, 15000)\) and \((80, 30000)\) is \( 375 \).

equation will be $y=375x$

**[Calc]**** ****Question**** ****Medium**

The scatterplot shows the performance index and score for customer engagement for 9 restaurant chains. How many of these chains have a erformance index greater than 4.0?

A) 8

B) 5

C) 4

D) 1

**▶️Answer/Explanation**

D) 1

Only One point.

**[Calc]**** ****Question** ** ****Medium**

The scatterplot shows the relationship between two variables, x and y. A line of best fit is also shown. For how many of the data points does the line of best fit predict a greater y-value than the actual y-value?

**▶️Answer/Explanation**

4

To determine how many data points the line of best fit predicts a greater y-value than the actual y-value, we need to count the number of points that lie below the line of best fit.

**[Calc]**** ****Question**** **medium

In a school debate club, each student earns 2 credits if they participate in a debate and lose, and 4 credits if they participate in a debate and win. A student receives an award after earning 100 credits. The credits needed for the award can be modeled by the equation 2𝑥 + 4𝑦 = 100, where x is the number of times a student participated in a debate and lost, and y is the number of times the student participated in a debate and won. Which graph represents this situation?

**▶️Answer/Explanation**

Ans: A

To determine which graph represents the equation \(2 x+4 y=100\), we need to analyze the intercepts and the general shape of the line represented by this equation.

First, let’s find the intercepts of the equation:

Finding the \(\mathrm{x}\)-intercept: Set \(y=0\) and solve for \(x\) :

\[

2 x+4(0)=100 \Longrightarrow 2 x=100 \Longrightarrow x=50

\]

So, the \(x\)-intercept is \((50,0)\).

Finding the \(y\)-intercept: Set \(x=0\) and solve for \(y\) :

\[

2(0)+4 y=100 \Longrightarrow 4 y=100 \Longrightarrow y=25

\]

So, the \(y\)-intercept is \((0,25)\).

**[Calc]**** ****Question**** **medium

According to a model, if 100 people see a sequence of three letters, 87 of them will recall this sequence immediately after seeing it. The model predicts that this number will decrease by 14% of the number the previous second for each second that passes. Which function represents this model, where 𝑓(𝑡) is the predicted number of people who will recall the sequence after t seconds have passed?

A. 𝑓(𝑡) = 14\((0.87)^{t}\)

B. 𝑓(𝑡) = 87\((0.14)^{t}\)

C. 𝑓(𝑡) = 87\((0.86)^{t}\)

D. 𝑓(𝑡) = 87\((1.14)^{t}\)

**▶️Answer/Explanation**

Ans: C

The model predicts that the number of people who recall the sequence will decrease by \(14\%\) of the previous second’s count for each second that passes. This means that the number of people recalling the sequence at time \(t\) can be represented as \(87\) multiplied by \(0.86\) (which is \(100\% – 14\% = 86\%\) of \(87\)) raised to the power of \(t\) (the number of seconds passed). Therefore, the correct function representation is:

\[ f(t) = 87 \times (0.86)^t \]

So, the correct answer is option C, \( f(t) = 87(0.86)^t \).

**[Calc]**** ****Question*** *** Medium**

In the given scatterplot, a line of best fit for the data is shown. At x = 2, what is the y-value predicted by the line of best fit?

A. 7

B. 3

C. 1

D. 0

**▶️Answer/Explanation**

Ans: B

- Locate \(x=2\) on the Scatterplot: Find the point on the \(x\)-axis where \(x=2\).
- Draw a Vertical Line to the Line of Best Fit: From \(x=2\), draw a vertical line up (or down) to where it intersects with the line of best fit.
- Determine the Corresponding \(\boldsymbol{y}\)-Value: The \(\boldsymbol{y}\)-coordinate of this intersection point is the predicted value for \(\boldsymbol{y}\) when \(\boldsymbol{x}=2\).

**[Calc]**** ****Question**** **medium

The gross domestic product (GDP) of Malta was approximately 250.72 million US dollars in 1970. From 1970 to 1980, a model indicates the GDP increased by 15% per year compared to the previous year’s GDP. Which function represents this model, where *f*(*t*) is the estimated GDP, in millions of US dollars, and *t *is the number of years after 1970?

A) \(f(t) = {(1.15)}^{250.72t}\)

B) \(f(t) = {(250.72)}^{1.15t}\)

C) \(f(t) = 1.15{(250.72)}^t\)

D) \(f(t) = 250.72{(1.15)}^t\)

**▶️Answer/Explanation**

**D) \(f(t) = 250.72{(1.15)}^t\)**

Given that the GDP of Malta was approximately 250.72 million US dollars in 1970 and increased by \(15\%\) per year compared to the previous year’s GDP, we need to find the function representing this model.

Let’s break down the problem:

1. The GDP in 1970 is the initial value, which is 250.72 million US dollars.

2. Each year, the GDP increases by \(15\%\) compared to the previous year’s GDP.

To represent this situation with a function, we can use exponential growth, where the GDP at any given year \(t\) can be represented as:

\[ f(t) = 250.72 \times (1 + 0.15)^t \]

Simplify the function:

\[ f(t) = 250.72 \times (1.15)^t \]

Comparing this with the given options, we find that option D) \(f(t) = 250.72 \times (1.15)^t\) matches the function representing the model.

**[Calc]**** ****Question** medium

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

For how many of the data points does the line of best fit predict a greater *y*-value than the actual *y*-value?

**▶️Answer/Explanation**

**3**

The data points are: (1, 1) (2, 4) (3, 2) (4, 4) (5, 6)

Let’s go through them one by one:

(1, 1): The x-coordinate is 1. Plugging 1 into the line of best fit equation, we get a predicted y-value slightly above 1. So the line over predicts for this point.

(2, 4): The x-coordinate is 2. The predicted y-value from the line appears to be around 2.5. The actual y-value of 4 is greater, so the line under predicts here.

(3, 2): The x-coordinate is 3. The predicted y-value from the line is around 3.5. This over predicts the actual y-value of 2.

(4, 4): The x-coordinate is 4. The predicted y-value is around 4.5, over predicting the actual 4.

(5, 6): The x-coordinate is 5. The predicted y-value appears to be around 5.5, under predicting the actual 6.

So in total, the line over predicts for 3 of the 5 data points.

**[No calc]**** ****Question**** ** medium

A research institute conducted phone and mail surveys. The total cost of conducting these surveys was \(\$ 5,000\). The line shown models the possible combinations of phone and mail surveys that the institute could have conducted.

According to the model, what was the cost for each phone survey conducted?

A)\($\)200

B)\($\)125

C)\($\)40

D)\($\)25

**▶️Answer/Explanation**

**C)\($\)40**

To find the cost per phone survey, we need to determine the equation of the line first.

The line passes through the points (0, 125) and (200, 0).

Using the slope-intercept form: y = mx + b We can calculate the slope m and y-intercept b.

\(m=\frac{y_2-y_1}{x_2-x_1}=\frac{0-125}{200-0}=\frac{-125}{200}=-0.625\)

\(b = 125\)

Therefore, the equation of the line is: $y = -0.625x + 125$

We know that the total cost is \($\)5,000. Substituting y = 125 and x = 0 (pure phone surveys) into the equation: 5000 = -0.625(0) + 125 Cost = 125 $\times$ C (Let C be the cost per phone survey)

Since the total cost is \($\)5000 = 125C C = \($\)40

**[Calc]**** ****Question**** **medium

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

Which data point has an actual *y*-value that is 2 more than the *y*-value predicted by the line of best fit for the corresponding *x*-value?

A)(2, 10)

B)(3, 20)

C)(4, 18)

D)(5, 30)

**▶️Answer/Explanation**

**D)(5, 30)**

**[No- Calc]**** ***Question ***Medium**

The equation h = 150 +10t gives the total number of housing units, h, in a community t months after a new zoning law was passed. How many housing units are added to the community each month after

the zoning law was passed?

A) 10

B) 150

C) 160

D) 1,500

**▶️Answer/Explanation**

Ans: A

The equation \(h = 150 + 10t\) gives the total number of housing units, \(h\), in a community \(t\) months after a new zoning law was passed. To find out how many housing units are added to the community each month, we look at the coefficient of \(t\), which is \(10\).

So, each month, \(10\) housing units are added to the community after the zoning law was passed. Therefore, the answer is A) 10.

**[Calc]**** ***Questions ***Medium**

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

What is an equation of the line of best fit?

A) y =3.7+1.3x

B) y=1.3+3.7x

C) y = 3.7-1.3x

D) y =1.3-3.7x

**▶️Answer/Explanation**

Ans: A

To find the equation of the line of best fit from the given graph, we need to determine the slope and the \(y\)-intercept. Let’s analyze the graph:

Determine the slope \((m)\) :

Choose two points on the line of best fit. For example, let’s use the points \((1,5)\) and \((8,14)\).

Use the slope formula:

\[

m=\frac{y_2-y_1}{x_2-x_1}=\frac{14-5}{8-1}=\frac{9}{7}=1.28

\]

Determine the \(y\)-intercept \((b)\) :

The \(y\)-intercept is the value of \(y\) when \(x=0\). From the graph, it appears to be around 3.7.

Therefore, the equation of the line of best fit is:

\[

y=1.28 x+3.7

\]

Comparing this to the given options, the equation that matches is:A

**[Calc]**** ***Questions ***Medium**

What interval represents all values of t during which Haimi drove in North Dakota?

A) 2 ≤t ≤10

B) 2≤t≤8

C) 0≤t≤8

D) 0≤t≤2

**▶️Answer/Explanation**

Ans: B

To determine the interval representing all values of \( t \) during which Haimi drove in North Dakota, we need to find the time it took her to drive through North Dakota, given the total distance and her constant speed.

Distance through Minnesota: 120 miles

Distance through North Dakota: 360 miles

First, calculate the time it took to drive through Minnesota:

\[ d = 60t \]

\[ 120 = 60t \]

\[ t = \frac{120}{60} \]

\[ t = 2 \text{ hours} \]

Next, calculate the total time to drive through North Dakota:

\[ d = 60t \]

\[ 360 = 60t \]

\[ t = \frac{360}{60} \]

\[ t = 6 \text{ hours} \]

Adding these 6 hours to the 2 hours already driven through Minnesota:

Start time entering North Dakota: 2 hours

End time leaving North Dakota: 2 hours + 6 hours = 8 hours

Therefore, the interval representing all values of \( t \) during which Haimi drove in North Dakota is:$\boxed{2 \leq t \leq 8}$

**[Calc]**** ***Question ***Medium**

The scatterplot shows a data set of 11 points and a line of best fit for the data. For how many data points is the y-value predicted by the line of best fit greater than the actual y-value?

A) Five

B) Six

C) Seven

D) Eight

**▶️Answer/Explanation**

Ans: A

To determine how many data points have a y-value predicted by the line of best fit that is greater than the actual y-value, we need to count the number of points below the line of best fit on the scatterplot.

Let’s analyze the graph:

There are 11 data points in total.

We count the points below the line of best fit:

- There are six points below the line of best fit.
- Therefore, for these six points, the y-value predicted by the line is greater than the actual y-value.

Hence, the correct answer is: **A) Five**

**[Calc]**** ****Question**** **** Medium**

The scatterplot shows the relationship between two variables, $x$ and $y$. A line of best fit is also shown. For how many of the data points is the actual $y$-value at least 1 greater than the $y$-value predicted by the line of best fit?

A) 1

B) 2

C) 3

D) 4

**▶️Answer/Explanation**

B

**[Calc]**** ****Question**** **** Medium**

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.

For what fraction of the data points in the scatterplot is the velocity of the water flow predicted by the line of best fit greater than the measured velocity?

**▶️Answer/Explanation**

$5 / 11,455,454$

**[Calc]**** ****Question**** **** Medium**

A set of data is represented by the scatterplot in the portion of the $x y$-plane shown. Which of the following linear equations best fits the data?

A) $y=-15.2+1.6 x$

B) $y=15.2+1.6 x$

C) $y=-15.2+16 x$

D) $y=15.2+16 x$

**▶️Answer/Explanation**

D

*Question*

Which equation is the most appropriate exponential model for the data shown in the scatterplot? 3.5

- \(y=\frac{1}{100}(10)^{x}\)
- \(y=2(5)^{x}\)
- \(y=6(2)^{x}\)
- \(y=100(2)^{-x}\)

**▶️Answer/Explanation**

C

*Question*

Data set X and data set Y are displayed by the two dot plots shown. Which of the following is(are) the same for both data sets?

1. The mean

2. The median

- I only
- II only
- I and II
- Neither I nor II

**▶️Answer/Explanation**

B

*Question*

.

The scatterplot shows 12 values from a data set. A line of best fit for the data is also shown. Which of the following is the best interpretation of the \(y\)-coordinate of the \(y\)-intercept of the line of best fit?

- For the value \(x\) =6, the line of best fit predicts the corresponding \(y\)-value to be approximately 0.
- For the value \(y\) =0, the line of best fit predicts the corresponding \(x\)-value to be approximately 3.
- For the value \(x\) = 0 , the line of best fit predicts the corresponding \(y\)-value to be approximately 6.
- For the value \(y\) = 3 , the line of best fit predicts the corresponding \(x\)-value to be approximately 0.

**▶️Answer/Explanation**

C

*Question*

Which equation is the most appropriate quadratic model for the data shown in the scatterplot?

- \(y\)=4\(x\)
^{2} - \(y\)=2\(x\)
^{2} - \(y\)=(1/2)\(x\)
^{2} - \(y\)=(1/4)\(x\)
^{2}

**▶️Answer/Explanation**

D

*Question*

The scatterplot in the \(xy\)-plane above shows nine points \((x,y)\) and a line of best fit. Of the following, which best estimates the amount by which the line underestimates the value of \(y\) when \(x\) = 50?

- 8
- 10
- 13
- 18
**▶️Answer/Explanation**Ans: D

*Questions *

The length $C(t)$, in inches, of a channel catfish in an Iowa river $t$ years after the first year of life can be approximated by the linear function $C$. Some values of $C(t)$ are given in the table above.

$$

F(t)=3 t+4

$$

The length $F(t)$, in inches, of a flathead catfish in the same Iowa river $t$ years after the first year of life can be approximated by the linear function $F$, defined by the equation above.

According to the model which of the following is closest to the expected age, to the nearest whole year, of a flathead catfish that is 31 inches long?

A. 10 years old

B. 13 years old

C. 98 years old

D. 106 years old

**▶️Answer/Explanation**

Ans: A

*Questions *

The length $C(t)$, in inches, of a channel catfish in an Iowa river $t$ years after the first year of life can be approximated by the linear function $C$. Some values of $C(t)$ are given in the table above.

$$

F(t)=3 t+4

$$

The length $F(t)$, in inches, of a flathead catfish in the same Iowa river $t$ years after the first year of life can be approximated by the linear function $F$, defined by the equation above.

Which of the following equations could define $C$ as a function of $t$ ?

A. $C(t)=2.5 t+6$

B. $C(t)=\frac{2}{5} t+8.5$

C. $C(t)=2.5 t+8.5$

D. $C(t)=\frac{2}{5} t+8.1$

**▶️Answer/Explanation**

Ans: A

*Questions *

The scatterplot above shows the maximum height \(h\), in feet (ft), and maximum speed \(s\), in miles per hour (mph), of 12 roller coasters as well as the line of best fit for the data. Of the following, which best represents an equation for the line of best fit?

- \(s = 0.21h + 32\)
- \(s = 0.43h + 32\)
- \(s = 0.21h + 62\)
- \(s = 0.43h + 62\)
**▶️Answer/Explanation**Ans: A

*Question*

The scatterplot above shows the average production cost, in cents per pound, of coffee in Ecuador for the years from 2002 to 2012. A line of best fit is also drawn. Which of the following is closest to the difference, in cents per pound, between the actual average production cost in 2012 and the average production cost in 2012 predicted by the given line of best fit?

- 4
- 8
- 16
- 50
**▶️Answer/Explanation**Ans: B

*Question*

In 1789, Benjamin Franklin gave an amount of money to Boston, Massachusetts. The money was to be invested for 100 years in a trust fund. If the value of the trust fund doubled every \(n\) years, which of the following graphs best models the value of the trust fund over time for the 100 years?

**▶️Answer/Explanation**Ans: C

*Questions *

The graph above shows the price that a chemical company charges for an order of fragrance oil, depending on the weight of the order. Based on the graph, which of the following statements must be true?

- The company charges more per pound for orders greater than 100 pounds than for orders less than 100 pounds.
- The company charges less per pound for orders greater than 100 pounds than for orders less than 100 pounds.
- The company charges less per pound for orders greater than 1,000 pounds than for orders less than 1,000 pounds.
- The company charges the same price per pound, regardless of order size.
**▶️Answer/Explanation**Ans: B

*Question*

The scatterplot above represents the salary \(y\), in thousands of dollars, and the number of years of experience, \(x\), for each of six employees at a company. 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?

- \(y=\frac{3}{2}x\)
- \(y=\frac{3}{2}x+\frac{95}{2}\)
- \(y=\frac{2}{3}x+\frac{95}{2}\)
- \(y=\frac{2}{3}x+55\)
**▶️Answer/Explanation**Ans: B

*Questions *

The velocity \(v\), in meters per second, of a falling object on Earth after \(t\) seconds, ignoring the effect of air resistance, is modeled by the equation \(v = 9.8t\). There is a different linear relationship between time and velocity on Mars, as shown in the table below.

If an object dropped toward the surface of Earth has a velocity of 58.8 meters per second after \(t\) seconds, what would be the velocity of the same object dropped toward the surface of Mars after \(t\) seconds, ignoring the effect of air resistance?

- 15.9 meters per second
- 22.2 meters per second
- 36.2 meters per second
- 88.8 meters per second
**▶️Answer/Explanation**Ans: B

*Questions *

During mineral formation, the same chemical compound can become different minerals depending on the temperature and pressure at the time of formation. A phase diagram is a graph that shows the conditions that are needed to form each mineral. The graph above is

a portion of the phase diagram for aluminosilicates, with the temperature \(T\), in degrees Celsius (°C), on the horizontal axis, and the pressure \(P\), in gigapascals (GPa), on the vertical axis.

\(P = -0.00146T+ 1.11\)

An equation of the boundary line between the andalusite and sillimanite regions is approximated by the equation above. What is the meaning of the \(T\)-intercept of this line?

- It is the maximum temperature at which sillimanite can form.
- It is the temperature at which both andalusite and sillimanite can form when there is no pressure applied.
- It is the increase in the number of degrees Celsius needed to remain on the boundary between andalusite and sillimanite if the pressure is reduced by 1 GPa.
- It is the decrease in the number of gigapascals of pressure needed to remain on the boundary between andalusite and sillimanite if the temperature is increased by 1°C.

**▶️Answer/Explanation**Ans: B