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

## 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   Hard

A fitness membership costs $$\ 45$$ per month. All new members receive a discount of $$\ 20$$ off the cost of their first month of membership. Which function $$c$$ gives the total cost $$c(t)$$, in dollars, that a new member pays after $$t$$ months of membership?
A) $$c(t)=20+45 t$$
B) $$c(t)=25+45 t$$
C) $$c(t)=20+45(t-1)$$
D) $$c(t)=25+45(t-1)$$

Ans:D

To determine the correct function $$c(t)$$ that represents the total cost for a new member after $$t$$ months of membership, let’s analyze the given information:

1. The regular monthly cost of membership is $$\45$$ .
2. New members receive a discount of $$\20$$ off their first month.

Let’s break down the costs:
The first month costs $$\45 – \20 = \25$$.
Each subsequent month costs $$\45$$.

The function $$c(t)$$ needs to account for the special pricing in the first month and the regular pricing for the subsequent months. Let’s define $$t$$ as the number of months:

For $$t = 1$$:
$c(1) = 25$

For $$t > 1$$:
$c(t) = 25 + 45(t – 1)$

This formula can be derived from:
$$\25$$ for the first month.
$$\45$$ for each of the remaining $$t – 1$$ months.

Thus, the correct function is:
$c(t) = 25 + 45(t – 1)$

D) $$c(t) = 25 + 45(t – 1)$$

[Calc]  Question  Hard

The scatterplot shows the number of housing units in 2010 and 2018 for each of 11 US states. A line of best fit with equation 𝑦 = 𝑎x, where a is a constant, is also shown. A point lies above this line if and only if it represents a state with an increase in housing units from 2010 to 2018 greater than 7%. What is the value of a?

Ans: 107/100, 1.07

To find the value of the constant a in the equation $$y=a x$$ representing the line of best fit, $$I$$ will use the given information that a point lies above the line if and only if it represents a state with an increase in housing units from 2010 to 2018 greater than $$7 \%$$.

Let’s consider a sample point on the line, say (400,000, 400,000a).
For this point to lie on the line $$y=a x$$, we must have:
\begin{aligned} & 400,000 a=a x \\ & a=1 \end{aligned}

So the equation of the line is $$\mathrm{y}=\mathrm{x}$$.
Now, for a point $$(\mathrm{x}, \mathrm{y})$$ to lie above this line, we must have $$\mathrm{y}>\mathrm{x}$$.
Rearranging, we get:
\begin{aligned} & y / x>1 \\ & (y-x) / x>0 \\ & (y-x) / x=(y / x)-1>0.07 \text { (since increase is greater than } 7 \%) \\ & y / x>1.07 \end{aligned}

Therefore, the value of a that satisfies the given condition is $$\mathrm{a}=1.07$$.

[Calc]  Question   Hard

Kiara uses her propane grill for an average of 11 hours each week. Her grill can run an average of
18 hours per 20-pound tank. Kiara would like to reduce her weekly expenditure on propane by 5.
Assuming propane costs 16 per 20-pound tank, which equation can Kiara use to determine how
many fewer average hours, h, she should use her grill each week ?

A) $$\frac{18}{16}h=6$$

B) $$\frac{18}{16}h=5$$

C) $$\frac{16}{18}h=6$$

D) $$\frac{16}{18}h=5$$

D) $$\frac{16}{18}h=5$$

Kiara uses her propane grill for an average of 11 hours each week. Her grill can run an average of 18 hours per 20-pound tank, and propane costs 16 per 20-pound tank. She wants to reduce her weekly expenditure on propane by 5. We need to find the equation to determine how many fewer average hours, $$h$$, she should use her grill each week.

1. Determine the current weekly propane usage:
Kiara uses 11 hours per week.
The grill runs for 18 hours per 20-pound tank.

The number of tanks used per week:
$\frac{11}{18} \text{ tanks/week}$

2. Calculate the current weekly cost:
Propane costs $16 per tank. $\text{Current weekly cost} = \left(\frac{11}{18}\right) \times 16$ 3. Determine the desired weekly cost reduction: Kiara wants to reduce her weekly expenditure by$5.
$\left(\frac{11 – h}{18}\right) \times 16 = \left(\frac{11}{18}\right) \times 16 – 5$

4. Formulate the equation:
To find $$h$$, the number of fewer hours she should use her grill:
$\frac{16}{18} h = 5$

Thus, the correct equation is:
$\boxed{\frac{16}{18} h = 5}$

[No calc]  Question  Hard

A company offers its salespeople two different weekly compensation plans. Salespeople on Plan X
earn 1,000 plus a 10% commission on their sales each week. Salespeople on Plan Y earn 500 plus a 20% commission on their sales each week. Which inequality models the amount in sales each week, d dollars, for which salespeople on Plan X earn more than salespeople on Plan Y?

A)  d < 5,000

B) d > 5,000

C) d < 1,500

D) d > 1,500

A)  d < 5,000

To determine the inequality that models the sales amount $$d$$ dollars for which salespeople on Plan X earn more than those on Plan Y, :

Write the weekly earnings for Plan X:
$\text{Earnings for Plan X} = 1000 + 0.10d$

Write the weekly earnings for Plan Y:
$\text{Earnings for Plan Y} = 500 + 0.20d$

Set up the inequality where Plan X earnings are greater than Plan Y earnings:
$1000 + 0.10d > 500 + 0.20d$

Subtract $$500$$ from both sides:
$500 + 0.10d > 0.20d$

Subtract $$0.10d$$ from both sides:
$500 > 0.10d$

Divide by $$0.10$$:
$d < 5000$

Thus, salespeople on Plan X earn more than those on Plan Y when $$d < 5000$$.

[Calc]  Question Hard

f(x)=0.28x-2.9
The given function f models the length, in centimeters (cm), of aboveground growth, known as shoot length, of cotton seedlings after emerging from seeds, where x represents the seed mass, in milligrams
(mg), and 68 ≤x ≤80

Which of the following is a graph of the model?

Ans: A

For the minimum value of x = 68: f(68) = 0.28(68) – 2.9 = 19.04 – 2.9 = 16.14

For the maximum value of x = 80: f(80) = 0.28(80) – 2.9 = 22.4 – 2.9 = 19.5

Therefore, the extreme values of the function f(x) = 0.28x – 2.9 within the given domain of 68 ≤ x ≤ 80 are:

Minimum value: f(68) = 16.14 cm Maximum value: f(80) = 19.5 cm

Only in Option A

[Calc]  Question  Hard

f(x)=0.28x-2.9
The given function f models the length, in centimeters (cm), of aboveground growth, known as shoot length, of cotton seedlings after emerging from seeds, where x represents the seed mass, in milligrams
(mg), and 68 ≤x ≤80

What is the best interpretation of 0.28 in this context?

A. The maximum mass of the seeds was 0.28 mg.

B. The maximum shoot length of the seedlings was 0.28 cm.

C. For every two seedlings with 1 cm difference in the shoot lengths, the estimated difference in the masses of the seeds is 0.28 mg.

D. For every two seeds with 1 mg difference in the masses, the estimated difference in the shoot lengths of the seedlings is 0.28 cm.

Ans: D

Given the function $$f(x) = 0.28x – 2.9$$ where $$f(x)$$ represents the shoot length in centimeters and $$x$$ represents the seed mass in milligrams, we need to interpret the coefficient 0.28 in this context.

The coefficient 0.28 is the rate of change of the shoot length with respect to the seed mass. Specifically, it represents how much the shoot length changes for each 1 mg increase in seed mass.

A. The maximum mass of the seeds was 0.28 mg.
This is incorrect because 0.28 is not a value for the maximum mass but a rate.

B. The maximum shoot length of the seedlings was 0.28 cm.
This is incorrect because 0.28 represents a rate of change, not an absolute measurement of shoot length.

C. For every two seedlings with 1 cm difference in the shoot lengths, the estimated difference in the masses of the seeds is 0.28 mg.
This is incorrect because it suggests a relationship between shoot length difference and seed mass difference, which is not directly what the coefficient represents.

D. For every two seeds with 1 mg difference in the masses, the estimated difference in the shoot lengths of the seedlings is 0.28 cm.
This is correct because it directly interprets the rate of change of shoot length with respect to seed mass. Specifically, it means for each 1 mg increase in seed mass, the shoot length increases by 0.28 cm.

Thus, the best interpretation of 0.28 in this context is:

D. For every two seeds with 1 mg difference in the masses, the estimated difference in the shoot lengths of the seedlings is 0.28 cm.

[No calc]  Question  Hard

In 2005, 10 phlox plants were planted in a garden. The number of phlox plants increased by 140%
each year. Which of the following equations best models the estimated number of plants, P, in the garden t years after 2005?

A) P = $$1.14{(10)}^t$$

B) P = $$2.4{(10)}^t$$

C) P =$$10{(1.14)}^t$$

D) P = $$10{(2.4)}^t$$

D) P = $$10{(2.4)}^t$$

To model the estimated number of phlox plants $$P$$ in the garden $$t$$ years after 2005, we need to consider the initial number of plants and the annual growth rate.

Given:
The initial number of plants in 2005 is 10.
The number of plants increases by 140% each year.

An increase of 140% each year means the plants multiply by $$1 + 1.40 = 2.40$$ each year.

The general form of an exponential growth model is:
$P = P_0 \times (growth \, factor)^t$

Where $$P_0$$ is the initial number of plants and the growth factor is $$2.40$$.

Thus, the equation that models the number of plants $$P$$ years after 2005 is:
$P = 10 \times (2.40)^t$

[Calc]  Question   Hard

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

The line of best fit underestimates one student’s reported average time spent using the Internet on Saturdays by more than 2 hours. For how many hours did this student report reading offline?

A)0.5

B)1.5

C)3.5

D)5.0

B)1.5

A line of best fit is a straight line that is drawn through a scatter plot of data points to represent the relationship between the variables being plotted. The line is drawn in such a way that it minimizes the distance between it and the data points1. If the line of best fit underestimates the data, it means that the actual values of the dependent variable are higher than the predicted values based on the line of best fit.

Looking at the graph, the point $$(1.5,5.0)$$ is way to far from the line of best fit.

[Calc]  Question Hard

A large company has 19 mainframe computers of a certain class. The scatterplot above shows the value and age for each of the 19 computers. A line of best fit for the data is also shown.

Based on the line of best fit, the estimated value of a 6-year-old computer is $k$ thousand dollars, where $k$ is an integer. What is the value of $k$ ?

15

[Calc]  Question Hard

A large company has 19 mainframe computers of a certain class. The scatterplot above shows the value and age for each of the 19 computers. A line of best fit for the data is also shown.

What is the number of computers for which the line of best fit predicts a value less than the actual value?

9

Questions

Selena created a scale model of an airplane where 1 centimeter on the model equals 6 meters on the airplane. The wingspan of the model is 10.7 centimeters. Selena wants to make a new model where a scale of 1 centimeter on the model equals 3 meters on the airplane. Which of the following best describes how the wingspan of the new model will compare to the wingspan of the first model?
A. The wingspan of the new model will be 3 centimeters shorter than the first model.
B. The wingspan of the new model will be 3 centimeters longer than the first model.
C. The wingspan of the new model will be $\frac{1}{2}$ as long as the wingspan of the first model.
D. The wingspan of the new model will be 2 times as long as the wingspan of the first model.

Ans: D

Questions

The points plotted in the coordinate plane above represent the possible numbers of wallflowers and cornflowers that someone can buy at the Garden the Store in order to spend exactly 24.00 total on the two types of flowers. The price of each wallflower is the same and the price of each cornflower is the same. What is the price, in dollars, of 1 cornflower? (Disregard the  sign when gridding your answer. For example, if your answer is 9.87, grid 9.87)

Ans: 3/2, 1.5

Questions

The scatterplot above shows the revenue, in millions of dollars, that a company earned over several years and a line of best fit for the data. In Year 4, the difference between the actual revenue and the predicted revenue is $$n$$ million dollars, where $$n$$ is a positive integer. What is the value of $$n$$ ? Round your answer to the nearest whole number. (Disregard the  sign when gridding your answer.)

Ans: 4,5,6

Question

The scatterplot above shows the average fuel economy for a certain class of car driven at 12 different speeds, The graph of a quadratic model for the data is also shown.

For what fraction of the 12 speeds does the model overestimate the average fuel economy?

Ans: 1/4, .25

Question

The scatterplot above shows the average fuel economy for a certain class of car driven at 12 different speeds, The graph of a quadratic model for the data is also shown.

The quadratic model predicts the average fuel economy to be 26 miles per gallon for how many different speeds?