## 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**

A sample of 50 employees from the finance department at Company XYZ was selected at random. The 50 employees completed a survey about a website’s ease of use, and \(72 \%\) of them thought the website was easy to use. Which of the following is the largest population to which the results of this survey can be generalized?

A) All employees in a finance department in the United States

B) All employees in Company XYZ

C) All employees in the finance department in Company XYZ

D) All employees in the sample

**▶️Answer/Explanation**

**Ans:C**

A sample of 50 employees from the finance department at Company XYZ was selected at random, and 72% of them thought the website was easy to use. We need to determine the largest population to which the results of this survey can be generalized.

Given that the sample was specifically from the finance department at Company XYZ, the results can most reliably be generalized to the population from which the sample was drawn.

Therefore, the largest population to which the results of this survey can be generalized is:

\[

\boxed{\text{All employees in the finance department in Company XYZ}}

\]

**[Calc]**** ****Question*** *** Easy**

The dot plot shows the 9 values of a data set with a mean value of a and a median value of b. The value of 46 is removed to create a new data set of 8 values with a mean value of y and a median value of z. Which statement best compares the mean values and the median values for the two data sets?

A. a=y and b < z

B. a = y and b > z

C. a <y and b = z

D. a>y and b=z

**▶️Answer/Explanation**

Ans: D

For the mean: Removing the maximum value (46) from the original data set will decrease the mean value, as the sum of the remaining values will be smaller than the original sum, while the number of values decreases from 9 to 8. Therefore, the mean value of the new data set (y) will be less than the mean value of the original data set (a).

For the median: The median is the middle value when the data is arranged in order. In this case, with 9 values in the original data set, the median (b) is the 5th value when arranged in order. After removing the maximum value (46), the new data set will have 8 values, and the median (z) will still be the 5th value when arranged in order, as the removal of the maximum value does not affect the order of the remaining values. Therefore, the median value (z) of the new data set will be the same as the median value (b) of the original data set.

Based on this analysis, the statement that best compares the mean values and median values for the two data sets is:

D. a > y and b = z

This statement correctly indicates that the mean value of the original data set (a) is greater than the mean value of the new data set (y), and the median value of the original data set (b) is equal to the median value of the new data set (z).

**[Calc]**** ****Question** ** Easy**

A solution is formed by adding m grams of propylene glycol to 100 grams of water. For this

solution, the freezing point, in kelvins, is modeled by the function T(m)= 273.2 – 0.327m. Which of the following is the best interpretation of the statement “T(22) is approximately equal to 266” in this context?

A) A solution formed by adding 22 grams of propylene glycol to 100 grams of water has an estimated freezing point of 266 kelvins.

B) A solution formed by adding 266 grams of propylene glycol to 100 grams of water has an

estimated freezing point of 22 kelvins.

C) For every 22 grams of propylene glycol added to 100 grams of water, the freezing point of the solution is estimated to decrease by 266 kelvins.

D) For every 266 grams of propylene glycol added to 100 grams of water, the freezing point of the solution is estimated to decrease by 22 kelvins.

**▶️Answer/Explanation**

A) A solution formed by adding 22 grams of propylene glycol to 100 grams of water has an estimated freezing point of 266 kelvins.

The function \(T(m) = 273.2 – 0.327m\) models the freezing point of a solution in kelvins, where \(m\) is the grams of propylene glycol added to 100 grams of water. We need to interpret the statement \(T(22) \approx 266\).

1. Substitute \(m = 22\) into the function:

\[

T(22) = 273.2 – 0.327 \times 22

\]

\[

T(22) = 273.2 – 7.194

\]

\[

T(22) \approx 266

\]

This means that adding 22 grams of propylene glycol to 100 grams of water results in a freezing point of approximately 266 kelvins.

Thus, the correct interpretation is:\[ \boxed{\text{A}} \]

**[Calc]**** ****Question**** Easy**

American marsupials and Australian marsupials are two primary groups of marsupials. The table shows the number of species in each order of living marsupial, by group.

Based on the table, what fraction of the Australian marsupial species are from the order Peramelemorphia?

A) $\frac{24}{211}$

B) $\frac{24}{235}$

C) $\frac{24}{334}$

D) $\frac{235}{334}$

**▶️Answer/Explanation**

B

*Question*

To determine if cooking with olive oil reduces the risk of heartburn for men, researchers interviewed a random sample of 5,500 men who had no history of heartburn. Study participants were identified as either regular or occasional olive oil users. Five years later, researchers interviewed the men again. They found that the proportion of men who experienced frequent heartburn was significantly lower for men identified as regular olive oil users. Which of the following is the most appropriate conclusion of the study?

A. Olive oil use causes a reduction in the risk of heartburn for men and women.

B. Olive oil use causes a reduction.in the risk of heartburn for men but not necessarily for women.

C. There is an association between olive oil use and the risk of heartburn for men and women, but it is not necessarily a cause-and-effect relationship.

D. There is an association between olive oil use and the risk of heartburn for men, but it is not necessarily a cause-and-effect relationship, and the association may not exist for women.

**▶️Answer/Explanation**

Ans: D

*Question*

Residents of a town were surveyed to determine whether they are satisfied with the concession stand at the local park. A random sample of 200 residents was selected. All 200 responded, and $87 \%$ said they are satisfied. Based on this information, which of the following statements must be true?

I. Of all the town residents, $87 \%$ would say they are satisfied with the concession stand at the local park.

II. If another random sample of 200 residents were surveyed, $87 \%$ would say they are satisfied.

A. Neither

B. I only

C. II only

D. I and II

**▶️Answer/Explanation**

Ans: A

*Questions *

A political scientist wants to predict how the residents of New Jersey will react to a new bill proposed in the state senate. Which of the following study designs is most likely to provide reliable results for the political scientist?

A. Mailing a questionnaire to each of 200 randomly selected residents of New Jersey

B. Surveying a group of 300 randomly selected New Jersey residents

C. Interviewing a group of students randomly selected from a large public university in New Jersey

D. Surveying a group of 1,500 randomly selected US residents

**▶️Answer/Explanation**

Ans: B