2024 SAT Standardized Test Math Practice Paper 13

6. Is the point (-2, -2) located inside, on, or outside the circle with equation (x + 3)² + (y – 1)² = 9 ?

Correct Answer: C

Answer Explanation:

Since x and y are points on the circle, plug in the point (-2, -2) into the left side of the equation. This gives you (-2 + 3)² + (-2 – 1)², which equals 1² + (-3)². Simplifying, you get 10. Because 10 is greater than r² (which is 9), the point must be outside the circle, which is (C).ml

7. A survey was conducted among a randomly chosen sample of full-time salaried workers about satisfaction in their current jobs. The table below shows a summary of the survey results.

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Of the people whose highest level of  education was a bachelor’s degree who reported job satisfaction, 1,000 people were randomly selected to complete a follow-up survey in which they were asked about their salary satisfaction. There were 658 people in this follow-up sample who said that they were satisfied with their salaries, and the other 342 people were not satisfied. Using the data from both the initial survey and the follow-up survey, which of the following statements is most likely true?

A. Approximately 16 million people with bachelor’s degrees would report salary satisfaction.
B. Approximately 24 million people with bachelor’s degrees would report salary satisfaction.
C. Approximately 47 million people with bachelor’s degrees would report salary satisfaction.
D. Approximately 72 million people with bachelor’s degrees would report salary satisfaction.

Correct Answer: A

Answer Explanation:

All of the answer choices refer to the number of salary-satisfied bachelor’s-degree-holders, so you must use the follow-up survey results to calculate that number. First, find the percent of bachelor’s-degree-holders who reported also being salary-satisfied in the follow-up survey. This number was 658 out of the 1,000 people, so divide 658 by 1,000 and then multiply by 100 to get the percent. The result is 65.8% salary-satisfied bachelor’s-degree-holders for the follow-up survey. Since the people in the follow-up were randomly selected, you can assume that they are generally representative of the bachelor’s-degree-holding population at large. Therefore, the 65.8% of salary-satisfied individuals should be true of all 24,236,000 job-satisfied bachelor’s-degree-holders. Watch the units on charts-this one is in the thousands, so there are 24,236,000 not 24,236 job-satisfied bachelor’s-degree-holders. Multiply 65.8%, or .658, by the total number of bachelor’s-degree-holders, 24,236,000, to find that there should be 15,947,288 salary-satisfied, job-satisfied bachelor’s-degree-holders. Choice (A) is the closest to this and is the credited response.

8. Line d has a slope of ​\( \frac{4}{5} \)​ and passes through the point (1, 1). Line e is parallel to line d and has a y-intercept 3 times that of line d. Which of the following is the equation of line e ?

A. 5y – 4x = 3
B. 5y – x = 4
C. 10y – 8x = 30
D. 20y + 25x = 12

Correct Answer: A

9. ​\( \frac{q²-q-42}{q+6}=\sqrt[]{q-5} \)​

The equation above can be solved for two solutions, one of which is extraneous. What is the value of the extraneous solution?

A. 5
B. 6
C. 8
D. 9

Correct Answer: B

10. A  gaming company conducted a study to find out what age groups preferred which types of games. The table below outlines the survey results.

Math 14 2

According to the information provided in the table, the gaming company concludes that if they can double the number of 19- to 22-year olds playing  sports games, and increase the number of sports gamers in the 9- to 13-year old age group, they will have equal total numbers of players for each game type if they double the number of players of adventure games in which age group?

A. 23- to 60-year olds
B. 19- to 22-year olds
C. 14- to 18-year olds
D. 9- to 13-year olds

Correct Answer: D

Answer Explanation:

First, determine the total number of gamers in each game type by adding up the columns. There are 110,000,000 gamers preferring first person shooters, 52,000,000 preferring sports games, and 85,000,000 preferring adventure games. You don’t know by how much the 9- to 13-year old group will increase in sport game preference, but presumably the increase will be made to match the currently largest group, first person shooters. Therefore, in order to raise adventure games to the level of first person shooters, you need to add 110,000,000 – 85,000,000 = 25,000,000 gamers to the adventure games group. If you are going to do so by doubling one of the age groups, then 25,000,000 is equal to the size of the current group. 9- to 13-year olds currently have 25,000,000 preferring adventure games, so (D) is your answer.

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