2024 SAT Standardized Test Math Practice Paper 13

The 2024 SAT standardized test is a critical assessment for college admissions. The math section covers a wide range of topics. To help students prepare, we’ve created a practice paper. This paper includes various math problems to help students become familiar with the test format and excel in their exam.

 

1. Y=​\( \frac{A}{A+W} \)​

A gardener prepares a mixture of fertilizer with concentration, by volume, equal to Y. It is prepared by mixing a volume of fertilizer given by A with a volume of water given by W. The expression above represents the mixture described. What physical quantity does the term A + W represent in the equation above?

A. The volume of the mixture
B. The mass of fertilizer added
C. The volume of the fertilizer in the mixture
D. The concentration of the fertilizer

Correct Answer: A

Answer Explanation:

Use Process of Elimination to solve this question. Choice (A) is possible so leave it. Choice (B) discusses the mass of the fertilizer, but no reference to mass is made in the question. Eliminate (B). According to the question, the quantity described in (C) is represented by A, so eliminate (C). According to the question, the quantity described in (D) is represented by Y, so eliminate (D). The correct answer is (A).

2. Two groups of subjects are combined in a psychological research experiment. The mode score for group A is 7 and the mode score for group B is 6. Which of the following conclusions can be made?

A. The mode for the whole group is 6.
B. The mode for the whole group is between 6 and 7.
C. The mode for the whole group is 7.
D. The mode cannot be determined from the given information.

Correct Answer: D

Answer Explanation:

The mode of the combined groups cannot be determined without knowing exactly what scores each group received. To illustrate this, plug in! Let’s say that the scores of Group A were {1, 1, 7, 7, 7}, and the scores for Group B were {1, 1, 6, 6, 6}. The scores of the whole group would, therefore, be {1, 1, 1, 1, 6, 6, 6, 7, 7, 7}. This set has a mode of 1, so eliminate (A), (B), and (C) and choose (D).

3. The map below shows the layout of streets in a city and the location of several places. Each horizontal or vertical line between two adjacent streets represents a city block, and each city block represents 0.6 miles.

Math 13 1

Josh needs to drive from Kelly’s Kitchen to Gary’s Grocery. If Josh drives the shortest distance possible on the roads shown above at a constant speed of 30 miles per hour, how long does it take him to make the trip from Kelly’s Kitchen to Gary’s Grocery?

A. 6 minutes
B. 10 minutes
C. 12 minutes
D. 20 minutes

Correct Answer: C

4. 2s – t = 10
5s = t + 12 – s

Which of the following is a true statement about the system of equations above?

A. There are infinitely many solutions to the system of equations.
B. When the system is solved for s, the result is 5.
C. When the system is solved for t, the result is 6.
D. There are no solutions to the system of equations.

Correct Answer: D

Answer Explanation:

The first step is to rewrite the bottom equation so that it is in the same format as the first equation. Move all of the variables in the bottom equation to the left side of the equation to get 6s – t = 12. If the answer is (A) and there are infinitely many solutions to the system of equations, then the two equations must be the same equation. To determine whether this is the case, multiply the top equation through by 3 to get 6s – t = 30. Since it cannot be the case that the equation 6s – t equals both 12 and 30, the correct answer is (D). There are no solutions to the system of equations.

5. The student council at Shermer High School wants to use student opinion to decide on one of three possible homecoming themes for the year. President Peterson thinks that the best way to determine popular opinion is for each of the 10 members of the student council to poll 10 of their friends and select the theme that receives the most votes. Vice President Vaidya wants to go to the cafeteria during lunch and poll 100 students to determine the winner. Treasurer Thompson says the best method would be to assign numbers to each of the 1,000 students in the school, randomly select 100 of them to poll, and select the winner based on the results. Secretary Stephens argues that they must poll each of the 250 members of the senior class to find the most popular theme. Whose method is most likely to accurately determine overall student opinion regarding the most popular homecoming theme?

A. President Peterson
B. Secretary Stephens
C. Treasurer Thompson
D. Vice-President Vaidya

Correct Answer: C

Answer Explanation:

Two factors are important in determining how to poll a group: the size of the sample and how that sample is selected. Secretary Stephens’s plan has the largest sample with 250 students, but all those students belong to the senior class. Perhaps the senior class would prefer a theme that the other three classes would not. The sample is skewed and not necessarily representative of the entire student body, so eliminate (B). The other three plans all poll 100 students, so the manner in which those students are selected becomes more important. President Peterson’s plan is also skewed specifically to friends of the student council members, whose opinions might not reflect the majority, so eliminate (A). Vice President Vaiyda’s plan has more potential for a varied sample, but it is still not as good as Treasurer Thompson’s plan, which guarantees that a random assortment of people will be chosen for the poll. Eliminate (D), and choose (C).

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