2024 SAT Standardized Test Math Practice Paper 16

6. A single frame of 35 mm film is about three-quarters of an inch long. A film reel holds up to 1,000 feet of film. How many reels are required for a two-hour, forty-seven minute film shot at 24 frames per second?

A. 13
B. 14
C. 15
D. 16

Correct Answer: D

6. Hua needs to receive completed surveys from at least 3,800 potential voters in her city. She has noticed that for every 5 surveys she sends out, only 1 survey is completed. Last week she received 1,350 completed surveys, and this week she received 900 completed surveys. Hua plans to send out s additional surveys. Which of the following inequalities shows all possible values for s that would ensure that Hua receives 3,800 completed surveys?

A. s ≥ 1,550
B. s ≥ 2,250
C. s ≥ 7,750
D. s ≥ 12,250

Correct Answer: C

Answer Explanation:

So far, Hua has received 1,350 + 900 = 2,250 surveys. Hua needs 3,800 – 2,250 = 1,550 additional surveys. Given that Hua receives 1 completed survey for every 5 she sends out, she will need to send out at least 5 × 1,550 = 7,750 surveys. Therefore, the correct answer is (C).

7.

Sat math 16 4

In the figure above C is the midpoint of BD and AC = DE. What is the value of n ?

A. 30
B. 45
C. 60
D. Cannot be determined from the information given

Correct Answer: B

Answer Explanation:

Since line AE is perpendicular to the line containing segment AB and the line containing segment DE, these two lines must be parallel. Therefore, ∠ABC is equal to ∠CDE because they are both small angles created by a line crossing two parallel lines. Since ∠DCE and ∠ACB are opposite each other, they must be equal as well, so these are two similar right triangles. The question also tells you that C is the midpoint of BD, which means that BC and CD are equal. When you have two sides and the included angle of one triangle congruent to two sides and the included angle of a second triangle, you know that the triangles are congruent. This means that AB = DE and AC = CE. Lastly, the question states that AC = DE, which means that AB = AC, and these must be isosceles right triangles. Angle ABC is therefore 45°, and n, which is opposite ∠ABC, must be 45° as well. The correct answer is (B).

8. Allie is a caterer who is building 4 sandwich platters. Each sandwich platter contains turkey slices that weigh 2 ounces each and bread slices that weigh 1 ounce each. In each platter, she has a total of 100 slices of turkey and bread that weigh a total of 160 ounces. Solving which of the following system of equations yields the number of turkey slices, t, and the number of bread slices, b, that are in the 4 sandwich platters?

A. t + b = 100
2t + b = 160
B. t + b = 160
2t + b = 100
C. t + b = 400
2t + b = 160
D. t + b = 400
2t + b = 640

Correct Answer: D

Answer Explanation:

Start with the easier equation and use Process of Elimination. The easier equation is related to the total number of turkey and bread slides, t + b, on the 4 platters. According to the question, each platter contains 100 slices, so the 4 platters contain 100 × 4 = 400 slices. Therefore, one of the equations in the correct answer must be t + b = 400. Eliminate (A) and (B) since neither of these answers contains that equation. The second equation deals with the weight of the slices. According to the problem, the slices on each platter weigh 160 ounces. Therefore, the total weight of the slices on all 4 platters is 160 × 4 = 640. Eliminate (C) because the total is wrong in the weight equation. The correct answer is (D).

9. 4a + 2z = 10
-3a + z = -10

Based on the system of equations above, what is the value of 10a ?

A. -10
B. -1
C. 3
D. 30

Correct Answer: D

Answer Explanation:

Whenever there are two equations with the same two variables, they can be solved simultaneously by adding or subtracting them. The key is to get one variable to disappear. Multiply the second equation by -2, to get 6a – 2z = 20. Stack the two equations and add them. Therefore, the correct answer is (D). Be careful of (C)-the question did NOT ask for the value of a.

10. Isabella has $1,000 to invest and explores a number of options at her local bank. After learning about her options, she decides to deposit her $1,000 into a high-yield savings account that compounds at an annual rate of 4%, compounded quarterly. The banker tells Isabella that her projected earnings in dollars, P, as a function of time in years, t, can best be represented by the equation P(t) = 1000(1.01)4t. Which of the following graphs best illustrates Isabella’s projected earnings over time?

Sat math 16 5

Correct Answer: B

Answer Explanation:

We know that Isabella starts with $1,000 in her account, so this eliminates (D). She is earning money from the interest, so the line must have a positive slope, eliminating (C), which has a constant slope. The two best choices are (A) and (B), but in (A) Isabella’s money doesn’t begin to increase until the 5-year mark, which doesn’t make sense-thus (B) is the best choice.


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