2024 SAT Standardized Test Math Practice Paper 14

6. During the month of July, the number of units, y, of a certain product sold per day can be modeled by the function y = -3.65x + 915, where x is the average daily temperature in degrees Fahrenheit. Which of the following statements must be true?

A. As the temperature increases, the number of units sold decreases.
B. As the temperature increases, the number of units sold remains constant.
C. As the temperature increases, the number of units sold increases.
D. There is no linear relationship between temperature and the number of units sold.

Correct Answer: A

Answer Explanation:

Whenever there are variables in the question, think Plugging In. The answers refer to what happens when the temperature, x, increases, so plug in more than one value of x. Plug in x = 1 into the equation to get y = -3.65(1) + 915 = -3.65 + 915 = 911.35. Next plug in x = 2 to get y = -3.65(2) + 915 = -7.3 + 915 = 907.7. As average daily temperature, x, increased, the number of units sold, y, decreased. Therefore, the correct answer is (A).

7. Newton’s law of gravitation describes the strength of the force F between two objects with masses M and m separated by a distance of r units and is defined as. F = ​\( \frac{GMm}{r²} \)​. Which of the following gives the value of Newton’s gravitational constant G, in terms of F, M, m, and r ?

A. G = Fr²Mm
B. G = ​\( \frac{Fr²}{Mm} \)
C. G = ​\( \frac{GMm}{r²} \)
D. G =  ​\( \frac{F}{r²Mm} \)

Correct Answer: B

Answer Explanation:

Plugging In could work on this one, but calculators aren’t permitted. Since the equation is fairly simple, solving may be a better approach. Multiply both sides of the equation by r² to get Fr² = GMm. Divide both sides of the equation by Mm to get ​\( \frac{Fr²}{Mm} \)​= G. The correct answer is (B).

8. Which of the following expressions is equivalent to (4s)​\( \frac{1}{3} \)​?

A. ​\( \frac{2}{\sqrt[]{s}} \)
B. ​\( \frac{1}{12s³} \)
C. ​\( 2\sqrt[]{s} \)
D. ​\( \sqrt[3]{4s} \)

Correct Answer: D

9. Oil is being drained from an oil tank at a constant linear rate. Four hours after draining of the tank began, the volume of oil in the tank was 740 gallons, and seven hours after draining of the tank began, the volume was 545 gallons. Which of the following functions best models v(t), the volume of oil in the tank, in gallons, t hours after draining of the tank began?

A. v(t) = 740 – t
B. v(t) = 740 – 65t
C. v(t) = 1000 – 195t
D. v(t) = 1000 – 65t

Correct Answer: D

Answer Explanation:

According to the question, if t = 4, then v(t) = 740. Plug 4 in for t in the answer choices and see if v(t) comes out to the target number 740. In (A) if t = 4, then v(t) = 740 – 4 = 736. Eliminate (A). In (B), if t = 4, then v(t) = 740 – 65(4) = 740 – 260 = 480. Eliminate (B). In (C), if t = 4, then v(t) = 1,000 – 195(4) = 1,000 – 780 = 220. Eliminate (C). The correct answer must therefore be (D).

10. What is the result of multiplying 8s² – 6s + 2 by 4s – 1 ?

A. 14s – 2
B. 16s² + 2s + 2
C. 32s³ – 16s² + 2s + 2
D. 32s³ – 32s² + 14s – 2

Correct Answer: D

Answer Explanation:

Whenever there are variables in the question and in the answers, think Plugging In. If s = 2, the first expression becomes 8(2²) – 6(2) + 2 = 8(4) – 12 + 2 = 32 – 12 + 2 = 22. Therefore, the first expression multiplied by the second expression is 22(7) = 154. Plug in 2 for s in the answers to see which choice equals the target number of 154. Choices (A), (B), and (C) yield 26, 70, and 198 respectively. Choice (D) yields 154 and is the correct answer.


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