2024 SAT Standardized Test Math Practice Paper 15

6. A 40-foot tall arch with a parabolic shape has a line drawn between the bases of the two legs of the arch. If the height above the ground, y, of the arch can be written as the function y(x) = a(x – 20)(x + 20), where x represents the horizontal distance along the line between the bases from a point on the ground directly under the highest point of the arch, then what is the value of negative constant a ?

A. ​\( -\frac{1}{40} \)
B. ​\( -\frac{1}{20} \)
C. ​\( -\frac{1}{10} \)
D. -20

Correct Answer: C

Answer Explanation:

When the quadratic is set to 0 the parabola crosses the x-axis at (-20, 0) and (20, 0). Because parabolas are symmetrical, the vertex of the parabola is at (0, 40). Plug this point into the equation to get 40 = a(0 – 20)(0 + 20). Simplify the right side of the equation to get 40 = a(-20)(20) or 40 = -400a. Solve for a to get a = ​\( -\frac{40}{400} \)​ = ​\( -\frac{1}{10} \)​. Therefore, the correct answer is (C).

7. If 16a² + 4a – 6 = 0, what is a possible value of a ?

A. -0.75
B. -0.5
C. 0
D. 1

Correct Answer: A

Answer Explanation:

Whenever the question asks for a specific value and the answer choices are numbers, think Plugging In the Answers. In (A), a = -0.75. Plug -0.75 in for a in the equation to get 16(-0.75)² + 4(-0.75) – 6 = 0. Solve the left side of the equation to get 16(0.5625) + (-3) – 6 = 0, or 9 – 3 – 6 = 0. Since, this statement is true, the correct answer is (A).

8. In order to make a profit, a zoo needs to sell at least 350 admission tickets each day. Four student groups, each of which includes 48 students, have purchased tickets for admission. If z represents the number of additional tickets sold today, and the zoo made its daily profit goal, which of the following inequalities could represent all possible values for z ?

A. 4(48) + z ≤ 350
B. 4(48) + z ≥ 350
C. 4(48) – z ≤ 350
D. 4(48) – z ≥ 350

Correct Answer: B

Answer Explanation:

So far the zoo has sold 4 × 48 = 192 tickets. To make a profit, the zoo will need to sell at least 350 – 192 = 158 additional tickets. So, z needs to be at least 158. Calculate z in each of the answers to see which gives you a value of z ≥ 158. In (A), z ≤ 350 – 4(48), so z ≤ 158. Eliminate (A). Choice (B) gives you z ≥ 158. Keep (B). Choice (C) gives you z ≥ -158. Eliminate (C). Choice (D) gives you z ≤ -158. Eliminate (D). Choice (B) is the correct answer.

9. A country’s birth rate is the number of births per year per 1,000 people in the country, and a country’s death rate is the number of deaths per year per 1,000 people. Immigration refers to the number of people who move into a country each year, and emigration refers to the number of people who move out of the country each year. A country’s population growth is determined by these four variables. Table 1 gives birth, death, immigration, and emigration rates in four countries and lines 1-4 in Figure 1 model the population for the four countries shown over time.

Sat math 15 3

Line 1 represents which country’s population?

A. East Zealand
B. West Zealand
C. North Zealand
D. South Zealand

Correct Answer: D

Answer Explanation:

Line 1 shows exponential growth, because the line curves upward. Because birth rate and death rate are per 1,000 people, a birth rate higher than a death rate will result in exponential growth (because births-deaths will increase as the population increases). Immigration and emigration numbers are per year and therefore have a linear effect on the graph (as the absolute change in the population due to immigration-emigration is constant). South Zealand has more births per 1,000 than deaths per 1,000, so (D) accurately reflects line 1.

10. At the start of a new movie at the Cineplex 16, there are 250 people in the theater. However, 10% of the people walk out of the theater within the first 15 minutes of the movie starting. If another 10% leave in the next 15 minutes and this rate continues for the duration of the movie, which of the following graphs correctly models the number of people in the theater during the movie?

Sat math 15 4

Correct Answer: A

Answer Explanation:

You can start with Process of Elimination. Since the number of people in the theater decreases over time, you can eliminate (D). Choices (A) and (B) are exponential functions, whereas (C) is linear. The number of people that leave the theater every 15 minutes is not constant, since it is proportional to the number of people currently in the theater; therefore, this function is not linear, and you can eliminate (C). Choice (A) must be correct since the function decreases quickly and then the number leaving every successive 15 minutes is less than the time before (10% of 250 is more than 10% of 225).


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