2024 SAT Test Math Practice 21


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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. Which of the following is equivalent to the expression ​\( x^4 \)​ – x³ – x² ?

A. x(x² – x – 1)
B. x(x – x² – x³)
C. x(x³ – x²)
D. x²(x² – x – 1)

Correct Answer: D

Answer Explanation:

To solve this question, simply factor out the largest value that fits within each of the terms in the expression provided. In this case, ​\( x^4 \)​, x³, and x² are all divisible by x², so that is what you will want to factor out. Doing so will leave you with x² (x² – x – 1), which is (D).

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2. Officer Blake drives his squad car 1 mile per minute while patrolling local highways during his shift. If he has driven 480 miles by the end of his shift, how many total hours did he drive his car at the above rate?

A. 8
B. 12
C. 16
D. 20

Correct Answer: A

Answer Explanation:

Since Officer Blake drives 480 miles at a rate of 1 mile per minute, his total drive time was 480 minutes. The question asks for Officer Blake’s driving time in hours, so you need to convert those minutes into hours. Since there are 60 minutes in 1 hour, you can divide 480 minutes by 60 to determine that Officer Blake drove for 8 hours, which is (A).

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3. In the inequality 37 ≤ – 2x + 1, what is the appropriate order of steps needed to solve the inequality for x ?

A. Add 1 to both sides, divide both sides by 2, and flip the inequality sign to ≥.
B. Subtract 1 from both sides, divide both sides by -2, and flip the inequality sign to ≥.
C. Add 1 to both sides, divide both sides by -2, and keep the original inequality sign.
D. Subtract 1 from both sides, divide both sides by 2, and keep the original inequality sign.

Correct Answer: B

Answer Explanation:

The goal here is to isolate x. Since the right-hand side of the equation is -2x + 1, you will want to subtract 1 from both sides, so eliminate (A) and (C). To get x by itself, you will want to divide by -2, not 2, so eliminate (D) and choose (B). Remember that when you multiply or divide across an inequality sign using a negative number, you need to flip the inequality sign in the opposite direction, as reflected in (B).

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4. What is the value of (2x² + 4x + 8) – (2x² – 4x + 7) ?

A. 4x² + 8x + 15
B. 2x² + x + 1
C. 8x + 1
D. 8x + 15

Correct Answer: C

Answer Explanation:

To solve this question, rearrange the expressions (2x² + 4x + 8) and (2x² – 4x + 7) in order to place the similar terms next to each other. Doing so will give you 2x² – 2x² + 4x – (-4x) + 8 – 7 (remember to distribute the negative sign for each of the terms in the second expression). Simplifying this new expression will yield 0 + 8x + 1, or 8x + 1, (C). Another way to approach this question would be to plug in a simple number for x, such as x = 2, and match your target value with the values in the answer choices.

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5. As part of a project for his cartography elective, Adam climbs several hills to create a relief map for the woods surrounding his house. He records the vertical heights of the five hills he climbed at 55 feet, 42 feet, 38 feet, 50 feet, and 48 feet. For his project, Adam must convert his measurements to inches. If 1 foot = 12 inches, what is the measurement, in inches, of the tallest hill Adam will have on his map?

A. 660
B. 600
C. 576
D. 456

Correct Answer: A

Answer Explanation:

The tallest hill that Adam measures is 55 feet high. Since 1 foot is equivalent to 12 inches, simply multiply 55 × 12 = 660 inches, (A).

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