2024 SAT Standardized Test Math Practice Paper 30

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. If x2 + 2xy + y2 = 64 and y – x = 12, which of the following could be the value of x ?

A. -10
B. -4
C. 2
D. 10

Correct Answer: A

Answer Explanation:

Factoring the left side of the equation x² + 2xy + y² = 64 gives (x + y)² = 64. Taking the square root of both sides of the equation, we find that x + y = 8 or -8. The other equation provides that y – x = 12, so y = x + 12 . Substitute this value of y into the first equation: either x + (x + 12) = 8, so 2x + 12 = 8, 2x = -4, and x = -2, or else or x + (x + 12) = -8, so 2x + 12 = -8, so 2x = -20, and x = -10. Therefore, x could be either -2 or -10, and only -10 is an option in the answers, so (A) is correct.

2. Samantha offers two different packages of yoga classes at her yoga studio. She offers two hot yoga sessions and three zero gravity yoga sessions at a total cost of $400. She also offers four hot yoga sessions and two zero gravity sessions at a price of $440. Samantha wants to offer a larger package for long-time clients in which the cost must exceed $800. If Samantha does not wish to include more than 13 sessions for the long-time client package, will she be able to create this package for her clients?

A. No, because the closest package that she can offer consists of three hot yoga and three zero gravity yoga sessions.
B. No, because the closest package that she can offer consists of four hot yoga and four zero gravity yoga sessions.
C. Yes, because she can offer five hot yoga and five zero gravity yoga sessions.
D. Yes, because she can offer six hot yoga and six zero gravity yoga sessions.

Correct Answer: D

Answer Explanation:

Translate from English to  math in bite-sized pieces. Make the price of a hot yoga lesson h and the price of a zero gravity yoga session z. If she offers 2 hot yoga and 3 zero gravity yoga sessions for $400, then 2h + 3z = 400. Similarly, if 4 hot yoga and 2 zero gravity yoga sessions are $440, then 4h + 2z = 440. Now, be sure to Read the Full Question: You want to know whether Samantha can create a package that’s greater than $800 but has fewer than 13 sessions. If you stack the two equations and then add them together, you get 6h + 5z = 880. In other words, she can offer 6 hot yoga and 5 zero gravity yoga sessions (11 total sessions) for $880. This satisfies her requirements, so you know the answer is “Yes”; eliminate (A) and (B). For (C), because you don’t know the price of each lesson individually, you don’t know yet whether 5 hot yoga and 5 zero gravity yoga sessions will be over $800; leave (C) for now. For (D), if 6 hot yoga and 5 zero gravity yoga sessions were over $800,then adding a zero gravity yoga session will still be over $800. Given what you already know, (D) must be true; choose (D).

3. Cuthbert is conducting a chemistry experiment that calls for a number of chemicals to be mixed in various quantities. The one amount of which he is unsure is grams of potassium, p . If Cuthbert is certain that (3p2 + 14p + 24) – 2(p2 + 7p + 20) = 0, what is one possible value of 3p + 6, the exact number of grams of potassium that Cuthbert would like to use for this experiment?

A. 20
B. 18
C. 12
D. 10

Correct Answer: B

Answer Explanation:

Begin by simplifying the equation given. (3p² + 14p + 24) – 2(p² + 7p + 20) = 3p² + 14p + 24 – 2p² – 14p – 40 = p² – 16 = 0. Factoring the left side of the simplified equation, we find that (p – 4)(p + 4) = 16. Solving for p, we find that p = ±4. The value of 3p + 6 must then be either 3(-4) + 6 = -6 or 3(4) + 6 = 18. The latter value is (B).

4. What is the value of (2 + 8i)(1 – 4i) – (3 – 2i)(6 + 4i) ?

A. 8
B. 26
C. 34
D. 50

Correct Answer: A

Answer Explanation:

Sat math 30 1

5. If ​\( 2\sqrt[]{x} \)​ = x – 3, which of the following is the solution set for x ?

A. {-1, 9}
B. {1, -9}
C. {9}
D. {1, 9}

Correct Answer: C

Answer Explanation:

Sat math 30 2

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