2024 SAT Standardized Test Math Practice Paper 10

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. Marco is ordering salt, which is only sold in 30-pound bags. He currently has 75 pounds of salt, and he needs to have a minimum of 200 pounds. Which of the following inequalities shows all possible values for the number of bags, b, that Marco needs to order to meet his minimum requirement?

A. b ≥ 4
B. b ≥ 5
C. b ≥ 6
D. b ≥ 7

Correct Answer: B

Answer Explanation:

Because Marco already has 75 pounds of salt, he needs 200 – 75 = 125 additional pounds. Estimate the number of bags he needs. 125 is close to 120, and 120 ÷ 30 = 4, so he must need more than 4 bags (because 125 is more than 120). This means that Marco needs at least 5 more bags. Therefore, the correct answer is (B).

2. A website hopes to sign up 100,000 subscribers. So far, the website has signed up an average of 500 subscribers per day for d days. Which of the following represents the number of additional subscribers, W, the website must sign up to reach its goal?

A. W = 500d
B. W = 99,500d
C. W = 100,000 – 500d
D. W = 100,000 + 500d

Correct Answer: C

Answer Explanation:

Whenever there are variables in the question and in the answers, think Plugging In. Let d = 2. The number of subscribers the website has signed up so far can be calculated as 500(2) = 1,000. Therefore, the website needs to sign up 100,000 – 1,000 = 99,000 additional subscribers. Plug 2 in for w in the answers to see which answer equals the target number of 99,000. Choice (A) becomes W = 500(2) = 1,000. This doesn’t match the target number, so eliminate (A). Choice (B) becomes W = 99,500(2) = 199,000. Eliminate (B). Choice (C) becomes W = 100,000 – 500(2) = 100,000 – 1,000 = 99,000. Keep (C), but check (D) just in case it also works. Choice (D) becomes W = 100,000 + 500(2) = 100,000 + 1,000 = 101,000. Eliminate (D). The correct answer is (C).

3. If f is a function and f(4) = 5, which of the following CANNOT be the definition of f ?

A. f(x) = x + 1
B. f(x) = 2x – 3
C. f(x) = 3x – 2
D. f(x) = 4x – 11

Correct Answer: C

Answer Explanation:

Since the question states f(4) = 5, then when x = 4, the result should be 5. Plug in x = 4 into each answer choice to see which equation does NOT equal 5. Choice (A) becomes f(4) = 4 + 1 = 5. This works, so eliminate (A). Choice (B) becomes f(4) = 2(4) – 3 = 8 – 3 = 5. Eliminate (B). Choice (C) becomes f(4) = 3(4) – 2 = 12 – 2 = 10. The correct answer is (C).

4. Régine is measuring how many solutions from Batch x and Batch y are acidic. She measured a total of 100 solutions from both batches. 40% of the solutions from Batch x and 70% of the solutions from Batch y were acidic, for a total of 48 acidic solutions. Solving which of the following systems of equations yields the number of solutions in Batch x and Batch y ?

A. x + y = 100
0.4x + 0.7y = 48

B. x + y = 48
0.4x + 0.7y = 100

C. x + y = 100 × 2
0.4x + 0.7y = 48

D. x + y = 100
40x + 70y = 48

Correct Answer: A

Answer Explanation:

Start with the easier equation first and use Process of Elimination. The easier equation has to do with the total number of solutions. According to the question, Régine measures a total of 100 solutions. This information can be expressed as x + y = 100. Eliminate (B) and (C) because neither of these answers includes this equation. Remember that percentage means divided by 100. Therefore, 40% = 0.4 and 70% = 0.7. Given this information, x should be associated with 0.4 and y should be associated with 0.7. On this basis eliminate (D). The correct answer is (A).

5.

Math 10 1

Which of the following equations best describes the figure above?

A. y = ​\( -x^4 \)​ + 6
B. y = -(x² + 6)
C. y = -x² + 6
D. y = ​\( x^4 \)​ + 6

Correct Answer: B

Answer Explanation:

The graph shown is a regular parabola that has been turned upside down and moved down 6. The equation of a regular parabola that points upward is y = x². Therefore, the graph of a parabola that points downwards is y = -x². Eliminate (D) because that answer is missing the negative sign. To move a parabola down 6 units, a 6 must be subtracted from the equation of the parabola. Eliminate (A) and (C), which add 6 instead. Choice (B) can be rewritten as y = -x² – 6. The correct answer is (B).


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