2024 SAT Standardized Test Math Practice Paper 1

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 equations has a vertex of (3, -3) ?

A. y = 5(x – 3)² – 3
B. y = 5(x + 3)² – 3
C. y = 5(x – 3)² + 3
D. y = 5(x + 3)² + 3

Correct Answer: A

Answer Explanation:

The vertex form of a parabola is y = a(x – h)² + k, where (h, k) denotes the vertex. Plug in the point (3, -3) into the vertex form to get y = a(x – 3)2 – 3. The correct answer is (A).

2. A beverage store charges a base price of x dollars for one keg of root beer. A sales tax of a certain percentage is applied to the base price, and an untaxed deposit for the keg is added. If the total amount, in dollars, paid at the time of purchase for one keg is given by the expression 1.07x + 17, then what is the sales tax, expressed as a percentage of the base price?

A. 0.07%
B. 1.07%
C. 7%
D. 17%

Correct Answer: C

Answer Explanation:

You can plug in to make sense of this equation. Say that x = $100. The amount of the keg would then be $107 + $17. The $17 must be the untaxed deposit since it is a flat fee rather than percentage based. Therefore, the tax is $7, which is 7% of the original $100 base price. The answer is (C).

3. Syed took out a cash advance of d dollars from a financing company. The company deducts a fee of ​\( \frac{1}{3} \)​ of the original advanced amount along with a wire transfer fee of $30.00. Which of the following represents the final advanced amount that Syed receives after all applied fees, in dollars?

Math sat 1 1

Correct Answer: D

Answer Explanation:

Whenever there are variables in the question, plug in. Be sure to plug in a number that is divisible by 3. Let d = 300. ​\( \frac{1}{3} \)​ of the original amount of $300 is $100, and that is deducted by the company, leaving Syed with $200. Now, subtract the wire transfer fee to get $200 – $30 = $170, which is the target number. Plug in 300 for d in the answers to see which answer is equal to the target number of 170. In (A), ​\( \frac{1}{3} \)​(300) – 30 = 70. This is not the target number, so eliminate (A). Likewise in (B), ​\( \frac{1}{3} \)​(300 – 30) = 90, and in (C), ​\( \frac{2}{3} \)​(300 – 30) = 180. Neither of these is the target number, so eliminate (B) and (C). In (D), ​\( \frac{2}{3} \)​(300) – 30 = 170, which is the target number. The correct answer is (D).

4. What is the equation of a line that contains the point (1, 6) and has a y-intercept of 4 ?

A. y = ​\( \frac{1}{2} \)​x + 4
B. y = x + 4
C. y = 2x + 4
D. y = 4x + 2

Correct Answer: C

Answer Explanation:

All of the answers are written in the slope-intercept form y = mx + b, where b is the y-intercept and x and y are points on the line. Eliminate (D) because the y-intercept in that equation is 2. For the remaining answer choices, plug in the x- and y-values to determine which equationworks. If x = 1 and y = 6, (A) becomes 6 = ​\( \frac{1}{2} \)​(1) + 4. Solve both sides of the equation to get 6 = 4. Eliminate (A). Choice (B) becomes 6 = 1 + 4​\( \frac{1}{2} \)​, so eliminate (B). Choice (C) becomes 6 = 2(1) + 4, or 6 = 6. Therefore, the correct answer is (C).

5. The number of bonus points, B(p), that a credit card holder receives is given by the function B(p) = 4p + 7, where p represents the number of purchases made. If the number of purchases is increased by 3, by how much does the number of bonus points increase?

A. 3
B. 4
C. 12
D. 19

Correct Answer: C

Answer Explanation:

Whenever there are variables in the question and the answer choices, think Plugging In. If 2 purchases were made, then p = 2, and the number of bonus points can be calculated as 4(2) + 7 = 8 + 7 = 15. If the number of purchases were then increased by 3, the new p equals 5 and the number of bonus points can be calculated as 4(5) + 7 = 27. The bonus points increased by 27 – 15 = 12. Therefore, the correct answer is (C).

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