2024 SAT Standardized Test Math Practice Paper 2

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 a possible equation for a circle that is tangent to both the x-axis and the line x = 4 ?

A. (x + 2)² + (y + 2)² = 4
B. (x + 2)² + (y – 2)² = 4
C. (x – 2)² + (y + 4)² = 4
D. (x – 6)² + (y – 2)² = 4

Correct Answer: D

Answer Explanation:

All the answer choices are equal to 4 (which is r2, making r = 2), so you need to focus on where the center of the circle lies. If the circle is tangent to both the x axis (which is equivalent to the line y = 0) and the line x = 4, then the center must be 2 units from y = 0 and 2 units from x = 4. Choices (A) and (B) both have centers with an x value of -2 (remember the standard form of the circle equation is (x – h)2 + (y – k)2 = r2, where (h, k) is the center and r is the radius), which is 6 units from x = 4. Eliminate (A) and (B). Choice (C) has a center at (2, -4). The x value is 2 units from x = 4; however, the y value is 4 units from y = 0. Eliminate (C) and choose (D).

2. Reactant A is placed in a beaker, to which Reactant B will be added. Reactants A and B will not react unless B gets to a certain concentration. Once the reaction starts, both concentrations decrease until B has been consumed. Which of the following graphs, showing concentration in moles as a function of time in seconds, represents the reaction?

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Correct Answer: B

Answer Explanation:

According to the question, Reactant A does not react unless B gets to a certain concentration. Therefore, the correct answer will have an initial flat line for A while the line for B is rising. Only graph (B) shows this initial relationship. Therefore, the correct answer is (B).

3.
-2y ≤ 8
y – 3 ≤ x
$ -\frac{1}{3} $y + 1 ≥ x

Which of the following graphs shows the solution to the system of inequalities above?

$Math sat 1 5$

Correct Answer: A

Answer Explanation:

All of the answers have the same lines graphed, so this question is really about the shading. Plugging In is probably the easiest way to approach this problem. Start with (0, 0) because this is an easy value to check. This works in all three equations since 0 ≤ 8, -3 ≤ 0, and 1 ≥ 0. Therefore, this value needs to be shaded as a possible answer. Eliminate (B), (C), and (D) because they do not include this point. The correct answer is (A).

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If rectangle ABCD has an area of 324 and the tangent of ∠BCA (not shown) is $ \frac{4}{9} $ , then which of the following is closest to the length of BD (not shown)?

A. 9.8
B. 27
C. 29.5
D. It cannot be determined from the given information.

Correct Answer: C

Answer Explanation:

First draw lines AC and BD. Now, since tangent is opposite over adjacent, $ \frac{BA}{BC} $ =$ \frac{4}{9} $ . Also, BA × BC = 324. Using these two equations as a system of equations can now help get what is needed. Rearrange the first equation by multiplying both sides by BC to get BA =$ \frac{4}{9} $ BC. Now substitute $ \frac{4}{9} $BC into the first equation to get $ \frac{4}{9} $BC (BC) = 324; this simplifies to $ \frac{4}{9} $BC² = 324. Multiply both sides by ($ \frac{4}{9} $) to get BC² = 729, and then take the square root to get BC = 27. Since the diagonal has to be larger than any of the sides, (A) and (B) are out. Choice (D) can also be eliminated because our previous calculations can get the length of DC, which is used in the Pythagorean theorem to get BD. Therefore, the correct answer is (C).

5. Which of the following is equivalent to $ \frac{2m+6}{4} $x $ \frac{6m-36}{3m+9} $?

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