2024 SAT Standardized Test Math Practice Paper 5

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.

Math sat 4 1

If the radius of the circle above is x, ∠AOB = 120°, and O is the center of the circle, what is the length of chord AB in terms of x ?

Math sat 4 2

Correct Answer: B

Answer Explanation:

You can start by Plugging In a value for x; try x = 4. Because angle AOB is 120° and the triangle is isosceles, angles A and B are each 30°. Cut triangle AOB in half to make two 30-60-90 triangles with a hypotenuse of 4 and sides of 2 and 2​\( \sqrt[]{3} \)​. The side with length 2​\( \sqrt[]{3} \)​ lies on chord AB. Double it to get the total length: 4​\( \sqrt[]{3} \)​ or just ​\( \sqrt[]{3^x} \)​, which is (B) when you put x = 4 into the answer choices.

2. Students in a physics class are studying how the angle at which a projectile is launched on level ground affects the projectile’s hang time and horizontal range. Hang time can be calculated using the formula ​\( t=\frac{2v·sin(θ)}{g} \)​ ,where t is the hang time in seconds, v is the initial launch velocity, θ is the projectile angle with respect to level ground, and g is the acceleration due to gravity, defined as 9.8 m/s². Horizontal range can be calculated using the formula ​\( R=\frac{v²sin(2θ)}{g} \)​ , where R is the distance the projectile travels from the launch site, in feet. Which of the following gives the value of v, in terms of R, t, and θ ?

Math sat 4 4

Correct Answer: C

Answer Explanation:

Math sat 4 3

3. If ​\( (i^413)(l^x)=1 \)​, then what is one possible value of x ?

A. 0
B. 1
C. 2
D. 3

Correct Answer: D

Answer Explanation:

​\( l^a \)​= 1 when a is a multiple of 4. Using your exponents rules, 413 + x must also be a multiple of 4. Plug in the answers and look for what makes 413 + x a multiple of 4. Only (D) works.

4. The function g is defined by g(x) = 2x² – dx – 6, where d is a constant. If one of the zeros of g is 6, what is the value of the other zero of g ?

Math sat 4 6

Correct Answer: C

Answer Explanation:

The zero of g is the value of the variable, in this case x, when the equation is set to 0. This is also called the root or solution of an equation. Set the equation to 0 to get 0 = 2x² – dx – 6. Plug 6 in for x to get 0 = 2(6²) – d(6) – 6. Simplify the equation to get 0 = 72 – 6d – 6, or 0 = 66 – 6d. Solve for d to get -66 = -6d, so 11 = d. Plug 11 in for d and set the quadratic to 0 to get 0 = 2x² – 11x – 6. Factor the equation to get 0 = (x – 6)(2x + 1). The other zero of the equation is when 2x + 1 = 0. Solve for x to get 2x =-1 ​​, or x =​\( \frac{-1}{2} \)​ . The correct answer is (C).

5. The flu shot for a flu season is created from four strains of the flu virus, named Strain A, B, C, and D, respectively. Medical researchers use the following data to determine the effectiveness of the vaccine over the flu season. Table 1 shows the effectiveness of the vaccine against each of these strains individually. The graph below the table shows the prevalence of each of these strains during each month of the flu season, represented as a percentage of the overall cases of flu that month.

Math sat 4 5

For the strain against which the flu shot was the most effective, approximately how effective was the shot overall when that strain was least prevalent?

A. 13%
B. 20%
C. 27%
D. 48%

Correct Answer: D

Answer Explanation:

The flu shot is most effective against Strain C, which is least prevalent in March. To determine the overall efficacy of the flu shot at this time, multiply the prevalence of each strain of flu by the efficacy of the flu shot against that strain, and then add those products to get a weighted average of the efficacy of the shot: (0.23 × 0.35) + (0.25 × 0.13) + (0.13 × 0.76) + (0.39 × 0.68) = 0.477 = 47.7%, which is closest to (D).

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