DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 27)

Subscribe to our ▶️ YouTube channel 🔴 for the latest videos, updates, and tips.

Problem 1 :

The table shows three values of x and their corresponding values of y, where y = f(x) + 4 and f is a quadratic function. What is the y-coordinate of the y-intercept of the graph of y = f(x) in the xy-plane?

Solution :

Problem 2 :

For the function f, for each increase in the value of x by c, where c is a positive constant, the value of f(x) increases by a factor of 27. Which of the following forms of the function f displays ¹⁄c as a coefficient of x?

Solution :

Problem 3 :

A laundry service is buying detergent and fabric softener from its supplier. The supplier will deliver no more than 300 pounds in a shipment. Each container of detergent weighs 7.35 pounds, and each container of fabric softener weighs 6.2 pounds. The service wants to buy at least twice as many containers of detergent as containers of fabric softener. Let d represent the number of containers of detergent, and let s represent the number of containers of fabric softener, where d and s are nonnegative integers. Which of the following systems of inequalities best represents this situation?

A) 7.35d + 6.2s ≤ 300 and d ≥ 2s

B) 7.35d + 6.2s ≤ 300 and 2d ≥ s

C) 14.7d + 6.2s ≤ 300 and d ≥ 2s

D) 14.7d + 6.2s ≤ 300 and 2d ≥ s

Solution :

Problem 4 :

A graphic designer is creating a logo for a company. The logo is shown in the figure above. The logo is in the shape of a trapezoid and consists of three congruent equilateral triangles. If the perimeter of the logo is 20 centimeters, what is the combined area of the shaded regions, in square centimeters, of the logo?

A) 2√3

B) 4√3

C) 8√3

D) 16

Solution :

Problem 5 :

The scatterplot shows the relationship between the length of time y, in hours, a certain bird spent in flight and the number of days after January 11, x.

What is the average rate of change, in hours per day, of the length of time the bird spent in flight on January 13 to the length of time the bird spent in flight on January 15?

Solution :

Problem 6 :

The mean score of 10 students of an algebra class was 85. When two new students enrolled, the mean increased to 86. What was the average of the new students?

Solution :

Problem 7 :

In the figure above, ABCD is a square and AB = 18. If M is the midpoint of AD, what is the area of ΔABE?

Solution :

Problem 8 :

If f(x/5) = x² – 3x + 1, what is the value of f(-1)?

Solution :

Problem 9 :

In the figure above, AD = 4, measure of ∠BAD is 45°, and measure of ∠BCD is 30°. What is the area of triangle ABC? (Round your answer to the nearest tenth).

Solution :

Problem 10 :

f(x) = x² + 2x + k

In the function above, k is a constant. If the minimum value of f(x) is 8, what is the value of k?

A) 4

B) 6

C) 8

D) 9

Solution :

Problem 11 :

In a right triangle, one of the angles is x°, if tan x° = 5/12, what is the value of sin x°?

Solution :

Problem 12 :

Dawson needs to measure the height of a building near his house. He chooses a point P on the ground where he can visually align the roof of his car with the edge of the building roof. The height of the car is 4 feet and the distance from point P to Q is 10 feet, as shown in the figure above. If the distance from point Q to point R is 80 feet, and the height of the building is k feet, what is the value of k?

Solution :