DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 225)

Problem 1 :

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 2 :

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 3 :

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

Solution :

Problem 4 :

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 5 :

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 6 :

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

Solution :

Problem 7 :

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 :

Problem 8 :

If a(x + 1) + b(x - 1) = 7x for all real number x, where a and b are constants, what is the value of a?

Solution :

Problem 9 :

According to the formula p = (⅔)k + 81, if trhe value of p is increased by 16, by how much does the value of k increase?

Solution :

Problem 10 :

x² + y² = 56

y = √x

According to the system of equations above, what is the value of x?

Solution :

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