DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 270)

Problem 1 :.

Point C is the center of the circle shown below. Points D and F both lie on the circle as shown. The perimeter of triangle CDF is 60 units. What is the area of shaded region? Round your answer to the nearest hundredth.

Solution :

Problem 2 :

f(x) = ax² + 36x + c

g(x) = jx² – 57x + ℓ

The functions f(x) and g(x) are both quadratic functions, and m is a positive constant. The parabola formed by the graph of y = f(x) has a vertex with a    y-coordinate of 3m. The parabola formed by the graph of y = g(x) has a vertex with a y-coordinate of m. If f(10) = f(14) and g(-3) = g(27), for how many values of x does f(x) = g(x)?

Note : a, c, j and ℓ are constants.

A)  Exactly one

B)  Exactly two

C)  Infinitely many

D)  Zero

Solution :

Problem 3 :

In triangle ABC, angle B is a right angle, the measure of angle A is 34°,and the length of segment BC is 13 inches. What is the area of triangle ABC in square inches?  

Solution :

Problem 4 :

For two acute angles, ∠A and ∠B, cos A = sin B. The measures, in degrees of, ∠A and ∠B are 9x + 10 and 48 + 5x respectively. What is the value of x?

Solution :

Problem 5 :

In triangle XYZ, the sum of the measures of angle X and angle Y is 90 degrees. The value of sin X = 5√3/12. What is the value of cos Y?

A)  5√13/12

B)  5√3/13

C)  10√5/21

D)  21/10√5

Solution :

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