DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 267)

Problem 1 :

The table shows three values of x and their corresponding values of y for the linear relationship between x and y. The x-intercept of the line occurs when x = -4. The number d is a negative constant. The number k is a constant. What is the value of dk?

Solution :

Problem 2 :

f(x) = ax² – 7x + c

The function f is defined above, where a and c are constants. The graph of y = f(x) is a parabola that has a vertex at the point (h, k), where h and k are constants. If f(-9) = f(-2) and c > 0, which of the following must be true?

I.  a < – 3/4

II. k > 16

A)  I only

B)  II only

C)  I and II

D)  Neither I nor II

Solution :

Problem 3 :

The triangle inequality theorem states that the sum of any two sides of a triangle must be greater than the length of the third side. A triangle has side lengths of 4x + 20, 2x + 8 and 7x – 11. Which inequality represents all possible values of x?

A)  x < 39

B)  8 < 2x < 78

C)  3 < x < 38

D)  23 < 5x < 195

Solution :

Problem 4 :

In the given circle, point B is the center. Point A, C and D lie on the circle. Point B lies on line segment AC. Line EA is tangent to the circle at point A. The diameter of the circle is 240 cm. The length of segment BE is twice that of segment AB. If minor arc CD is kπ cm, what is the value of k?

Solution :

Problem 5 :

A circle is centered at point O with coordinates (0, 0) in the xy-plane. The circle contains point A with coordinates (25, 0) and point B with coordinates (k, 24), where k is a negative constant. What is the value of cosine ∠AOB?

Solution :

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