DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 49)

Problem 1 :

f(x) = ax² + bx + c

The quadratic function f is defined as shown. In the xy-plane, the two x-intercepts of the graph of f(x) are (k, 0) and (11, 0), where k is a constant. If f(4) = f(12), What is the value of k?

A)  1

B)  3

C)  5

D)  7

Solution :

Problem 2 :

The expression 8x(2x² – 5) + 2(20x – 1) is equivalent to 2(ax³ – 1), where a is a constant. What is the value of a?

Solution :

Problem 3 :

h(x) = 2(x – 4)² – 32

The quadratic function h is defined as shown. In the xy-plane, the graph of y = h(x) intersects the x-axis at the points (0, 0) and (t, 0) where t is a constant. What is the value of t?

A)  1

B)  2

C)  4

D)  8

Solution :

Problem 4 :

The function f is defined by f(x) = 3^x. The function g is a increasing linear function. In the xy-plane, the graphs of y = f(x) and y = g(x) intersect at two points (a, j) and (b, k), where j < k. When g(x) > f(x), which of the following must be true?

A)  x > k

B) x < j

C)  x < j  or  x > b

D)  a < x < b

Solution :

Problem 5 :

If √3x² - 6x - 24 = 0, what is the value of x² - 2√3x?

A)  √3

B)  3

C)  8

D)  8√3

Solution :

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