DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 57)

Problem 1 :

f(x) = ax² + bx + c

In the given quadratic function, a and c are constants. The graph of y = f(x) in the xy-plane is a parabola that opens upward and has a vertex at the point (h, k), where h and k are constants. If k < 0 and f(-9) = f(3), which of the following must be true?

I. a ≥ 1

II. c < 0

A) I only

B) II only

C) I and II

D) Neither I nor II

Solution :

Problem 2 :

Which of the following is equivalent to (√a + √b)^2/3, where a > 0 and b > 0?

A)  (a + b)³ .

B)  ³√(a + b)

C)  (a + 2√ab + b)^1/3

D)  ³√(a + 2ab + b)

Solution :

Problem 3 :

Two different points on a number line are both 3 units from the point with coordinate -4. The solution to which of the following equations gives the coordinates of both points?

A)  |x + 4| = 3

B)  |x - 4| = 3

C)  |x + 3| = 4

D)  |x - 3| = 4

Solution :

Problem 4 :

x² – ax + 12 = 0

In the equation above, a is a constant and a > 0. If the equation has two integer solutions, what is the smallest possible value of a?

Solution :

Problem 5 :

A line intersects two parallel lines, forming four acute angles and four obtuse angles. The measure of one of the acute angles is (7x – 610)º. The sum of the measures of one of the acute angles and three of the obtuse angles is (-14x + w)º. What is the value of w?

Solution :

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