Digital SAT Math Problems and Solutions (Part

Problem 1 :

(ax + b)(5x² – bx + 4) = 20x³ – 9x² – 2x + 12

The equation is above is true for all x, where a and b are constants. What is the value of ab?

A)  18

B)  20

C)  24

D)  40

Solution :

Problem 2 :

Function f is defined by f(x) = -a^x + b, where a and b are constants. In the xy-plane, the graph of y = f(x) – 12 has a y-intercept at (0, -75/7). The product of a and b is 320/7. What is the value of a?

Solution :

Problem 3 :

The table shows the distribution of students in a certain college by age group. If a person in this college is chosen at random, which of the following is closest to the probability of selecting a student who is 35 years or older given that the person is at least 23 years old?

A)  0.08

B)  0.29

C)  0.33

D)  0.47

Solution :

Problem 4 :

f(x) = -2x² + bx + c

In the given quadratic function, 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 k < 0 and f(-5) = f(7), which of the following must be true?

I. c < -1

II. b ≥ 3

A)  I only

B)  II only

C)  I and II

D)  Neither I or nor II

Solution :

Problem 5 :

A certain park has an area of 11,863,808 square yards. What is the area in square miles of this park? (1 mile = 1,760 yards)

A)  1.96

B)  3.83

C)  3,444.39

D)  6,740.8

Solution :

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