Problem 1 :
(ax + b)(5x^{2} - bx + 4) = 20x^{3} - 9x^{2} - 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) = -2x^{2} + 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 :
Digital SAT Problems and Solutions (Part - 1)
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