DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 228)
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Problem 1 :
(2x – 2)(x – 7) = 2(x – a)2 – b
In the equation above, a and b are constants. If the equation is true for all real values of x, what is the value of b?
Solution :
Problem 2 :
The function f is defined by f(x) = x3 – ax2 + bx – 4, where a and b are constants. In the xy-plane, the graph of f intersects the x-axis at the three points (–1, 0), (–2, 0) and (k, 0). What is the value of k?
Solution :
Problem 3 :
The graphs of y = x2 and y = mx – 1 are shown in the xy-plane above, where m is the slope of the line. If the graph of y = mx – 1 is tangent to the graph of y = x2, what is the value of m?
Solution :
Problem 4 :
x + 16 < 2x + 1 < x + 46
Which of the following is equivalent to the inequality above?
A) |x – 15| < 45
B) |x – 29| ≤ 15
C) |x – 30| < 15
D) |x + 15| < 30
Solution :
Problem 5 :
In the figure above, ΔABC and ΔDBE are similar and AD/AB = 1/3. If the area ΔABC is 45, what is the area of the shaded region?
A) 15
B) 17.5
C) 25
D) 30
Solution :
Problem 6 :
During a trip, Jonathan had driven a total of 75 miles by 6:20 PM and a total of 85 miles by 6:40 PM. He drove at the same rate for the entire trip. At what time had he driven a total of 140 miles?
(A) 7:30 PM
(B) 8:00 PM
(C) 8:30 PM
(D) 9:00 PM
Solution :
Problem 7 :
The equation above is true for all real values of x ≠ ⅔, where k is a constant. What is the value of k ?
(A) -4
(B) 0
(C) 1
(D) 2
Solution :
Problem 8 :
Which of the following is equivalent to the expression above?
Solution :
Problem 9 :
In the figure above, what is the value of x?
Solution :
Problem 10 :
In the table above, if y = x2 + x - 2, what is the value of k?
Solution :
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