DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 238)

Problem 1 :

f(x) = a(x – b)² + 10

In the xy-plane, the graph of the function f above has x-intercepts at –2 and 6. What is the value of a?

A)  –5

B)  – 5/8

C)  5/8

D)  5

Solution :

Problem 2 :

2x – 3y = 1

ax + by = c

In the system of equations above, a, b and c are constants. For which of the following values of a, b and c does the system have only one solution?

A)  a = 2, b = –3 and c = 1

B)  a = 4, b = –6 and c = 5

C)  a = 6, b = –9 and c = 5

D)  a = 10, b = 10 and c = 1

Solution :

Problem 3 :

In the xy-plane above, what are the coordinates of point M?

A)  (2, 0)

B)  (3, 0)

C)  (4, 0)

D)  (5, 0)

Solution :

Problem 4 :

Based on the equation above, if there is an increase of 27 in F, how much is the increase in C?

A)  9

B)  15

C)  27

D)  59

Solution :

Problem 5 :

The equation is true for all values of x except 1 and 2, where a and b are constants. What is the value of a?

A)  –4

B) –2

C)  3

D)  4

Solution :

Problem 6 :

Four values for the functions f and g are shown in the table above. If g(m) = 6, what is the value of f(m)?

Solution :

Problem 7 :

x² - 5x + c = 0

In the quadratic equation above, c is a constant. If the equation has two solutions for x, one of which is -3, what is the value of the other solution?

Solution :

Problem 8 :

If x = y^a, y = z^b and z = x^c, then the value of abc is

A)  2

B)  1

C)  3

D)  4

Solution :

Problem 9 :

Solution :

Problem 10 :

If 2^x ⋅ 3^y ⋅ 5^z = 360, then what is the value of xyz?

Solution :

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