DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 223)

Problem 1 :

When the graph of y = x² is moved to the right 3 units and down 4 units, which of the following is the equation of the resulting graph?

A)  y = (x – 1)(x – 5)

B)  y = (x + 1)(x – 4)

C)  y = (x – 2)(x – 4)

D)  y = (x + 2)(x – 2)

Solution :

Problem 2 :

For a quadratic function f(x) = x² + bx + c in the xy-plane, f(2) = f(6) = 4, what is the value of c?

A)  4

B)  8

C)  12

D)  16

Solution :

Problem 3 :

y = (x – 5)²

y = k

In the system of equations above, k is a constant. If the system has two points of intersection and the distance between these two points is 10, what is the value of k?

A)  20

B)  25

C)  30

D)  35

Solution :

Problem 4 :

x² + 6x + 2 = 0

If a and b are the roots of the equation above, what is the value of (a + 1)(b + 1)?

A)  9

B)  10.5

C)  11

D)  12

Solution :

Problem 5 :

For a polynomial p(x), the remainder when p(x) is divided by (x – 1) is 2 and the remainder when p(x) is divided by (x + 1) is –4. If p(x) is divided by (x² – 1), what is the remainder?

A)  2x + 1

B)  3x – 1

C)  4x + 1

D)  3x + 1

Solution :

Problem 6 :

A certain business is marketing its product and has determined that, when it raised the selling price of its product, its sales went down. The number of units sold, P, is modeled by the equation P = 1200 - 20s, where s is the selling price, in dollars. Based on this model, what is the decrease in selling price from 700 units sold to 900 units sold?

A)  5

B)  10

C)  15

D)  20

Solution :

Problem 7 :

(x² + y²)² - (x² - y²)²

Which of the following is equivalent to the expression above?

A)  x⁴ - y⁴

B)  2(x² + y²)

A)  2x²y²

A)  4x²y²

Solution :

Problem 8 :

Kimberly earns k dollars per week. At this rate how many weeks will it take her to earn p dollars?

A)  p/k

B)  k/p

C)  kp

D)  10p/k

Solution :

Problem 9 :

If 2a/b = 5, what is the value of 5b/a?

A)  2

B)  4

C)  10

D)  12.5

Solution :

Problem 10 :

2x + by = 10

ax + 4y = 15

In the system of equations above, a and b are constants and a = 2b. If the system has no solution, which of the following could be a possible value of a?

A)  -2

B)  1/2

C)  4

D)  8

Solution :

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