DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 224)

Problem 1 :

If cos (3x + 20)° = sin (x + 10)°, what is the value of sin(2x)°?

A)  1/√2

B)  1/2

C)  √3/2

d)  √3

Solution :

Problem 2 :

In the function f defined by f(x – 1) = x² – 1, which of the following represents f(x)?

A)  f(x) = x²

B)  f(x) = x² + 1

C)  f(x) = x² + 2x

D)  f(x) = x² + 2x – 1

Solution :

Problem 3 :

The graph of a circle, whose equation is x² + y² = 100, is shown in the xy-plane above. if the graph of y = x + k, where k is a constant, is tangent to the graph of the circle, which of the following is closest to the value of k?

A)  12.03

B)  14.14

C)  15.05

D)  17.31

Solution :

Problem 4 :

P = 245,000(1 - 0.002)^t/2

The equation above can be used to model the population of a certain city t years after 1800. According to this model, the population is predicted to decrease by 0.2% every k months. What is the value of k?

Solution :

Problem 5 :

If the graph of f(x) = x² – 2x + k intersects the line f(x) = 3 at exactly one point, what is the value of k?

Solution :

Problem 6 :

f(x) = ax² - 15

For the function f above, a is a constant and f(3) = 10. Which of the following is equal to the value of f(5)? 

A)  f(0)

B)  f(-3)

C)  f(3)

D)  f(-5)

Solution :

Problem 7 :

A certain job can be done in 20 hours by 4 people. How many people are needed to do the same jon in 10 hours?

A)  2

B)  4

A)  8

A)  10

Solution :

Problem 8 :

Which of the following is equivalent to

f(x) = x² - 6x + 7

A)  f(x) = (x + 3)² + 5

B)  f(x) = (x - 3)² + 2

C)  f(x) = (x - 3)² - 2

D)  f(x) = (x - 7)(x + 1)

Solution :

Problem 9 :

If 24x² - kx + 16 = (3x + 4)(ax -b) for all values of x, where a, b and k are constants, what is the value of k?

A)  -44

B)  -12

C)  12

D)  44

Solution :

Problem 10 :

In the xy-plane, the equation of line ℓ is x + 3y = 5. If line m is perpendicular to line ℓ, what is a possible equation of line m?

A)  y = -⅓x + 2

B)  y = ⅓x - 1

C)  y = -3x + 1

D)  y = 3x + ⅔

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