DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 28)

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Problem 1 :

y = 6x + 18

One of the equations in a system of two linear equations is given. The system has no solution. Which equation could be the second equation in the system?

A) -6x + y = 18

B) -6x + y = 22

C) -12x + y = 36

D) -12x + y = 18

Solution :

Problem 2 :

y > 14

4x + y < 18

The point (x, 53) is a solution to the system of inequalities in the xy-plane. Which of the following could be the value of x?

A) -9

B) -5

C) 5

D) 9

Solution :

Problem 3 :

Which expression is equivalent to

where x > 7?

Solution :

Problem 4 :

f(t) = 8,000(0.65)^t

The given function f models the number of coupons a company sent to their customers at the end of each year, where t represents the number of years since the end of 1998, and 0 ≤ t ≤ 5 .If y = f(t) is graphed in the ty-plane, which of the following is the best interpretation of the y-intercept of the graph in this context?

A) The minimum estimated number of coupons the company sent to their customers during the 5 years was 1,428.

B) The minimum estimated number of coupons the company sent to their customers during the 5 years was 8,000.

C) The estimated number of coupons the company sent to their customers at the end of 1998 was 1,428.

D) The estimated number of coupons the company sent to their customers at the end of 1998 was 8,000.

Solution :

Problem 5 :

Triangle XYZ is similar to triangle RST such that X, Y and Z correspond to R, S and T respectively. The measure of ∠Z is 20° and 2XY = RS. What is the measure of ∠T?

A) 2°

B) 10°

C) 20°

D) 40°

Solution :

Problem 6 :

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 7 :

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 8 :

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 9 :

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 10 :

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 11 :

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 12 :

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 13 :

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 14 :

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 15 :

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

Problem 16 :

f(x) = x²/2 - 20x + k

In the function above, k is a constant. In the xy-plane, for what value of x does f(x) have the same value of f(10)?

Solution :

Problem 17 :

In the isosceles right triangle above, AB = BC = 10√2. Points D and E are the midpoints AB and BC respectively. What is the area of the shaded region ?

Solution :

Problem 18 :

In the xy-plane above, the area of square ABCD is equal to the area of triangle CDP. What is the value of a?

Solution :

Problem 19 :

An advertising medium charges d dollars for a basic fixed fee plus c cents for every 10 letters for an advertising compaign. If 300 letters are used for an advertising compaign, which of the following expressions represents the total amount, in dollars, of the advertisement?

A) 3c/10 + d

B) 3c + d

C) 30c + d

D) 300c + d

Solution :

Problem 20 :

A right circular cylinder has a height that is 4 inches less than its radius. If the cylinder’s surface area is 896π square inches, what is its radius in inches?

A) 8

B) 12

C) 16

D) 20

Solution :