DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 23)

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Problem 1 :

The graph of y = f(x) + 14 is shown. Which equation defines function f?

Solution :

Problem 2 :

f(x) = (x + 6)(x + 5)(x - 4)

The function f is given. Which table of values represents y = f(x) - 3?

Solution :

Problem 3 :

For the function q, the value of q(x) decreases by 45% for every increase in the value of x by 1. If q(o) = 14, which equation defines q?

A) q(x) = 0.55(14)^x

B) q(x) = 1.45(14)^x

C) q(x) = 14(0.55)^x

D) q(x) = 14(1.45)^x

Solution :

Problem 4 :

RS = 20

ST = 48

TR = 52

The side lengths of right triangle RST are given. Triangle RST is similar to triangle UVW where S corresponds to V and T corresponds to W. What is the value of tan W ?

Solution :

Problem 5 :

One gallon of paint will cover 220 square feet of a surface area. A room has a total wall area of w square feet. Which equation represents the total amount of paint P, in gallons, needed to paint the walls of the room twice?

Solution :

Problem 6 :

Which of the following are zeros of the function

Solution :

Problem 7 :

Radioactive decay is an exponential function where the amount, y, of radioactive material is reduced by one half over certain period of time t. The table above represents such exponential decay over 400 years. How much of this material, in grams, would remain radioactive after 1000 years?

A) 0.78125

B) 0.90254

C) 1.5625

D) 3.125

Solution :

Problem 8 :

Which of the following describes the transformation of the quadratic function f(x) = x² that results in the function g(x) = x² + 12x + 20?

A) The graph of f has been translated 12 units to the right and moved up 20 units.

B) The graph of f has been translated 6 units to the right and moved down 20 units.

C) The graph of f has been translated 6 units to the left and moved up 16 units.

D) The graph of f has been translated 6 units to the left and moved down 16 units.

Solution :

Problem 9 :

Isosceles trapezoid ABCD is shown above. AB = 2a, BC = a and ∠BAD = 60°. What is the area of the isosceles trapezoid?

A) a²√2/2

B) 2a²√3

C) a²√3/2

D) a²√3

Solution :

Problem 10 :

In the xy-plane above, the graphs of y = x² and y = mx + k intersect at x = -2 and x = 3. What is the value of k?

A) 1

B) 2

C) 3

D) 4

Solution :

Problem 11 :

Before a big test, James memorized 10 percent more words than Zach. Zach memorized 30 percent more words than Amy. If Amy memorized a words, how many words did James memorize in terms of a?

A) (1.10)(1.30)a

B) a/[(1.10)(1.30)]

C) a/[(0.9)(0.7)

D) 1.40a

Solution :

Problem 12 :

A certain pizza restaurant cuts slices out at every 4 inches along the edge of a pizza, as shown in the figure above. What is the maximum number of full pizza slices that can be cut out from a circular pizza with a radius of 10 inches?

(A) -4

(B) 0

(C) 1

(D) 2

Solution :

Problem 13 :

The table above shows the distribution of age and social media presence for 720 employees at a company, If an employee who uses social media is selected at random, what is the probability the employee is age 30 or older?

(A) 1/3

(B) 4/9

(D) 2/3

Solution :

Problem 14 :

The function f is defined by f(x) = x² + bx + c, where b and c are constants. If the graph of f has x-intercepts at -5 and 3, which of the following correctly gives the values of b and c?

(A) b = -5 and c = 3

(B) b = -3 and c = 5

(D) b = 2 and c = -15

Solution :

Problem 15 :

In the xy-plane, the line y = mx + b, where m and b are cosntants, is a reflection of line l across the y-axis. At which of the following points do the two lines intersect?

(A) (0, b)

(B) (0, -b)

(D) (m, 0)

Solution :

Problem 16 :

Albert and Bunny are 100 feet apart. Each person walks at a steady pace toward the other. If Albert walks at a constant rate of 3 feet per second and Bunny walks at a constant rate of 4 feet per second, how far will Albert walk in feet, when they meet?

A) 100/7

B) 300/7

C) 400/7

D) 70

Solution :

Problem 17 :

Which of the following is equivalent to the expression

x³ + x²y – x – y ?

A) (x + y)(x² + 1)

B) (x + y)(x² – 2y)

C) (xy + 1)(x² + 1)

D) (x + y)(x + 1)(x – 1)

Solution :

Problem 18 :

In the figure above, the area of triangle ABC is 96. If AD = 9 and BD = 15, what is the length of CD?

A) 7

B) 8

C) 9

D) 14

Solution :

Problem 19 :

3x + 4y = 12

The graph of the equation above in the xy-plane is a line, ℓ. Line m is perpendicular to line ℓ at point (a, b) and passes through the origin. Which of the following is the value of a?

A) 1.44

B) 4.8

C) 5

D) 5.4

Solution :