DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 248)

Problem 1 :

In the equation above, if a is positive and b is negative, which of the following must be true?

A)  k > 1

B)  k > a

C)  k < b

D)  k < 1

Solution :

Problem 2 :

If the volume of a cube is 27(a³/8), where a is a positive constant, which of the following gives the surface area of the cube?

A)  27(a²/4)

B)  27(a²/2)

C)  9(a²/4)

D)  3(a²/2)

Solution :

Problem 3 :

The graph of the linear function f is shown in the xy-plane above. If the graph of g, defined by g(x) = 4f(x - 2) + k, where k is a constant, passes through the point (1, -4), what is the value of g(3)?

A)  -20

B)  -17

C)  12

D)  17

Solution :

Problem 4 :

In the figure above, an altitude of a right triangle from the right angle splits the hypotenuse into segments of lengths AD and DC. Which of the following is closest to the value of AD?

A)  7.5

B)  8.5

C)  10

D)  12

Solution :

Problem 5 :

x² + y² + 10x – 16y = p

The equation above defines a circle in the xy-plane and p is a constant. If the area of the circle is 81π, what is the value of p?

A)  11

B)  8

C)  –8

D)  –11

Solution :

Problem 6 :

A teacher conducted a survey to determine the effect of eating breakfast on the same day an exam is taken. The results of the curvey are shown in the table above. If one of the students who did not pass the exam is chosen at random, what is the probability that the person chosen ate breakfast on the same day of the exam?

A)  3/25

B)  2/5

C)  3/5

D)  2/3

Solution :

Problem 7 :

y = x² + 10x + 16

The equation above represents a parabola in the xy-plane. Which of the following equivalent forms of the equation displays the minimum value of y as a constant or coefficient?

A)  y = (x + 8)(x + 2)

B)  y - 16 = x(x + 10)

C)  y = (x + 5)² - 9

D)  y = (x - 5)² + 9

Solution :

Problem 8 :

A class of 45 students is divided into two groups. If one group has 9 students less than the other, how many students are in the smaller group?

A)  12

B)  18

C)  24

D)  27

Solution :

Problem 9 :

The function f is graphed in the xy-plane above.

If f(c) = f(3), which of the following could be the value of c?

A)  -3

B)  -2

C)  -1

D)  2

Solution :

Problem 10 :

If m and b are real numbers and m is greater than zero and b is greater than zero, then the line whose equation is y = mx + b can not contain which of the following points?

A)  (0, 1)

B)  (1, 1)

C)  (-1, 1)

D)  (0, -1)

Solution :

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