DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 4)

Subscribe to our ▶️ YouTube channel 🔴 for the latest videos, updates, and tips.

Problem 1 :

The longest side of right triangle ABC is opposite angle B. If sin(A) = 9/41, what is the value of sin(C)?

Solution :

Problem 2 :

Function g reaches its maximum value when x = a.

If g(x) = –6x² – 30x – 24, what is the value of a?

Solution :

Problem 3 :

The linear function f(x), given above, is perpendicular to g(x) when graphed in the xy-plane. If g(0) = 0, what is the value of g(2)?

Solution :

Problem 4 :

y = 5kx² + 2x + 3

y/10 = -x

The system of equations above has exactly one solution. If k is a constant, what is the value of k?

Solution :

Problem 5 :

33, 34, 38, 41, 43, 44, 47

Which of the following is the median of the data listed
above?

A) 38

B) 40

C) 41

D) 42

Solution :

Problem 6 :

If x^ac ⋅ x^bc= x³⁰, x > 1 and a + b = 5, what is the value of c?

A) 3

B) 5

C) 6

D) 10

Solution :

Problem 7 :

Kaylani used fabric measuring 5 yards in length to make each suit for a men’s choir. The relationship between the number of suits that Kaylani made, x, and the total length of fabric that she purchased y, in yards, is represented by the equation y - 5x = 6. What is the best interpretation of 6 in this context?

A) Kaylani made 6 suits.

B) Kaylani purchased a total of 6 yards of fabric.

C) Kaylani used a total of 6 yards of fabric to make the suits.

D) Kaylani purchased 6 yards more fabric than she used to make the suits.

Solution :

Problem 8 :

The function g is defined by g(x) = (x + 14)(t - x), where t is a constant. In the xy-plane, the graph of y = g(x)passes through the point (24, 0). What is the value of g(0)?

Solution :

Problem 9 :

The result of increasing the quantity x by 400% is 60. What is the value of x?

A) 12

B) 15

C) 240

D) 340

Solution :

Problem 10 :

What is the slope of the graph of y = ⅓(29x + 10) + 5x in the xy-plane?

Solution :

Problem 11 :

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 12 :

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 13 :

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 14 :

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 15 :

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 16 :

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 17 :

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 18 :

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 19 :

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 20 :

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 :