DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 42)

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Problem 1 :

x² + y² – 6x – 8y = 0

The equation of a circle in the xy-plane is shown above. What is the area of the circle?

A) 15.7

B) 31.4

C) 62.8

D) 78.5

Solution :

Problem 2 :

If 3x - y = 12, what is the value of

Solution :

Problem 3 :

A ball is kicked off of a platform modeled by the equation y = -5x² + bx + 10, such that y is height in feet, x is seconds and b is a constant. The ball reaches a maximum height of 11.25 feet and it takes 2 seconds to hit the ground. How many seconds does it take for the ball to reach its maximum height?

Solution :

Problem 4 :

57x² + (57b + a)x + ab = 0

In the given equation, a and b are positive constants. The product of the solutions to the given equation is kab, where k is a constant. What is the value of k?

Solution :

Problem 5 :

2x + 3y = 7

10x + 15y = 35

For each real number r, which of the following points lies on the graph of each equation in the xy-plane for the given system?

Solution :

Problem 6 :

In the given system of equations, p is a constant. If the system has no solution, what is the value of p?

Solution :

Problem 7 :

A carton contains k boxes of paper cups and each box contains 100 paper cups. If the carton costs d dollars, what is the cost per paper cup in cents?

A) kd

B) d/k

C) d/100k

D) 100k/d

Solution :

Problem 8 :

In the xy-plane above, lines ℓ and m are parallel and intersect the x-axis at x = a and x = b respectively. If a + b = 8, what is the value of a?

A) 1.5

B) 2

C) 2.5

D) 3

Solution :

Problem 9 :

(k – 2a)x + k – 11 = 5

In the equation above, a and k are constants. If the equation has infinitely many solutions, what is the value of a?

A) 8

B) 16

C) 20

D) 24

Solution :

Problem 10 :

If the value of k^-5 is twice the value of 4k^-2, what is the value of k?

A) -1/2

B) -1/3

C) 2

D) 3

Solution :

Problem 11 :

The lines with equations y = 2x/3 and y = 2x – 8 are shown in the xy-plane above. What is the area of triangle OPR?

Solution :

Problem 12 :

In the figures above, both of the water tanks are in the shape of a right circular cone. If the larger tank can hold 125 gallons of water, how many gallons of water can the smaller tank hold?

A) 5

B) 25

C) 31.25

D) 62.5

Solution :

Problem 13 :

In the figure above, right triangle RST bordered by three semicircles on each side. If the area of semicircle I is 8 and the area of semicircle II is 24, what is the length of ST?

A) 16/√π

B) 16/π

C) 8/√π

D) 8/π

Solution :

Problem 14 :

The graph of g is shown in the xy-plane above. If f(x) = 2g(x) – 5, what is the average rate of change of f(x) between -2 and 4?

A) 1/2

B) 1/3

C) -1/4

D) -1/3

Problem 15 :

If the value of k^-5 is twice the value of 4k^-2, what is the value of k?

A) 1/4

B) 1/2

C) 2

D) 4

Problem 16 :

In the figure above, a right cylinder is inscribed in a sphere with radius 10. If the radius of the circular base of the cylinder is 6, what is the volume of the cylinder?

A) 144π

B) 288π

C) 576π

D) 720π

Solution :

Problem 17 :

A grove has 6 rows of birch trees 5 rows of mapple trees. Each row of birch trees has 8 trees of 20 feet or taller and 6 trees of shorter than 20 feet. Each row of mapple trees has 9 trees of 20 feet or taller and 7 trees of shorter than 20 feet. A tree from one of these rows will be selected at random. What is the probability of selecting a maple tree, given that the tree is 20 feet or taller?

A) 9/164

B) 3/10

C) 15/31

D) 9/17

Solution :

Problem 18 :

Let f(x) = √x and g(x) = 7x + b. In an xy-plane, if the graph of the function y = f[g(x)] passes through the point (4, 6), then what is the value of b?