DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 25)

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

Problem 1 :

y = 2x² – 21x + 64

y = 3x + a

In the given system of equations, a is a constant. The graphs of the equations in the given system intersect at exactly one point (x, y) in the xy-plane. What is the value of x?

A) -8

B) -6

C) 6

D) 8

Solution :

Problem 2 :

The table gives the coordinates of two points on a line in the xy-plane. The y-intercept of the line is (k - 5, b), where k and b are constants. What is the value of b?

Solution :

Problem 3 :

A certain park has an area of 11,863,808 square yards. What is the area in square miles of this park?

(1 mile = 1,760 yards)

A) 1.96

B) 3.83

C) 3,444.39

D) 6,740.8

Solution :

Problem 4 :

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

Solution :

Problem 5 :

The scatterplot above shows the federal-mandated minimum wage every 10 years between 1940 and 2010. A line of best fit is shown, and its equation is y = 0.096x − 0.488. What does the line of best fit predict about the increase in the minimum wage over the 70-year period?

A. Each year between 1940 and 2010, the average increase in minimum wage was 0.096 dollars.

B. Each year between 1940 and 2010, the average increase in minimum wage was 0.49 dollars.

C. Every 10 years between 1940 and 2010, the average increase in minimum wage was 0.096 dollars.

D. Every 10 years between 1940 and 2010, the average increase in minimum wage was 0.488 dollars.

Solution :

Problem 6 :

Friday, Peter drives from home to his office in 24 minutes. Saturday, there is no traffic, so he can drive to his office 15 miles per hour faster and gets to the office in 15 minutes. How far, in miles, is it from home to his office?

A) 10

B) 12

C) 20

D) 25

Solution :

Problem 7 :

In the xy-plane above, the graph of the equation y = a(x + 4)(x – 2) has a vertex at point P. if the graph intersects the x-axis at points R and S, what is the area of ΔRPS?

A) -54a

B) -27a

C) 27a

D) 54a

Solution :

Problem 8 :

When 2x² – 5x + 4 is divided by (x – 1)(x + 1), the resulting remainder is ax + b, where a and b are constants. What is the value of a + b?

Solution :

Problem 9 :

In the figure above, ∠XAB and ∠XYA are inscribed in the circle. If AB is the diameter of the circle, and the measure of ∠XAB is 65°, what is the value of x?

Solution :

Problem 10 :

x² – 8x – 3 + y² – 6y = k²

The graph of the equation above in the xy-plane is a circle, where k is a positive real number. If the radius of the circle is 8, what is the value of k?

Solution :

Problem 11 :

A faulty register records only $5 for every $8 deposit. If the register shows a total balance of $40, what is the actual balance?

(A) $25

(B) $64

(D) $80

Solution :

Problem 12 :

If (x - 2)² + (y - 3)² + (z + 4)² = 0, what is the value of (x + y + z)?

(A) -4

(B) 0

(D) 2

Solution :

Problem 13 :

If 3^{x - 3} = 27, what is the value of x?

(A) -4

(B) 0

(D) 2

Solution :

Problem 14 :

The triangle above is isosceles and b > a. Which of the following must be FALSE?

(A) AB = BC

(B) AB = AC

(D) a = c

Solution :

Problem 15 :

The graph of a parabola has x-intercepts at ⅗ and -½. Which of the following could be the equation of the parabola?

(A) y = (5x - 1)(2x + 3)

(B) y = (5x + 1)(2x - 3)

(D) y = (5x + 3)(2x - 1)

Solution :

Problem 16 :

y = f(x)

y = k

In the system of equations above, k is a constant. The function y = f(x) is shown in the xy-plane above for -8 ≤ x ≤ 14. On this closed interval, for how many values of k does the system have exactly 4 solutions?

A) 1

B) 2

C) 3

D) 4

Solution :

Problem 17 :

In the figure above, O and P are the centers of the circles. If the lengths of radii of the circles are each 10, what is the area of the shaded region?

A) 50√3

B) 25√3

C) 25√3/2

D) 25√3/4

Solution :