DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 37)

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Problem 1 :

Find the value of a + b + c?

Solution :

Problem 2 :

If f(2x + 3) = -x² + 4x + 6, what is the value of f(5)?

A) 1

B) 11

C) 9

D) 6

Solution :

Problem 3 :

In the xy-plane, the point (p, r) lies on the line with equation y = x + b, where b is a constant. The point with coordinates (2p, 5r) lies on the line with equation y = 2x + b. If p ≠ 0, what is the value of r/p?

Solution :

Problem 4 :

Find the value of x and y in the following system :

√x - √y = 4

2√x + 3√y = 18

Solution :

Problem 5 :

Solution :

Problem 6 :

In the figire above, the center of the circle is O. The area of the shaded region is 80π and the measure of x is 2π/5 radians. What is the radius of the circle?

A) 6

B) 8

C) 9

D) 10

Solution :

Problem 7 :

Lines ℓ and m are perpendicular and intersect at point T(1, 3) as shown in the xy-plane above. If the slope of line ℓ is 1, what is the area of ΔRST?

A) 1

B) 1.5

C) 2

D) 2.5

Solution :

Problem 8 :

The figure above shows triangle ABC. The length of AC is 10 and the altitude of the triangle is 20. If M and N are the midpoints of AB and BC respectively, what is the area of the shaded region?

Solution :

Problem 9 :

(a – 1)x² + (b – 2)x + ab = 4x² + 5x + k

In the equation above, a, b and k are constants. If the equation is true for all values of x, what is the value of k?

Solution :

Problem 10 :

If P(x) = 2√(x - 5) + 3x, what is the minimum value of P?

Solution :

Problem 11 :

In the figure shown above, BC is the diameter of the circle. If the length of BC is equal to 132 and the length of AB is equal to √363, what is the value of BC/BD?

Solution :

Problem 12 :

x² + bx + c = 0

In the given equation, b and c are constants. If -b + √(b² - 4c) = 18 and -b - √(b² - 4c) = 10, what is one possible value of x?

Solution :

Problem 13 :

A fitness membership costs $45 per month. All new members receive a discount of $20 off the cost of their first month of membership. Which function c gives the total cost c(t), in dollars, that a new member pays after t months of membership?

A) c(t) = 20 + 45t

B) c(t) = 25 + 45t

C) c(t) = 20 + 45(t – 1)

D) c(t) = 25 + 45(t – 1)

Solution :

Problem 14 :

P(x) = 3x³ + ax – 2

In the function above, a is a constant. If the remainder when P(x) is divided by x + 1 is 2, what is the value of a?

A) -7

B) -5

C) 5

D) 7

Solution :

Problem 15 :

The graph of ax + by = 5 is shown in the xy-plane above. Which of the following must be true?

A) a < 0 and b < 0

B) a > 0 and b < 0

C) a < 0 and b > 0

D) a > 0 and b > 0

Solution :

Problem 16 :

A triangle has vertices A(3, 2), B(3, 6) and C(7, 2). Another triangle has vertices P(3, 2), Q(3, 6 + k) and R(7 + k, 2) and one acute angle at the vertex Q. If k > 0, then what is the measure of the other acute angle?

Solution :

Problem 17 :

7x – 9y = 39

35x – 45y = 195

For any real number r, which of the following points lies on the graph of both the equations?

Solution :

Problem 18 :

38z¹⁴ + bz⁷ + 30 has a factor of (rz⁷ + q), where r and q are positive integers. What is the maximum value of b?

Solution :

Problem 19 :

In the equation given below, k is a positive constant. The product of the solutions to the equation is 154. What is the value of k?

Solution :

Problem 20 :

The profit P from a car wash is modeled by the equation above, where n is the number of cars and k is a constant. Which of the following expressions represents n?