10 Hard SAT Math Questions
(Part - 1)

Question 1 :

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

Answer :

Question 2 :

Sphere A has a radius of 6x and sphere B has a radius of 114x. The volume of sphere B is how many times the volume of sphere A?

Answer :

Question 3 :

The function g(x) = √(6x + 20) . If g(a) = –6a, where a is a constant, what is the value of a?

A) –3/2

B) –2/3

C) 2/3

D) 3/2

Answer :

Question 4 :

The quadratic equation ax² + 160x + c = 0 has at least one solution. What is the greatest possible value of ac?

Answer :

Question 5 :

30r¹⁶ + br⁸ + 48

In the given expression, b is a positive integer. If pr⁸ + c is a factor of the expression, where p and c are positive integers, what is the greatest possible value of b?

Answer :

Question 6 :

A quadratic function models the height, in feet, of an object above the ground in terms of time, in seconds, after the object was launched. According to the model, the object was launched from a height of 10 feet and reached its maximum height of 1,099 feet in 33 seconds after it was launched. Based on the model, what was the height, in feet, of the object 44 seconds after it was launched?

Answer :

Question 7 :

Right rectangular prism A is similar to right rectangular prism B. The surface area of right rectangular prism A is 75 square inches, and the surface area of right rectangular prism B is 4,800 square inches. The volume of right rectangular prism A is 35 cubic inches. What is the volume, in cubic inches, of right rectangular prism B?

Answer :

Question 8 :

x(3k – 11) + 25 = 37x + 60

In the given equation, k is a positive integer. If the given equation has exactly one solution, what cannot be the value of k?

A) 14

B) 16

C) 41

D) 55

Answer :

Question 9 :

A certain town has an area of 6.25 square miles. Which of the following is closest to the area, in square yards, of this town? (1 mile = 1,760 yards)

A) 11,000

B) 67,188

C) 1,100,000

D) 19,360,000

Answer :

Question 10 :

y = –2x² – 40

y = px + 10

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

A) -6

B) -5

C) 8

D) 20

Answer :