Challenging SAT Math Questions

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Question 1 :

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 2 :

There are two angles A and B, where the measure of angle A is 3π/2 radians and the measure of angle B is 7π/6 radians less than the measure of angle A. What is the measure of angle B, in degrees?

A) 270

B) 210

C) 120

D) 60

Answer :

Given : Measure of angle B is 7π/6 radians less than the measure of angle A.

m∠B = m∠A - 7π/6

Given : m∠A = 3π/2.

m∠B = 3π/2 - 7π/6

m∠B = 9π/6 - 7π/6

m∠B = (9π - 7π)/6

m∠B = 2π/6

m∠B = π/3

Convert radians to degrees.

m∠B = π/3 ⋅ 180°/π

m∠B = 180°/3

m∠B = 60°

The correct answer choice is (D).

Question 3 :

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

Answer :

Question 4 :

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 :

Formula for volume of a sphere = (4/3)πr³.

Volume of sphere A = (4/3)π(6x)³

= (4/3)π ⋅ 6³⋅ x³

= (4/3)π ⋅ 216⋅ x³

= 288πx³

Volume of sphere B = (4/3)π(114x)³

= (4/3)π ⋅ 114³⋅ x³

= (4/3)π ⋅ 1481544⋅ x³

= 1975395πx³

= 6859 ⋅ 288πx³

Volume of sphere B = 6859 ⋅ Volume of sphere A

Therefore, volume of sphere B is 6859 times of volume of sphere A.

Question 5 :

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 6 :

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

Answer :

The given quadratic equation is in standard form and it has at least one solution.

Then, we have

b² - 4ac ≥ 0

In the given quadratic equation, a = a, b = 160 and c = c.

160² - 4ac ≥ 0

25600 - 4ac ≥ 0

Subtract 25600 from both sides.

-4ac ≥ -25600

Divide both sides by -4.

ac ≥ 6400

Therefore, the greatest possible value of ac is 6400.

Question 7 :

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 8 :

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 :