10 Hard SAT Math Questions (Part - 4)

Question 1 :

5x² – 40px + 5y² + 70py = 325p²

In the xy-plane, the graph of the given equation is a circle, where p is a constant. The center of the circle is (–8, 14). If a square is incribed in the circle, what is the area of the square ?

Solution :

Question 2 :

The speed of an object is increasing at a rate of 33 inches per second squared. What is the rate, in miles per hour squared?

Use (12 inches = 1 foot) and (5,280 feet = 1 mile)

Answer :

Question 3 :

In the given system of equations, g and h are constants. The system has no solution. The ratio g to h is equivalent to the ratio 15 to k, where k is a constant. What is the value of k?

Answer :

Question 4 :

Which of the following expressions has 6x – 5b as a factor, where b is a positive integer constant?

A) 24x² – 22x – 15b

B) 24x² + 18x – 15b

C) 24x² + 36x – 15b

D) 24x² – 484x – 15b

Answer :

Question 5 :

The function f is defined by f(x) = a √(-x + b), where a and b are constants. In the xy-plane, the graph of y = f(x) passes through the point (5, 0), and f(–12) > f(–7). Which of the following must be true?

A) a < f(b)

B) a > b

C) f(3) < f(-2b)

D) a < b

Answer :

Question 6 :

The table shows three values of x and their corresponding values of y for the linear relationship between x and y. The x-intercept of the line occurs when x = -4. The number d is a negative constant. The number k is a constant. What is the value of dk?

Answer :

Question 7 :

f(x) = ax² – 7x + c

The function f is defined above, where a and c are constants. The graph of y = f(x) is a parabola that has a vertex at the point (h, k), where h and k are constants. If f(-9) = f(-2) and c > 0, which of the following must be true?

I. a < – 3/4

II. k > 16

A) I only

B) II only

C) I and II

D) Neither I nor II

Answer :

Question 8 :

The triangle inequality theorem states that the sum of any two sides of a triangle must be greater than the length of the third side. A triangle has side lengths of 4x + 20, 2x + 8 and 7x – 11. Which inequality represents all possible values of x?

A) x < 39

B) 8 < 2x < 78

C) 3 < x < 38

D) 23 < 5x < 195

Answer :

Question 9 :

In the given circle, point B is the center. Point A, C and D lie on the circle. Point B lies on line segment AC. Line EA is tangent to the circle at point A. The diameter of the circle is 240 cm. The length of segment BE is twice that of segment AB. If minor arc CD is kπ cm, what is the value of k?

Answer :

Question 10 :

A circle is centered at point O with coordinates (0, 0) in the xy-plane. The circle contains point A with coordinates (25, 0) and point B with coordinates (k, 24), where k is a negative constant. What is the value of cosine ∠AOB?