10 Hard SAT Math Questions (Part - 26)

Question 1 :

If (x - 7)/5 = (x - 4)/3, the value x - 4 is between which of the following pairs of values ?

A) -9 and -4

B) -1 and 1

C) 2 and 5

D) 7 and 11

Answer :

Question 2 :

A circle with a center B(0, 0) is a unit circle on the xy-plane. Point A(1, 0) and C lie on the circle. If the measurement of angle ABC is 975π/60 in radians. What is the x-coordinate of point C?

A) √2/2

B) -√2/2

C) 0

D) √2/3

Answer :

Question 3 :

A handyman charges a flat rate of $218 for the first 3 hours of work and $68 for each additional hour of work. Which equation gives the total amount y, in dollars, that the handyman charges for x hours of work, where x > 3?

A) y = 68x + 218
B) y = 218x + 68
C) y = 68x + 14
D) y = 68x + 422

Answer :

Question 4 :

For a certain circuit P, in watts; current C, in amperes; voltage V, in volts; and resistance R, in ohms, are related as CV³/P = √PR, where P, C, V and R are positive. When R = 34, which equation correctly expresses P in terms of C and V?

A) P = CV³/√34

B) P = CV³/√34P

C) P = ³√(34/C²V⁴)

D) P = ³√(34/C²V⁶)

Answer :

Question 5 :

f(x) = x + 7

g(x) = 5x² - kx + 245

The function f and g are given. In functiong, k is a constant. If f(x) ⋅ g(x) = 5x³ + 1,715, what is the value of k?

Answer :

Question 6 :

A circle is inscribed inside of square ABCD. Segment AC is the diagonal of the square, and its length is 30 cm. What is the radius of the circle in cm?

A) 15√2/2

B) 15

C) 15√2

D) 30

Answer :

Question 7 :

A metal mold in the shape of a rectangular prism has a length of 27 inches, a width of 48 inches, and a height of 180 inches. The equation c = v(d) calculates the cost of filling the metal mold, where c is the total cost in dollars, v is the volume in cubic yards, and d is the cost per cubic yard. If c is equal to $970, what is the value of d in dollars? (Note 1 yard = 36 inches)

Answer :

Question 8 :

The expression x²⁷(x - 7)/3x³ + 7x²⁷/3x³ is equivalent to ⅓x^k, where k is a constant and x > 0. What is the value of k?

A) 3

B) 27/3

C) 25

D) 28

Answer :

Question 9 :

Megan engages in up to 3 types of exercise each week for a total of 14 hours while training for an ironman competition. Megan runs the same number of minutes each week. The equation y = 780 – x – 200 represents the situation where Megan swims for x minutes during a week and bikes for any remaining training time y, in minutes. If this equation is graphed in the xy-plane, which of the following statements is true?

A) During a week when Megan runs for 780 minutes, she bikes for 200 minutes.

B) Each week, Megan swims and bikes for a total of 780 minutes.

C) During a week when Megan doesn’t bike, she swims for 390 minutes.

D) During a week when Megan doesn’t swim, she runs for 260 minutes.

Answer :

Question 10 :

The functions f and g are defined by the equations shown, where a and b are integer constants, a > b and b > 0. If y = f(x) and y = g(x) are graphed in the xy-plane, which of the following equations displays, as a constant or a coefficient, the maximum of the graph of the corresponding function when x ≥ 0.