10 Hard SAT Math Questions (Part - 10)

Question 1 :

The measure of angle BDC, in radians, is equal to aπ/b, where a and b are constants. What is the smallest possible value of a + b?

Answer :

Question 2 :

f(x) = |8 – 5x|

The function f is defined by the given equation. For what value of k does f(k) = 6k + 3?

Answer :

Question 3 :

The given equation relates the molal boiling point elevation K, the ideal-gas constant R, the solvent boiling point T, the solvent molecular weight M, and the molal heat of vaporization H. Which equation correctly expresses the solvent boiling point in terms of the other quantities?

Answer :

Question 4 :

Given : sin (a°) = cos (b°), where a and b are constants. The number a is 70% greater than the number b. What is the value of a?

Answer :

Question 5 :

For a group of 28 or more people, an arcade charges $9 per person for the first 28 people and $15 for each additional person. How many total people were in attendance, if the group paid $447 to go to the arcade?

Answer :

Question 6 :

An artist shades in her drawing at a rate of 1.3 square inches per second. What is this rate, in square decimeters per hour? (1 inch = 0.254 decimeter). Round your answer to the nearest tenth.

Answer :

Question 7 :

In triangles PQR and XYZ, angles R and Z each have a measure of 38°. The length of side QR is equal to 11. The length of side YZ is equal to 27.5. Which additional piece of information is sufficient to prove that triangle PQR is similar to triangle XYZ?

A)  The measure of angle P is 46°.

B)  The measure of angle Q is 49° and the measure of angle Y is 94°.

C)  The length of side PR is 14 and the length of side XZ is 35.

D)  No additional information is necessary.

Answer :

Question 8 :

Point P lies on the unit circle and its position is determined by constructing an angle of 119 π/6 radians with positive x-axis. What is the x-coordinate of Point P ?

A) – √3/2

B)  2√3/2

C)  √3/2

D)  –1/2 

Answer :

Question 9 :

y = 3x² – 5x – 12

40x – 4y = a

In the given system of equations, a is a positive constant. The system has exactly one distinct real solution. What is the value of a?

Answer :

Question 10 :

x² – 12x + 7 = 0

One solution to the given equation is j – √k, where j and k are constants. What is the value of jk?

Answer :

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