10 Hard SAT Math Questions (Part - 20)

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Question 1 :

The vertex of the function f(x) is given as (9, –13) and the point (3, –4) lies on the parabola. If g(x) = 4f(x – 2), what is the value of g(0) – f(0)?

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Question 2 :

The density of a certain type of wood is 770 kilograms per cubic meter. A sample of this type of wood is in the shape of a cube, where each edge has a length of 0.7 meters. To the nearest whole number, what is the mass, in kilograms, of this sample?

A) 264

B) 377

C) 1,571

D) 2,245

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Question 3 :

In ΔABC, ∠B is a right angle and the length of AB is 456 millimeters. If the cos C = 7/25, what is the length, in millimeters, of BC?

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Question 4 :

In triangle ABC and triangle DEF, sides BC and EF each have a side length of 37 inches, and angles B and E each have an angle measure of 63°. Which of the following additional pieces of information is (are) sufficient to prove whether triangle ABC is congruent to triangle DEF?

I. The measures of angles A and C are equal.

II. The lengths of sides AC and DF are equal.

III. The measures of angles A and D are equal.

A) I is sufficient, but II and III are not.

B) II is sufficient, but I and III are not.

C) III is sufficient, but I and II are not.

B) II and III are sufficient, but I is not.

Answer :

Question 5 :

77x² + (7j + 11k)x + jk = 0

In the given equation, j and k are positive constants. The product of the solutions to the given equation is ajk, where a is a constant. What is the value of a?

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Question 6 :

The number j is 2,400% greater than the number k. The number k is 350% greater than 8. What is the value of j?

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Question 7 :

A square is inscribed in a circle with the equation x² + y² – 8x + 10y = 27. What is the area of the square?

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Question 8 :

The equation below relates distinct positive real numbers a, b and c. Which equation correctly expresses c in terms of a and b?

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Question 9 :

Triangle ABC is inscribed in a circle with a radius of 85. The length of AC is 170 and the length of BC is 168. What is the value of AB/BC?

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Question 10 :

For the exponential function f, the value of f(2) is k, where k is a constant. Which of the following equivalent forms of the function f shows the value of k as the coefficient or the base?

A) f(x) = 729(3)^x^{+ 2}

B) f(x) = 6,561(3)^x

C) f(x) = 177,147(3)^{x – 3}

D) f(x) = 59,049(3)^{x – 2}

Answer :