10 Hard SAT Math Questions (Part - 3)

Question 1 :

Point C is the center of the circle shown below. Points D and F both lie on the circle as shown. The perimeter of triangle CDF is 60 units. What is the area of shaded region? Round your answer to the nearest hundredth.

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Question 2 :

f(x) = ax² + 36x + c

g(x) = jx² – 57x + ℓ

The functions f(x) and g(x) are both quadratic functions, and m is a positive constant. The parabola formed by the graph of y = f(x) has a vertex with a y-coordinate of 3m. The parabola formed by the graph of y = g(x) has a vertex with a y-coordinate of m. If f(10) = f(14) and g(-3) = g(27), for how many values of x does f(x) = g(x)?

Note : a, c, j and ℓ are constants.

A) Exactly one

B) Exactly two

C) Infinitely many

D) Zero

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Question 3 :

In triangle ABC, angle B is a right angle, the measure of angle A is 34°,and the length of segment BC is 13 inches. What is the area of triangle ABC in square inches?

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Question 4 :

For two acute angles, ∠A and ∠B, cos A = sin B. The measures, in degrees of, ∠A and ∠B are 9x + 10 and 48 + 5x respectively. What is the value of x?

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Question 5 :

In triangle XYZ, the sum of the measures of angle X and angle Y is 90 degrees. The value of sin X = 5√3/12. What is the value of cos Y?

A) 5√13/12

B) 5√3/13

C) 10√5/21

D) 21/10√5

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Question 6 :

A set of five consecutive even integers is ordered from least to greatest. The sum of the first and fourth even integers is 5,860% more than the quotient of the fifth even integer and 30. The first even integer is p% less than the fifth even integer, where p is a constant. What is the value of p? (Round your answer to the nearest hundredth).

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Question 7 :

A circle is inscribed in an equilateral triangle as shown above. Point L is the center of the circle. Points A, B and C all lie on the circle and the sides of the triangle. The perimeter of the triangle is 90√3. The length of arc AC is equal to kπ. What is the value of k?

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Question 8 :

The numbers a, b and p are all positive constants where 3 < a < 20 and 8 < b < 12.If the positive difference of a and 3 is p% less than the product of 5 and b, which equation correctly expresses p in terms of a and b?

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Question 9 :

A mathematician has two right circular cones. Cone A and Cone B are similar. Cone A has a surface area of 1,225π square inches and cone B has a surface area of 1,600π square inches. The radius of Cone A is 133 inches. The height of Cone B is 345 inches. What is the slant height, in inches of Cone B?

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Question 10 :

A line intersects two parallel lines, forming four acute angles and four obtuse angles. The measure of one of these eight angles is (9x – 220)°. The sum of the four of the eight angles is s°. Which of the following could NOT be equivalent to s, for all values of x?

A) 360

B) –18x + 980

C) –36x + 1,600

D) 18x – 700

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