The 10 Hardest SAT Math Questions

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Question 1 :

The graph of y = f(x – 2) – 13 is shown. The function f is defined by which of the following equations?

A) f(x) = –x – 3

B) f(x) = –x + 3

C) f(x) = –x + 5

D) f(x) = –x – 8

Answer :

Question 2 :

For a quadratic function f(x), (x – 5) is a factor, x = r is a zero and the minimum point on the graph of f(x) is (k, –32). If k is 4 less than r, what is the value of r?

Answer :

Question 3 :

∠A and ∠B are two acute angles and cos A = sin B. The measures, in degrees, of ∠A and ∠B are 3x + 10and 5x – 80, respectively. What is the value of tan (11x + 5)?

Answer :

Question 4 :

A football coach charges each player $75 for the first month and $45 for each additional month.Which of the following functions correctly represents the total revenue f(p), in dollars, for p months and q players, where p and q are positive integers?

A) f(p) = 45pq + 30

B) f(p) = 45pq + 75

C) f(p) = 45pq + 30q

D) f(p) = 45pq + 75q

Answer :

Question 5 :

g(x) = -5x + k

For the function g(x) above, which of the following gives the equation for the function g(x) - 15, given that the point (-7, 2) lies on the graph of g(x) - 50?

A) h(x) = -5x + 17

B) h(x) = -5x − 2

C) h(x) = -5x + 2

D) h(x) = -5x + 32

Answer :

Question 6 :

The graph of the exponential function g(x) = p^x – q passes through the points (k, 4) and (2k, 346). What is a possible value of q?

Answer :

Question 7 :

For the function f, for every increase by 1/3 in the value of x, the value of f(x) increases by a factor of k, where k is a constant. Which of the following forms of function f displays the value of k as the base or coefficient?

A) f(x) = 64(3)^6x

B) f(x) = 64(2)^9x

C) f(x) = 64(27)^x

D) f(x) = 64(8)^3x

Answer :

Question 8 :

f(x) = ax² – 150x + k + 1

In the quadratic function f(x) above, a and k are constants, where 4 ≤ k ≤ 9. If f(x) has at least one real zero, what is the greatest possible value of a?

Answer :

Question 9 :

A regular polygon has 36 sides and the measure of each interior angle of the polygon is 34k, in degrees. What is the value of k?

Answer :

Question 10 :

The function f is defined by f(x + 2) = (x + 1)^x. Which of the following equations defines f(x)?

A) f(x) = (x + 1)^x^{+ 2}

B) f(x) = (x + 3)^x

C) f(x) = (x + 3)^x^{+ 2}

D) f(x) = (x – 1)^x^{– 2}

Answer :