10 Hard SAT Math Questions (Part - 21)

Question 1 :

f(x) = a[(x + 9)² – b][(x + 9)² – c]

In the function, a, b and c are constants. The graph of y = f(x) passes through the points (–7, 15), (0, 299) and (–5, 0). To the nearest whole number, what is the value of f(–4) + f(–15)?

Answer :

Question 2 :

Two numbers r and s are each greater than zero, and the fourth root of r is equal to the seventh root of s. For what value of x is r^{4x – 5} equal to s?

Answer :

Question 3 :

The given equation ax² + 98x + c = 0 has at least 1 real root and a factor of kx + j. What is the greatest possible value of ac?

Answer :

Question 4 :

The table gives two values of x and their corresponding values of g(x), where

and f is a linear function. What is the y-coordinate of the y-intercept of the graph y = f(x) in the xy-plane?

Answer :

Question 5 :

What is the value of sin x°⋅ cos (90 – x)° + sin (90 – x)° ⋅ cos x°?

A)  0.5

B)  1

C)  2

D)  90

Answer :

Question 6 :

There are red, blue, green, and black marbles in a bag. There are 26 black marbles, 8 green marbles, and 26 blue and red marbles. Given that a randomly selected marble is not black, the probability of selecting a red marble is 5/17. What is the number of blue marbles in the bag?

Answer :

Question 7 :

In the given equation, s and r are constants, and s > 0. If the equation has infinitely many solutions, what is the value of s?

Answer :

Question 8 :

A gardener is purchasing topsoil for a new garden. The garden is in the shape of a rectangular prism. The dimensions of the garden are 54 feet by 192 feet by 2 feet. If it costs $96 per cubic yard of topsoil, how much does the gardener need to spend in dollars?
(1 yard = 3 feet)

Answer :

Question 9 :

In the xy-plane, which of the following points lies on a circle with the equation (x + k)² + (y - j)² = 841 ?

A)  (k + 20, j + 21)

B)  (k - 20, j - 21)

C)  (-k + 21, j + 20)

D)  (-k - 21, -j - 20)

Answer :

Question 10 :

Which of the following inequalities gives all possible values of k where the equation below has no solution?

A)  k < -3/4

B)  k > -3/4

C)  k ≤ 3/4

D)  k ≥ 3/4

Answer :

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