10 Hard SAT Math Questions (Part - 23)

Question 1 :

The function f is defined by f(x) = a√(x + b), where a and b are constants and a ≠ 0. In the xy-plane, the graph of y = f(x) passes through the point (–24, 0), and f(24) < 0. Which of the following must be true?

A) f(0) = 24

B) f(0) = -24

C) a > b

D) a < b

Answer :

Question 2 :

The function f is defined by f(x) = a(2.2^x + 2.2^b), where a and b are integer constants and 0 < a < b. The functions g and h are equivalent to function f, where k and m are constants. Which of the following equations displays the y-coordinate of the y-intercept of the graph of y = f(x) in the xy-plane as a constant or coefficient?

I. g(x) = a(2.2^x + k)

II. h(x) = a(2.2)^x + m

A) I only

B) II only

C) I and II

D) Neither I nor II

Answer :

Question 3 :

h(x) = 5(x – m)(x – n)(x – r)

The function h is defined by the given equation, where m, n and r distinct constants. When m < x < r, the value of h(x) is positive. The graph of y = h(x) constains the point (s, t), where s and t are constants. If t = 9, which of the following could be true?

I. n < s

II. s < m

III. r < s < n

A) I only

B) II only

C) III only

D) None of them

Answer :

Question 4 :

-19(6x - 4)² + 6(6x - 3)²

The given expression can be rewritten as (a/9)x² + (b/9)x + c/9, where a, b and c are constants. What is the value of a + b + c?

Answer :

Question 5 :

A rectangular area consists of 3,179 equal squares where each square has an area of k. If the length of the rectangular area is 2.75 times the width and the width is equal to x√k, what is the value of x?

Answer :

Question 6 :

f(x) = x² + 5x - 6

g(x) = x² + 2x - 35

The quadratic function f(x) has 2 solutions j and k, where j < k. The quadratic function g(x) has 2 solutions ℓ and m, where ℓ < m. The quadratic function h(x) = x² + 7x + c has solutions of k + ℓand m + j, and can be rewritten as (x + a)(x + b), what is the value of c?

Answer :

Question 7 :

For the exponential function f(x) = 16^x^{+ 4}, which of the following answer choices expresses the minimum value as either a constant or coefficient when x ≥ 0?

A) f(x) = 64(16)^x

B) f(x) = 65,536(16)^x

C) f(x) = 1,048,576(16)^x

D) (1/65,356)(16)^x

Answer :

Question 8 :

For the given parabola f(x) = ax² + bx + c, a, b and c are constants. The x-intercepts of the parabola are at (14, 0) and (k, 0). If f(27) = f(11), what is the value of k?

Answer :

Question 9 :

A quadratic function models a projectile’s height, in meters, above the ground in terms of time, in seconds, after it was launched. The model estimates that the projectile was launched from an initial height of a meters and reached a maximum height of 134 meters 6 seconds after it was launched. How many seconds after launch does the model estimate it will return to a height of a meters?

A) 6

B) 8

C) 9

D) 12

Answer :

Question 10 :

M(t) = 10(½)^t/5730

The function M models the mass of the radioactive isotope carbom-14 in a sample, in picograms, t years after the initial measurement. How much time, in years, does it take for the mass of carbon-14 in the sample to decrease to 5 picograms?

Answer :