Solving the HARDEST SAT Math Questions ONLY using Desmos

Question 1 :

f(t) = 55t – 2t²

The function f is defined by the given equation. The function g is defined by g(t) = f(t) + 3. Which expression represents the maixmum value of g(t)?

A)  3 + (55/4)²

B)  3 + 2(55/4)²

C)  3 - 2(55/4)²

D)  3 - (55/4)²

Question 2 :

The function g is defined by g(x) =|x|/a – 14, where a < 0. What is the product of g(15a) and g(7a)?

Question 3 :

Consider the line q which be written as y = mx + b. It is given that the points (2a, 4 – 3a) and (4a, 4 – 6a) lie on the line q. Determine the value of b.

Question 4 :

One of the factors of 2b³ – 24b² + 70b is b – c, where c is a constant. What is the largest possible value of c?

Question 5 :

The functions g and h are defined by the given equations, where x ≥ 0. Which of the following equations displays, as a constant or coefficient, the minimum value of the function it defines, where x ≥ 0 ?

I.  g(x) = 18(1.16)(1.14)^{x + 2}

II.  h(x) = 18(1.4)^{x + 4}

A)  I only

B)  II only

C)  I and II

D)  Neither I nor II

Answers (1-5)

Question 6 :

Function f is defined by f(x) = ax² + bx + c. The graph of y = f(x) in the xy-plane passes through the points (-5, 0) and (6, 0). If the value of a + b + c is 210, what is the value of b?

Question 7 :

Based on the equation above, what is the value of 3x – 2?

A)  –4

B)  – 4/5

C)  – 2/3

D)  4

Question 8 :

f(x) = 2(x – 3)² + 5

Which of the following is equivalent to f(x)?

A)  2x² – 12x + 23

B)  2x² – 12x + 5 

C)  2x² + 12x + 5 

D)  2x² + 12x + 23 

Question 9 :

What is the value of expression above?

Question 10 :

a is 250% more than b, b is 50% less than c and c is 60% more than 225. What is the value of a + b + c?

Answers (6-10)

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