Q: Which of the following is the correct solution to $$\tan(\theta) = \sqrt{3}$$ for $$0 \leq \theta \u003c 2\pi$$?

$$\theta = \dfrac{\pi}{3}, \dfrac{4\pi}{3}$$

Question 1

Which of the following is the correct solution set for the inequality $$2x^2 - 5x + 2$$ \u003c 0$$?

Accepted Answer

$$(1, 2)$$

Question 2

A population of bacteria triples every 4 hours. If the initial population is 200, which function models the population $$P(t)$$ after $$t$$ hours?

Accepted Answer

$$P(t) = 200 \cdot 3$$^{t/4}$$

Question 3

Which of the following is the inverse function of $$f(x) = \dfrac{2x-5}{3}$$?

Accepted Answer

$$f^{-1}(x$$) = \dfrac{3x-5}{2}$$

Question 4

A ball is thrown upward from the top of a 50-meter building with an initial velocity of 20 m/s. Its height $$h (in $$meters) after $$t$$ seconds is given by $$h(t) = -5t^2$ + 20t + 50. $$After how many seconds does the ball reach its maximum height?

Accepted Answer

$$t = 2$$

Question 5

Which of the following is the correct factorization of $$x^3 - 8$?

Accepted Answer

$$(x-2)(x^2+2x+4$$)$$

Question 6

Given $$f(x) = x^2$ and g(x$$) = \sqrt{x}$$, what is the domain of the composite function f$$ \circ g$$?

Accepted Answer

$$[0, \infty)$$

Question 7

A right triangle has legs of length 5 and 12. What is the length of the hypotenuse?

Accepted Answer

$$13$$

Question 8

Which of the following equations represents a circle with center at $$(2, -3)$$ and radius $$5$$?

Accepted Answer

$$(x-2)^2$$ + $$(y+3)^2 = 25$

Question 9

Solve for $$x$$: $$\log_2$(x) + \log_2$(x-2) = 3$$

Accepted Answer

$$x = 4$$

Question 10

A car's value depreciates by 15% each year. If the car is currently worth $$20,000, which function models its value V(t$$)$$ after t$ years?

Accepted Answer

$$V(t) = 20000 \cdot (0.85)^t$$

Question 11

Which of the following is the solution to the system of equations: $$\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}$$?

Accepted Answer

$$(2, 1)$$

Question 12

Which of the following is the correct graph for the function $$y = |x-3|$$?

Accepted Answer

A V-shaped graph with vertex at $$(3, 0)$$

Question 13

If $$\sin(	heta) = \dfrac{3}{5}$$ and $$	heta is in $$the first quadrant, what is $$\cos(	heta)$$?

Accepted Answer

$$\dfrac{4}{5}$$

Question 14

Which of the following is the solution to $$2^{x+1} = 16$?

Accepted Answer

$$x = 3$$

Question 15

A triangle has sides of length 7, 24, and 25. What is the area of the triangle?

Accepted Answer

$$84$$

Question 16

Which of the following is the correct solution to $$	an(	heta) = \sqrt{3}$$ for $$0 \leq 	heta \u003c 2\pi$$?

Accepted Answer

$$	heta = \dfrac{\pi}{3}, \dfrac{4\pi}{3}$$

Question 17

Which of the following is the correct solution to the equation $$|2x-5| = 7$$?

Accepted Answer

$$x = 6 or$$ $$x = -1$$

Question 18

A radioactive substance decays according to $$A(t) = A_0$ e$$^{-0.03t}$$, where t$ is in years. What is the half-life of the substance (to the nearest year)?

Accepted Answer

$$23$$

Question 19

Which of the following is the correct solution to the quadratic equation $$x^2 - 6x + 13 = 0$?

Accepted Answer

$$x = 3 \pm 2i$$

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