Q: Which of the following describes the end behavior of the polynomial $$f(x) = -3x^5$ + 2x^3$ - x + 7$$?

As $$x \to \infty$$, $$f(x) \to -\infty$$; as $$x \to -\infty$$, $$f(x) \to \infty$$

Question 1

Which of the following is the correct factored form of the polynomial $$18x^3y^2$ - 12x^3$y - 24x^2$y$?

Accepted Answer

$$6x^2y(3xy - 2y - 4$$)$$

Question 2

A quadratic equation $$ax^2 + bx + c = 0$ has a discriminant b^2$ - 4ac = -12. $$What can you conclude about its solutions?

Accepted Answer

There are two distinct nonreal complex solutions.

Question 3

A projectile is launched upward from the ground with an initial velocity of $$73.5 m/s. $$Its height after $$t$$ seconds is given by $$s = -4.9t^2$ + 73.5t. $$After how many seconds will the projectile return to the ground?

Accepted Answer

$$t = 0 or$$ $$t = 15$$ seconds

Question 4

Which of the following is the correct formula for the sum of the first $$n$$ terms of an arithmetic sequence with first term $$a_1$$ and common difference $$d$$?

Accepted Answer

$$S_n = \frac{n}{2}(a_1$ + a_n)$$

Question 5

Given the function $$f(x) = 2x^2$ - 8x + 6$$, what are the coordinates of its vertex?

Accepted Answer

$$(2, -2)$$

Question 6

Which of the following describes the end behavior of the polynomial $$f(x) = -3x^5$ + 2x^3$ - x + 7$$?

Accepted Answer

As $$x 	o \infty$$, $$f(x) 	o -\infty$$; as $$x 	o -\infty$$, $$f(x) 	o \infty$$

Question 7

Which of the following is the correct solution to the equation $$\sqrt{x + 4} = x - 2$$?

Accepted Answer

$$x = 5$$

Question 8

If $$f(x) = 3x - 2$$ and $$g(x) = x^2$ + 1$$, what is $$(f \circ g)(2)$$?

Accepted Answer

$$f(g(2)) = 3(5) - 2 = 13$$

Question 9

Which of the following is the correct equation for a circle with center $$(2, -3)$$ and radius $$5$$?

Accepted Answer

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

Question 10

A system of equations is given by $$2x + 3y = 7$$ and $$4x - y = 5. $$What is the solution $$(x, y)$$?

Accepted Answer

Question 11

Which of the following is the correct formula for the future value $$A of an $$investment of $$P$$ dollars at an annual interest rate $$r$$, compounded $$n$$ times per year for $$t$$ years?

Accepted Answer

$$A = P(1 + \frac{r}{n}$$)^{nt}$$

Question 12

Which of the following is the correct solution set in interval notation for the inequality $$2x - 7 \u003c 5$$?

Accepted Answer

$$(-\infty, 6)$$

Question 13

Which of the following is the correct formula for the $$nth $$term of a geometric sequence with first term $$a_1$$ and common ratio $$r$$?

Accepted Answer

$$a_n = a_1$ r$$^{n-1}$$

Question 14

Which of the following is the correct binomial expansion for $$(x + y)^3$?

Accepted Answer

$$x^3$$ + $$3x^2y$$ + $$3xy^2$$ + $$y^3$$

Question 15

Which of the following is the correct solution to the equation $$|2x - 5| = 9$$?

Accepted Answer

$$x = 7 or$$ $$x = -2$$

Question 16

Which of the following is the correct solution for $$\log_2$(x) = 3$$?

Accepted Answer

$$x = 8$$

Question 17

Which of the following is the correct equation for a line passing through $$(1, 2)$$ with slope $$-3$$?

Accepted Answer

$$y - 2 = -3(x - 1)$$

Question 18

Which of the following is the correct formula for the midpoint $$M of $$the segment with endpoints $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$?

Accepted Answer

$$M = (\frac{x_1$ + x_2$}{2}, \frac{y_1$ + y_2$}{2})$$

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