Advanced Quizzes — Quiz 26

Questions in this quiz (13)

1. A function is defined by $$f(x)=2x^2-5x+1$$. If $$f(a)=f(4)$$, where $$a\ne4$$, what is the value of $$a$$?

   • $$-\frac{3}{2}$$
   • $$-\frac{1}{2}$$
   • $$\frac{1}{2}$$
   • $$\frac{3}{2}$$

2. In the coordinate plane, the graph of $$y=ax^2+bx+c$$ has $$x$$-intercepts at $$-\frac{2}{3}$$ and $$5$$. The graph passes through the point $$(0,-20)$$. What is the value of $$a$$?

   • $$2$$
   • $$3$$
   • $$4$$
   • $$6$$

3. A company's profit $$P$$, in thousands of dollars, is modeled by $$P(t)=200(1.08)^t-150$$, where $$t$$ is the number of years after the company was founded. According to the model, after approximately how many years will the company's profit first exceed $$300$$ thousand dollars?

   • $$11$$
   • $$13$$
   • $$15$$
   • $$17$$

4. The expression $$\frac{x^3+8}{x+2}+\frac{x^2-4}{x-2}$$ is equivalent to which of the following for all appropriate values of $$x$$?

   • $$2x^2+4$$
   • $$x^2+2x$$
   • $$2x^2+2x+4$$
   • $$x^2-x+6$$

5. In the coordinate plane, the circle $$(x-2)^2+(y+1)^2=r^2$$ passes through the point $$(8,7)$$. What is the area of the circle?

   • $$50\pi$$
   • $$72\pi$$
   • $$100\pi$$
   • $$136\pi$$

6. A data set consists of $$13$$ distinct integers arranged in increasing order. The median is $$18$$ and the mean is $$22$$. Each of the $$6$$ integers greater than the median is increased by $$4$$, and each of the $$6$$ integers less than the median is decreased by $$4$$. Which of the following must be true?

   • The mean increases and the median increases.
   • The mean remains unchanged and the median remains unchanged.
   • The mean remains unchanged and the median increases.
   • The mean decreases and the median remains unchanged.

7. If $$\frac{a}{b}+\frac{b}{a}=14$$, what is the value of $$\frac{a^2}{b^2}+\frac{b^2}{a^2}$$?

   • $$192$$
   • $$194$$
   • $$196$$
   • $$198$$

8. A regular decagon is inscribed in a circle of radius $$12$$. What is the perimeter of the decagon?

   • $$120\sin(18^\circ)$$
   • $$240\sin(18^\circ)$$
   • $$120\sin(36^\circ)$$
   • $$240\sin(36^\circ)$$

9. In triangle $$ABC$$, point $$D$$ lies on side $$BC$$ such that $$\frac{BD}{DC}=3:2$$. If the area of triangle $$ABC$$ is $$50$$, what is the area of triangle $$ABD$$?

   • $$20$$
   • $$25$$
   • $$30$$
   • $$35$$

10. The polynomial $$P(x)=64x^3-nk^3$$ has a factor of $$4x-3k$$, where $$k$$ > $$0$$. What is the value of $$n$$?

    • 27

11. A manufacturer produces two products, $$A$$ and $$B$$. Product $$A$$ generates a profit of $$p$$ dollars per unit and Product $$B$$ generates a profit of $$q$$ dollars per unit. Last month, the company sold $$30\%$$ more units of Product $$A$$ than Product $$B$$. If the company sold a total of $$N$$ units and generated a total profit of $$T$$ dollars, which of the following expressions represents $$T$$?

    • $$\frac{N}{2}(1.3p+q)$$
    • $$\frac{N}{2.3}(1.3p+q)$$
    • $$\frac{N}{2.3}(p+1.3q)$$
    • $$\frac{N}{1.3}(p+q)$$

12. In the coordinate plane, points $$A(0,0)$$, $$B(10,0)$$, and $$C(16,8)$$ are vertices of a triangle. A line through $$A$$ is parallel to $$BC$$, and a line through $$B$$ is parallel to $$AC$$. The two lines intersect at point $$D$$. What is the $$x$$-coordinate of $$D$$?

    • -6

13. If $$x+\frac{1}{x}=5$$, what is the value of $$x^3+\frac{1}{x^3}$$?

    • $$110$$
    • $$115$$
    • $$120$$
    • $$125$$