Mini Exam 19 — Timed Mini Exams

Questions in this quiz (10)

1. Two chords, $$\overline{MN}$$ and $$\overline{PQ}$$, intersect at point $$R$$ inside a circle. The length of segment $$MR$$ is $$8$$, the length of segment $$RN$$ is $$3$$, and the length of segment $$PR$$ is $$4$$. What is the length of segment $$RQ$$?

   • $$4$$
   • $$5$$
   • $$6$$
   • $$8$$

2. A ladder is leaning against a vertical wall. The top of the ladder reaches a height of $$12$$ feet on the wall from the ground. The base of the ladder is $$5$$ feet away from the wall. What is the measure of the angle, to the nearest degree, that the ladder makes with the ground?

   • $$67^\circ$$
   • $$60^\circ$$
   • $$52^\circ$$
   • $$45^\circ$$

3. The price of a bicycle was initially 500 dollars. First, the price increased by $$20\%$$. Then, the new price decreased by $$10\%$$. What was the final price of the bicycle?

   • $540
   • $550
   • $600
   • $450

4. The equation $$m(x-2)+4x=8x+2n$$ where $$m$$ and $$n$$ are constants, has infinitely many solutions for $$x$$. What is the value of $$m+n$$?

   • $$10$$
   • $$12$$
   • $$16$$
   • $$0$$

5. A survey was conducted among a random sample of $$1,000$$ residents of a city to determine whether they support a proposed park. Based on the survey, it was estimated that $$62\%$$ of the city's residents support the proposal, with an associated margin of error of $$4\%$$. Which of the following is the most appropriate conclusion?

   • It is plausible that exactly $$62\%$$ of the city's residents support the proposal.
   • It is plausible that between $$58\%$$ and $$66\%$$ of the city's residents support the proposal.
   • It is plausible that fewer than $$58\%$$ of the city's residents support the proposal.
   • The survey results are invalid because only $$1,000$$ residents were surveyed.

6. A survey was conducted among $$300$$ students regarding participation in school clubs. $$120$$ students participate in the Science Club. $$90$$ students participate in the Math Club. $$45$$ students participate in both clubs. If a student is chosen at random from those who participate in the Science Club, what is the probability that the student also participates in the Math Club?

   • $$\frac{3}{8}$$
   • $$\frac{1}{4}$$
   • $$\frac{3}{10}$$
   • $$\frac{1}{2}$$

7. The function $$g$$ is defined by $$g(x)=-2(x-4)^2+9$$. What is the maximum value of $$g(x)$$?

   • $$4$$
   • $$7$$
   • $$9$$
   • $$11$$

8. A circle in the $$xy$$-plane has center at the origin. A line is tangent to the circle at the point $$(8,6)$$. Which of the following is an equation of the tangent line?

   • $$8x+6y=100$$
   • $$6x+8y=100$$
   • $$8x-6y=28$$
   • $$6x-8y=0$$

9. The graph of the function $$f$$ is shown in the $$xy$$-plane. The function $$f$$ is defined by $$f(x)=ax^2+bx+c$$, where $$a$$, $$b$$, and $$c$$ are constants. Based on the graph, what is the minimum value of $$f(x)$$?

   • $$-2$$
   • $$-1$$
   • $$0$$
   • $$1$$

10. The graph of a linear function $$f$$ passes through the point $$(-2,5)$$. If the $$x$$-intercept of the graph of $$f$$ is the same as the $$y$$-intercept of the line with equation $$y=-3x+6$$, what is the value of $$f(7)$$?

    • $$-7$$
    • $$-\frac{5}{8}$$
    • $$1$$
    • $$5$$