Mini Exam 52 — Timed Mini Exams

Questions in this quiz (10)

1. If one of the solutions to the equation $$2x^2+8x+k=0$$ is $$x=-5$$, what is the other solution?

   • 1

2. Simplify the expression. $$\frac{(x-y)^2}{x^4-y^4}\cdot\frac{x^2+y^2}{y^2}\div\frac{x-y}{xy+y^2}$$

   • $$\frac{x^2}{y}$$
   • $$\frac1y$$
   • $$\frac{x^2}{y^3}$$
   • $$\frac{x}{y^2}$$

3. A function $$f(x)$$ is first reflected over the $$x$$-axis, then shifted four units right, squeezed vertically by a factor of $$\frac12$$, and then shifted six units down. Which of the following could represent the resulting function?

   • $$-2f(x-4)-6$$
   • $$\frac12f(x-4)-6$$
   • $$-\frac12f(x-4)-6$$
   • $$-2f(x+4)+6$$

4. The function $$f$$ is defined by a polynomial. Some values are shown below. Which of the following must be a factor of $$f(x)$$?

   • $$x-3$$
   • $$x-2$$
   • $$x+1$$
   • $$x-5$$

5. If $$a$$ and $$b$$ are positive numbers that satisfy $$\sqrt{a^2+2b^2}=a-3b,$$ what is the value of $$\frac ab$$?

   • $$\frac76$$
   • $$\frac76$$
   • $$\frac76$$
   • $$\frac76$$

6. David bought a bottle of juice containing $$3$$ pints of juice. Using the conversion table, find, to the nearest whole, the amount of juice David bought, in milliliters.

   • $$48$$
   • $$32$$
   • $$48$$
   • $$1421$$

7. John has $$4000$$ dollars in savings. He invests part of his savings in debt mutual funds that pay $$4\%$$ annual interest and the remaining part in bonds that pay $$6\%$$ annual interest. Let $$m$$ be the amount he invested in funds and $$b$$ be the amount invested in bonds. John's total income in one year from these investments is $$203.7$$ dollars. Which of the following systems of equations represents this relationship?

   • $$0.04m+0.06b=203.7$$$$m+b=4000$$
   • $$0.06m+0.04b=203.7$$$$m+b=4000$$
   • $$1.04m+1.06b=4000$$$$m+b=203.7$$
   • $$0.04m+0.06b=203.7$$$$m+b=4203.7$$

8. The table shows the performance of a team during one season, categorized by weather and whether the team won or lost. What fraction of the games during which there was bad weather did the team win?

   • $$\frac34$$
   • $$\frac25$$
   • $$\frac13$$
   • $$\frac23$$

9. A local newspaper reported the mean salary of $$16$$ employees in a certain company. The salaries are given in the table. Why is the mean salary alone not a useful measure of center for the distribution?

   • Sample size is too small to calculate the mean.
   • The data has a mode which may cause the distribution to be skewed.
   • Outliers may cause the distribution to be skewed.
   • Range of the data is more than $$1000$$.

10. The function is given by $$f(x)=5^{-(3+x)}.$$ Which of the following equivalent forms of the given function displays the $$y$$-coordinate of the $$y$$-intercept as a constant or coefficient?

    • $$f(x)=\left(\frac15\right)^{3+x}$$
    • $$f(x)=\frac1{125}\left(\frac15\right)^x$$
    • $$f(x)=5^{-3-x}$$
    • $$f(x)=\frac1{5^{3+x}}$$