Mini Exam 50 — Timed Mini Exams

Questions in this quiz (10)

1. For a polynomial $$P(x)$$, $$P\left(\frac23\right)=7$$. Which of the following must be true about $$P(x)$$?

   • $$3x-2$$ is a factor of $$P(x)$$
   • $$x-5$$ is a factor of $$P(x)$$
   • When $$P(x)$$ is divided by $$3x-2$$, the remainder is $$7$$.
   • When $$P(x)$$ is divided by $$x-5$$, the remainder is $$\frac23$$.

2. If $$(x+2)(x-c)=x^2-px-10,$$ what is the value of $$c-p$$?

   • 2

3. The members of the senate consist of $$50$$ democrats and $$70$$ liberals. How many liberals must be removed so that $$\frac57$$ of all the remaining members of the senate are democrats?

   • 50

4. John buys both items and pays $$4\%$$ tax on the final discounted price. If the final cost is $$\$78.78$$, what is the original price of the blouse, $$x$$, in dollars?

   • 60

5. Last year Team A played $$50$$ games in total. The table shows predictions and corresponding outcomes. According to the results, what is the probability that the prediction was incorrect?

   • $$\frac{13}{50}$$
   • $$\frac{37}{50}$$
   • $$\frac{26}{50}$$
   • $$\frac6{50}$$

6. The median price of houses in district B is $$\$20,000$$, but the mean price of the houses in this district is $$\$15,000$$. Which of the following is a justified reason for such a difference in the mean and median prices of the houses?

   • Some houses are fashionable, some are not.
   • Some houses are one-floored, some are two-floored.
   • There are few houses that are priced much higher than the rest.
   • There are few houses that are priced much lower than the rest.

7. Of the following scenarios, which one would result in an exponential function?

   • Each year, $$10\%$$ of the initial value of a car is subtracted from the car's total value.
   • Each year, $$\$2,000$$ is subtracted from a car's total value.
   • Each year, $$10\%$$ of the initial value of a car and $$\$2,000$$ is subtracted from the car's total value.
   • Each year, $$10\%$$ of the current value of a car is subtracted from the car's total value.

8. Zoya wants to know what the most popular shampoo brand in the city is. Which of the following sample spaces is the most appropriate for this purpose?

   • The youngest $$50$$ people who exit from the supermarket.
   • The first $$50$$ people who exit from the supermarket.
   • Every third person who exits from the supermarket until $$50$$ people are surveyed.
   • Only women who exit from the supermarket until $$50$$ women are surveyed.

9. If $$\tan x=5$$ and $$0^\circ\le x\le90^\circ,$$ which of the following is the exact value of $$\sin x$$?

   • $$\frac1{\sqrt{26}}$$
   • $$\frac15$$
   • $$\frac5{\sqrt{26}}$$
   • $$\frac{\sqrt{26}}5$$

10. In the figure, $$\overline{DE}$$ is parallel to $$\overline{AC}$$. If $$BD=1,$$ $$DE=3,$$ and $$AC=12,$$ what is the length of $$\overline{AD}$$?

    • 3