Full Practice Exam 29 — Module 1

Questions in this quiz (22)

1. Which value of $$x$$ is not a solution to the equation? $$\frac{2x^2-18}{x-3}=2x+6$$

   • $$-3$$
   • $$3$$
   • $$6$$
   • $$9$$

2. A store advertises a $$20\%$$ discount followed by an additional $$15\%$$ discount on the sale price. If a customer pays $$\$272$$ after both discounts, what was the original price of the item?

   • $$\$320$$
   • $$\$350$$
   • $$\$400$$
   • $$\$425$$

3. A scale model of a bridge is built at a ratio of $$1:750$$. The actual bridge is $$1.8$$ kilometers long. What is the length of the model in centimeters?

   • $$180$$
   • $$240$$
   • $$300$$
   • $$360$$

4. The formula $$P=\frac{Fv}{t^2}$$ relates four variables. Which expression gives $$t$$ in terms of $$P,F,$$ and $$v$$?

   • $$t=\frac{Fv}{P}$$
   • $$t=\sqrt{\frac{Fv}{P}}$$
   • $$t=\sqrt{\frac{P}{Fv}}$$
   • $$t=\frac{P}{Fv}$$

5. If $$y=ax^2-3x+7$$ and the graph passes through the point $$(4,39)$$, what is the value of $$a$$?

   • $$1$$
   • $$2$$
   • $$4$$
   • $$\frac{11}{4}$$

6. A train travels $$420$$ miles in $$3.5$$ hours. At the same rate, how many miles will the train travel in $$5.25$$ hours?

   • $$525$$
   • $$600$$
   • $$630$$
   • $$720$$

7. The system $$3x+2y=19$$ $$5x-y=8$$ has solution $$(a,b)$$. What is the value of $$ab$$?

   • $$\frac{2485}{169}$$

8. The capacity of a small container is one fourth the capacity of a large container. If the combined capacity of the two containers is $$150$$ liters, what is the capacity of the large container?

   • $$30$$ liters
   • $$60$$ liters
   • $$90$$ liters
   • $$120$$ liters

9. Parallelogram $$ADEC$$ has a side $$\overline{DE}$$ of length $$10$$ units and a side $$\overline{DA}$$ of length $$5$$ units. The length from $$A$$ to $$B$$ is $$3$$ units. What is the area of the parallelogram in square units?

   • $$40$$

10. A population of bacteria grows geometrically. Initially there are $$500$$ bacteria, and the population doubles every $$6$$ hours. Which function models the population $$P$$ after $$t$$ hours?

    • $$P(t)=500(2)^t$$
    • $$P(t)=500(2)^{t/6}$$
    • $$P(t)=500\left(\frac12\right)^{t/6}$$
    • $$P(t)=500(6)^t$$

11. The table shows the densities of several metals in grams per cubic centimeter. $$ \begin{array}{c|c} \text{Material} & \text{Density}\\ \hline \text{Aluminum} & 2.7\\ \text{Copper} & 8.9\\ \text{Iron} & 7.9\\ \text{Silver} & 10.5\\ \text{Zinc} & 7.1 \end{array} $$ What is the mass of a copper object with a volume of $$250\text{ cm}^3$$?

    • $$222.5\text{ g}$$
    • $$1,975\text{ g}$$
    • $$2,225\text{ g}$$
    • $$22,250\text{ g}$$

12. Which of the following is closest to the price, in U.S. dollars, of an ounce of gold in the year $$1970$$?

    • $$\$245$$
    • $$\$520$$
    • $$\$610$$
    • $$\$1,225$$

13. The mean of eight numbers is $$42$$. If one of the numbers is removed, the mean of the remaining seven numbers is $$39$$. What number was removed?

    • $$45$$
    • $$54$$
    • $$63$$
    • $$72$$

14. If $$\sin\theta=\frac35$$ and $$0^\circ<\theta<90^\circ$$, what is the value of $$\cos(90^\circ-\theta)?$$

    • $$\frac45$$
    • $$\frac35$$
    • $$\frac25$$
    • $$\frac34$$

15. Which of the following models the function as presented in the graph?

    • $$f(x)=x^2$$
    • $$f(x)=x^2+1$$
    • $$f(x)=2^x$$
    • $$f(x)=3^x+1$$

16. Which expression is not a factor of $$x^3-2x^2-15x?$$

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

17. A box contains $$5$$ red marbles, $$4$$ blue marbles, and $$3$$ green marbles. A marble is selected, replaced, and the box is mixed before another selection. What is the probability that both selected marbles are blue?

    • $$\frac19$$
    • $$\frac1{12}$$
    • $$\frac1{16}$$
    • $$\frac1{25}$$

18. If $$x+\frac1x=5,$$ what is the value of $$x^2+\frac1{x^2}?$$

    • $$21$$
    • $$23$$
    • $$25$$
    • $$27$$

19. A circle has radius $$r$$. If the radius increases by $$50\%$$, by what percent does the area increase?

    • $$50\%$$
    • $$100\%$$
    • $$125\%$$
    • $$150\%$$

20. The function $$f(x)=\frac{x^2-16}{x-4}$$ is defined for all real numbers except $$x=4$$. What is the value of $$f(7)?$$

    • $$7$$
    • $$9$$
    • $$11$$
    • $$13$$

21. A function is defined by $$f(x)=x^k,$$ where $$k$$ is a constant. If $$f(2)=32,$$ what is the value of $$f(8)$$?

    • $$512$$
    • $$1,024$$
    • $$4,096$$
    • $$32,768$$

22. The height of a rectangle is $$4$$ units greater than its width. If the area of the rectangle is $$96$$ square units, what is the perimeter of the rectangle?

    • $$32$$
    • $$36$$
    • $$40$$
    • $$44$$