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You are reading an older version of this FlexBook® textbook: CK-12 Algebra - Basic Go to the latest version.

12.9: Chapter 12 Review

Difficulty Level: At Grade Created by: CK-12

Define the following terms used in this chapter.

  1. Inverse variation
  2. Asymptotes
  3. Hyperbola
  4. Points of discontinuity
  5. Least common multiple
  6. Random sampling
  7. Stratified sampling
  8. Biased
  9. Cherry picking
  10. What quadrants are the branches of the hyperbola located if \begin{align*}k<0\end{align*}k<0?

Are the following examples of direct variation or inverse variation?

  1. The number of slices \begin{align*}n\end{align*}n people get from sharing one pizza
  2. The thickness of a phone book given \begin{align*}n\end{align*}n telephone numbers
  3. The amount of coffee \begin{align*}n\end{align*}n people receive from a single pot
  4. The total cost of pears given the nectarines cost $0.99 per pound

For each variation equation:

  1. Translate the sentence into an inverse variation equation.
  2. Find \begin{align*}k\end{align*}k, the constant of variation.
  3. Find the unknown value.
  1. \begin{align*}y\end{align*}y varies inversely as \begin{align*}x\end{align*}x. When \begin{align*}x=5, y=\frac{2}{15}\end{align*}x=5,y=215. Find \begin{align*}y\end{align*}y when \begin{align*}x=- \frac{1}{2}\end{align*}x=12.
  2. \begin{align*}y\end{align*}y is inversely proportional to the square root of \begin{align*}y\end{align*}y. When \begin{align*}x=16, y=0.5625\end{align*}x=16,y=0.5625. Find \begin{align*}y\end{align*}y when \begin{align*}x=\frac{1}{8}\end{align*}x=18.
  3. Habitat for Humanity uses volunteers to build houses. The number of days it takes to build a house varies inversely as the number of volunteers. It takes eight days to build a house with twenty volunteers. How many days will it take sixteen volunteers to complete the same job?
  4. The Law of the Fulcrum states the distance you sit to balance a seesaw varies inversely as your weight. If Gary weighs 20.43 kg and sits 1.8 meters from the fulcrum, how far would Shelley sit, assuming she weighs 36.32 kilograms?

For each function:

  1. Graph it on a Cartesian plane.
  2. State its domain and range.
  3. Determine any horizontal and/or vertical asymptotes the function may have.
  1. \begin{align*}y=\frac{4}{x}\end{align*}y=4x
  2. \begin{align*}f(x)=\frac{2}{4-x}\end{align*}f(x)=24x
  3. \begin{align*}g(x)=\frac{-1}{x+1}\end{align*}g(x)=1x+1
  4. \begin{align*}y=\frac{6}{3x+1}-2\end{align*}y=63x+12
  5. \begin{align*}f(x)=\frac{3}{x}-5\end{align*}f(x)=3x5

Perform the indicated operation.

  1. \begin{align*}\frac{5a}{6}-\frac{5b}{4b}\end{align*}5a65b4b
  2. \begin{align*}\frac{4}{3m}+\frac{4m}{5}\end{align*}43m+4m5
  3. \begin{align*}\frac{3x}{2xy}+\frac{4}{3}\end{align*}3x2xy+43
  4. \begin{align*}\frac{2}{5n-2}+\frac{2n}{2}\end{align*}25n2+2n2
  5. \begin{align*}\frac{2x+1}{3x+9}-\frac{x+5}{3x+9}\end{align*}2x+13x+9x+53x+9
  6. \begin{align*}\frac{5m+n}{30n^4}-\frac{4m+n}{30n^4}\end{align*}5m+n30n44m+n30n4
  7. \begin{align*}\frac{r-6}{4r^2-12r+8}-\frac{r+6}{4r^2-12r+8}\end{align*}r64r212r+8r+64r212r+8
  8. \begin{align*}\frac{2}{16x^3 y^2}+\frac{x-2y}{16x^3 y^2}\end{align*}216x3y2+x2y16x3y2
  9. \begin{align*}\frac{n-6}{n+2}+\frac{2n}{5}\end{align*}n6n+2+2n5
  10. \begin{align*}\frac{8}{4}-\frac{x+5}{x+8}\end{align*}84x+5x+8
  11. \begin{align*}\frac{3x}{2(x+1)}+\frac{6}{7x-6}\end{align*}3x2(x+1)+67x6
  12. \begin{align*}\frac{11}{8} \cdot \frac{20x^2}{2}\end{align*}11820x22
  13. \begin{align*}\frac{17r}{16} \cdot \frac{7r^4}{16}\end{align*}17r167r416
  14. \begin{align*}\frac{15}{18} \cdot \frac{14}{17t}\end{align*}15181417t
  15. \begin{align*}\frac{2(b-11)}{14b} \cdot \frac{b+5}{(b+5)(b-11)}\end{align*}2(b11)14bb+5(b+5)(b11)
  16. \begin{align*}\frac{17w^2}{w+4} \cdot \frac{18(w+4)}{17w^2 (w-9)}\end{align*}17w2w+418(w+4)17w2(w9)
  17. \begin{align*}\frac{10s^3-30s^2}{30s^2-10s^3} \cdot \frac{s-3}{8}\end{align*}10s330s230s210s3s38
  18. \begin{align*}\frac{1}{f-5} \div \frac{f+3}{f^2+6f+9}\end{align*}1f5÷f+3f2+6f+9
  19. \begin{align*}\frac{(a+8)(a+3)}{4(a+3)} \div \frac{10a^2 (a+10)}{4}\end{align*}(a+8)(a+3)4(a+3)÷10a2(a+10)4
  20. \begin{align*}\frac{1}{(h-10)(h+7)} \div \frac{(h-4)}{4h(h-10)}\end{align*}1(h10)(h+7)÷(h4)4h(h10)
  21. \begin{align*}\frac{2(5x-8)}{4x^2 (8-5x)} \div \frac{6}{4x^2}\end{align*}2(5x8)4x2(85x)÷64x2
  22. \begin{align*}\frac{2(q-7)}{40q(q+1)} \div \frac{1}{40q(q+1)}\end{align*}2(q7)40q(q+1)÷140q(q+1)

Solve each equation.

  1. \begin{align*}\frac{3}{3x^2}=\frac{1}{x}+\frac{1}{3x^2}\end{align*}33x2=1x+13x2
  2. \begin{align*}\frac{2}{5x^2}=-\frac{12}{x-3}\end{align*}25x2=12x3
  3. \begin{align*}\frac{7x}{x-6}=\frac{3}{4x+16}\end{align*}7xx6=34x+16
  4. \begin{align*}\frac{4}{c-2}=\frac{3}{c+4}\end{align*}4c2=3c+4
  5. \begin{align*}\frac{d-4}{4d^2}=\frac{1}{4d^2}+\frac{1}{4d}\end{align*}d44d2=14d2+14d
  6. \begin{align*}\frac{1}{2}=\frac{2z-12}{z} - \frac{z+1}{4z}\end{align*}12=2z12zz+14z
  7. \begin{align*}\frac{1}{n}=\frac{1}{n^2} +\frac{6}{n}\end{align*}1n=1n2+6n
  8. \begin{align*}\frac{1}{2a}=\frac{1}{2a^2}+\frac{1}{a}\end{align*}
  9. \begin{align*}\frac{k+4}{k^2} =\frac{5k-30}{3k^2}+\frac{1}{3k^2}\end{align*}
  10. It takes Jayden seven hours to paint a room. Andie can do it in five hours. How long will it take to paint the room if Jayden and Andie work together?
  11. Kiefer can mow the lawn in 4.5 hours. Brad can do it in two hours. How long will it take if they worked together?
  12. Melissa can mop the floor in 1.75 hours. With Brad’s help, it took only 50 minutes. How long would it take Brad to mop it alone?
  13. Working together, it took Frankie and Ricky eight hours to frame a room. It would take Frankie fifteen hours doing it alone. How long would it take Ricky to do it alone?
  14. A parallel circuit has \begin{align*}R_1=50 \Omega\end{align*} and \begin{align*}R_t=16 \Omega\end{align*}. Find \begin{align*}R_2\end{align*}.
  15. A parallel circuit has \begin{align*}R_1=6 \Omega\end{align*} and \begin{align*}R_2=9 \Omega\end{align*}. Find \begin{align*}R_T\end{align*}.
  16. A series circuit has \begin{align*}R_1=200 \Omega\end{align*} and \begin{align*}R_t=300 \Omega\end{align*}. Find \begin{align*}R_2\end{align*}.
  17. A series circuit has \begin{align*}R_1=11 \Omega\end{align*} and \begin{align*}R_2=25 \Omega\end{align*}. Find \begin{align*}R_T\end{align*}.
  18. Write the formula for the total resistance for a parallel circuit with three individual resistors.
  19. What would be the bias in this situation? To determine the popularity of a new snack chip, a survey is conducted by asking 75 people walking down the chip aisle in a supermarket which chip they prefer.
  20. Describe the steps necessary to design and conduct a survey.
  21. You need to survey potential voters for an upcoming school board election. Design a survey with at least three questions you could ask. How will you plan to conduct the survey?
  22. What is a stratified sample? Name one case where a stratified sample would be more beneficial.

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