11 Chapter Test

Do you know HOW?

Write an equation of the inverse variation that includes the given point.

1. (2, 2)
2. ( − 8 , − 4 ) open negative 8 comma negative 4 close

Identify the excluded value for each rational function.

3. f ( x ) = 19 + x x − 5 f , open x close , equals . fraction 19 plus x , over x minus 5 end fraction
4. y = 2 x 8 x − 12 y equals . fraction 2 x , over 8 x minus 12 end fraction

Identify the asymptotes of each function. Then graph the function.

5. y = 6 x y equals , 6 over x
6. y = 1 x + 3 y equals , 1 over x , plus 3
7. f ( x ) = 4 x − 2 f , open x close , equals . fraction 4 , over x minus 2 end fraction

Simplify each expression. State any excluded values.

8. 6 p − 30 3 p − 15 fraction 6 p minus 30 , over 3 p minus 15 end fraction
9. n 2 + 4 n − 5 n + 5 fraction n squared , plus 4 n minus 5 , over n plus 5 end fraction

Multiply or divide.

10. 3 x − 2 ⋅ x 2 − 4 12 fraction 3 , over x minus 2 end fraction . dot . fraction x squared , minus 4 , over 12 end fraction
11. 5 x x 2 + 2 x ÷ 30 x 2 x + 2 fraction 5 x , over x squared , plus 2 x end fraction . divides . fraction 30 , x squared , over x plus 2 end fraction

Divide.

12. ( 12 x 4 + 9 x 3 − 10 x 2 ) ÷ 3 x 3 open 12 , x to the fourth , plus 9 , x cubed , minus 10 , x squared , close divides 3 , x cubed
13. ( 4 x 4 − 6 x 3 − 2 x 2 − 2 x ) ÷ ( 2 x − 1 ) open 4 , x to the fourth , minus 6 , x cubed , minus 2 , x squared , minus 2 x close divides open 2 x minus 1 close

Find the LCD of each pair of expressions.

14. 5 h , 6 3 h 5 over h , comma , fraction 6 , over 3 h end fraction
15. 4 a 2 b 3 , 3 9 a b 4 fraction 4 , over eh squared , b cubed end fraction . comma . fraction 3 , over 9 eh , b to the fourth end fraction

Add or subtract.

16. 4 b − 2 3 b + b b + 2 fraction 4 b minus 2 , over 3 b end fraction . plus . fraction b , over b plus 2 end fraction
17. 9 n − 8 n + 1 9 over n , minus . fraction 8 , over n plus 1 end fraction

Solve each equation. Check your solutions.

18. v 3 + v v + 5 = − 4 v + 5 v over 3 , plus . fraction v , over v plus 5 end fraction . equals . fraction negative 4 , over v plus 5 end fraction
19. 16 x + 10 = 8 2 x − 1 fraction 16 , over x plus 10 end fraction . equals . fraction 8 , over 2 x minus 1 end fraction
20. Cleaning Mark can clean his father's office in 30 min. His younger sister Lynn can clean the office in 40 min. How long will it take the two of them together to clean the office?

Do you UNDERSTAND?

21. Open-Ended Write a rational expression for which 6 and 3 are excluded values.
22. Geometry The height of a square prism is 3 n + 1 . 3 n plus 1 .  The volume of the prism is 3 n 3 + 13 n 2 + 16 n + 4 . 3 , n cubed , plus 13 , n squared , plus 16 n plus 4 .  What is the area of the square base of the prism?
23. Reasoning Rosa divided a polynomial p(x) by x − 4 x minus 4  and obtained this result: 2 x + 12 + 59 x − 4 . 2 x plus 12 plus . fraction 59 , over x minus 4 end fraction . .  What is p(x)?
24. Error Analysis Your friend says the solution of the rational equation m m − 3 + 1 4 = 3 m − 3 fraction m , over m minus 3 end fraction . plus , 1 fourth , equals . fraction 3 , over m minus 3 end fraction  is 3. Explain the error that your friend may have made.
25. Reasoning Consider the equation 3 x − a = x x − a . fraction 3 , over x minus eh end fraction . equals . fraction x , over x minus eh end fraction . .  For what value(s) of a does the equation have exactly one solution? No solution? Explain.

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