Algebra 2: Chapter 9 Review Guide
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Alicia can row 6 miles downstream in the same time it takes her to row 4 miles upstream. She rows
downstream 3 miles/hour faster than she rows upstream. Find Alicia’s rowing rate each way. Round your
answers to the nearest tenth, if necessary.
a. 4 mi/h downstream, 2.7 mi/h upstream
b. 20 mi/h downstream, 13.3 mi/h upstream
c. 2.7 mi/h downstream, 4 mi/h upstream
d. 9 mi/h downstream, 6 mi/h upstream
Short Answer
2. Suppose that x and y vary inversely, and x = 2 when y = 5. Write the function that models the inverse
variation.
Is the relationship between the variables in the table a direct variation, an inverse variation, or neither?
If it is a direct or inverse variation, write a function to model it.
3.
x
–3
–1
3
4
y
21
7
–21
–28
4. Suppose that x and y vary inversely and that
when x = 9. Write a function that models the inverse
variation and find y when x = 6.
5. Suppose that y varies jointly with w and x and inversely with z and y = 60 when w = 5, x = 16 and z = 8. Write
the equation that models the relationship. Then find y when w = 4, x = 15 and z = 5.
6. The amount of oil used by a ship traveling at a uniform speed varies jointly with the distance and the square
of the speed. The ship uses 279 barrels of oil in traveling 90 miles at 44 mi/h. How many barrels of oil are
used when the ship travels 27 miles at 51 mi/h? Round your answer to the nearest barrel, if necessary.
Describe the combined variation that is modeled by the formula or equation.
7.
Graph the function.
8.
y
10
8
6
4
2
–10 –8
–6
–4
–2
–2
2
4
6
8
10
x
2
4
6
8
10
x
–4
–6
–8
–10
9. 6xy = 14
y
10
8
6
4
2
–10 –8
–6
–4
–2
–2
–4
–6
–8
–10
Find any points of discontinuity for the rational function.
10.
11.
12. Describe the vertical asymptote(s) and hole(s) for the graph of
13. Find the horizontal asymptote of the graph of
.
.
Simplify the rational expression. State any restrictions on the variable.
14.
15.
Multiply or divide. State any restrictions on the variables.
16.
17.
18.
19.
20. Find the least common multiple of
Add or subtract. Simplify if possible.
21.
22.
23.
Simplify the complex fraction.
24.
Solve the equation. Check the solution.
25.
and
.
26.
Algebra 2: Chapter 9 Review Guide
Answer Section
MULTIPLE CHOICE
1. D
SHORT ANSWER
2.
3. direct variation;
4.
or
5.
12
or 2.4
5
;
72
6. 112 barrels
7. y varies directly as w and inversely as the square of x.
8.
y
10
5
–10
–5
5
–5
–10
10 x
9.
y
10
5
–10
–5
5
–5
–10
10.
11.
12.
13.
14.
x = –6, x = 2
x = 9, x = –8
asymptote: x = –4 and hole: x = 1
no horizontal asymptote
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25. –9
37
26. 
60
10 x