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Algebra 2
Worksheet 8.1, 8.2, 8.3, 8.5
Name:___________________________
Write an equation that models each function:
1. Y varies directly as x, and y=30 when x= -6.
2. Y varies inversely as x, and y=5 when x=3.
Determine whether each data set represents a direction variation, an inverse variation, or neither.
3.
4.
X
8
12
16
X
3
1
0.5
Y
2
3
4
Y
5
15
30
Write a direct variation to model the problem and then solve.
5. The number of chaperones, c, needed for the class trip varies directly as the number of students, s, going on the trip, and
c = 7 when s = 56. How many chaperones are needed if 104 students go on the class trip?
Simplify. Identify any x-values for which the expression is undefined.
6.
7.
x  3x  2
x 2  3x  4
2
4x
2x4
Simplify. Assume all expressions are defined.
9.
10.
4 x  16 x 2  2 x  3

2x  6
x4
x  3 x2  2x  1

x  1 x 2  5x  6
8.
x2  x3
2 x 2  5x  3
6
11.
12.
5x 6 10 x 2

x2 y
y
x2  2x  8
2 x 2  8x

x 2  2 x  15 2 x 2  10 x
Find the least common Multiple for each pair.
13.
3x 2 y 6 and
14.
5x 3 y 2
x 2  x  2 and
x2  x  6
Add or subtract. Identify any x-values for which the expression is undefined.
15.
x  12 3x  2

2x  5 2x  5
16.
x4
2x

x  x  12
x4
2
17.
x6
2x

x  7 x  18 x  9
2
Solve each equation.
18.
x
6
5
x
21.
19.
15 6
 3
4
x
20.
22.
4
1

x 4
x2
2
5x
x  24

x6
x6
2x  5
x
11
 
x 8
2
x 8
Answers for Worksheet 8.1, 8.2, 8.3, 8.5
1. y=kx
2. y  kx
y= -5x
y  15
x
3. Direct k  1
4. Inverse k = 15
5. c  1 s
6. x  4; 1
x2
x 4
8. x 1; 3
 x2
2x  3
4
8
c 13
7. x  0 2 x2
9. 2(x-1)
2
10. x 1
x2
13. 15x3 y6


x  4   x  3
18. x = 6; -1
21. No Solution
19. x = 8
x 3
2
14. (x-3)(x-1)(x+2)
2 x4
16. x  4;  3 2 x  7


12. x  2
2
11. x
15. x  5 ;
17. x  9;  2
20. x = -4
22. No Solution
2
2x 14
2x  5
2 x 2  5x  6
 x  9 x  2





