Name: ________________________ Period: ___________________ Date: __________
PreCalc 11 Chapter 7 Rev Pack v1
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Identify the non-permissible value of the variable for this rational expression:
z2  4
z2  4
A. z  2
C. z  4
B. z  2
D. all values are permissible
____
2. Determine the non-permissible values for this rational expression:
9x  3
6x 2  10x  4
1
A. x   and x  2
C. x  2
3
1
B. x  and x  2
D. x  2
3
____
3. Simplify this rational expression and state the non-permissible values of the variable.
n 2  25
2
n  9n  20
n5
n5
A.
; n  5 and n  4
C.
; n  5 and n  4
n4
n4
n5
n5
B.
; n  5 and n  4
D.
; n  5 and n  4
n4
n4
____
4. Determine the non-permissible values for this rational expression:
6m
18m2  6m
1
1
A. m  6 and m  18
C. m   and m  
6
18
1
1
B. m  0 and m  
D. m  0 and m 
3
3
8
ID: A
Name: ________________________
____
____
5. Simplify this expression:
5b 6 7b 3

6
4
35b 3
,b  0
A.
24
10b 3
,b  0
B.
21
B.
____
C.
D.
10b 9
,b  0
21
35b 9
,b  0
24
6. Simplify this expression:
5(n  8)
7

7
9(n  8)
A.
____
ID: A
5
, n  8
9
5(n  8) 2
9
7. Simplify.
6 8

p 3
14
,p  0
A.
3p
8p  18
, p  3
B.
p3
8.
Simplify.
8
7

7x 3x
1
,x  0
A.
4x
25
,x  0
B.
21x
C.
5(n  8)
, n  8
9(n  8)
D.
5
9
C.
D.
C.
D.
2
14
, p  3
p3
8p  18
,p  0
3p
1
,x  0
21x
1
,x  0
4
Name: ________________________
____
ID: A
9. Simplify.
5x  2 x  5
 2
3x
x
A.
B.
4x  3
,x  0
3x 2
4x  7
, x  0, x  3
3x  x 2
____ 10. Simplify.
1 3x 2  1

 5x
x
4x
17x 2  5
A.
,x 0
4x
3x 2  5x  2
B.
,x 0
3x
C.
D.
C.
D.
5(x 2  x  3)
,x  0
3x 2
5(x 2  x  3)
, x  0, x  3
3x  x 2
17x 2  5
,x 0
4x 2
3x 2  5x  2
,x 0
4x
____ 11. Simplify.
3  2y 3  y

6y 2
2y 3
A.
B.
3y
,y  0
6y 3
y 2  9y  9
,y  0
6y 3
____ 12. Simplify.
3z
6z

z3 z3
3
, z  3
A.
z3
3z
, z  3
B.
z3
C.
D.
C.
y 2  3y  3
,y  0
2y 3
y
,y  0
6y 3
3z
, z0
z3
D. none of the above
3
Name: ________________________
____ 13. Simplify.
6
5

x  4 (x  4) 2
6x  19
, x  4
A.
x4
B.
1
, x  4
x4
ID: A
C.
D.
1
, x  4
(x  4) 2
6x  19
, x  4
(x  4) 2
____ 14. Simplify.
m2 m1

m6 m4
m1
, m  6, m  4, m  10
A.
m  10
m1
, m  6, m  4
B.
(m  6)(m  4)
C.
D.
2m2  11m  2
, m  6, m  4
(m  6)(m  4)
2m2  11m  2
, m  6, m  4, m  10
m  10
____ 15. Solve.
2x  7 1

x2
7
A. x  7
B. x  14
C. x  7 or x  7
D. no solution
____ 16. Solve.
m
1

m2  6m  8 m2  4
A. a  4 or a  2
B. a  4 or a  1
C. a  4 or a  1
D. a  4 or a  2
____ 17. Solve.
4
n3

n3
n
A. n  1 or n  9
B. n  1 or n  9
C. n  1 or n  9
D. no solution
4
Name: ________________________
____ 18. Solve.
2
2w  10
w
 2

w  8 w  5w  24 w  3
A. w  4
B. w  4 or w  4
ID: A
C. w  8
D. w  4
____ 19. A baking company claims that their cookies contain “40 % chocolate chips by mass”. To uphold their claim,
what mass of chocolate chips should they add to 18 kg of cookie dough? Give the answer to the nearest tenth
where necessary.
A. 10.8 kg
B. 18 kg
C. 12 kg
D. 25.2 kg
.
____ 20. What volume of undiluted hydrogen peroxide should be added to 6500 mL of water to make a 25 % hydrogen
peroxide solution? Give the answer to the nearest millilitre.
A. 2167 mL
B. 65 mL
C. 1300 mL
D. 1625 mL
.
____ 21. Dayna plants a tomato seed and a sunflower seed for a science project. She finds that on average her
sunflower plant grows three times as fast as her tomato plant. It takes the tomato 16 days longer to reach a
height of 15 cm. What is the growth rate, in centimetres per day, of the tomato seedling? Give the answer to
the nearest hundredth where necessary.
A. 0.94 cm/day
B. 0.63 cm/day
C. 2.81 cm/day
D. 6.25 cm/day
.
____ 22. Devon travels 120 km to Edmonton by car, and then returns by bus. The average speed of the car is 20 km/h
greater than the average speed of the bus. If Devon’s total travel time is 162 min, what is the average speed of
the bus?
A. 109 km/h
B. 80 km/h
C. 69 km/h
D. 89 km/h
5
Name: ________________________
ID: A
Short Answer
23. Simplify this rational expression. State the non-permissible values of the variable.
10x 2  25x  15
90  40x 2
24. Write this rational expression in simplest form. State the non-permissible values of x.
x 4  625y 4
5x 2  21xy  20y 2
25. Simplify this expression:
m2 p 5 10mp 3

4mp 3
3m5 p
26. Simplify this expression:
a  2b a 2  4b 2

a  5b a 2  25b 2
27. Simplify this expression:
12m2  2m  2 20m2  25m  5

5m2  2m  3 20m2  10m  10
28. Simplify this expression:
9x 2  4xy  5y 2 3y  4x 3y  4x
 2

x  y 2 6y  6x
81x 2  25y 2
29. Simplify.
4
5
 5 2
2
5
3x y
4x y
6
Name: ________________________
ID: A
30. Simplify.
a  1 a2  1

3ab 3
5a 3
31. Simplify.
5
5
d2 

2d m
32. Solve.
4
5
4


3y 4y 3
33. A liquid fertilizer requires dilution before use. How much liquid fertilizer must be added to 540 mL of water
to make a 40% fertilizer solution?
.
34. Diluted acetic acid can be used as an environmentally friendly cleaning solution. What volume of acetic acid,
in litres, should be added to 360 mL of water to make a 4% acetic acid solution?
.
Problem
35. Write this rational expression in simplest form. State the non-permissible values of the variable. Show your
work.
x 4  34x 2  225
4x 4  8x 3  60x 2
7
Name: ________________________
ID: A
36. Simplify this expression and state the non-permissible values. Show your work.
9
1 2
m
3
1
m
37. Write two equivalent forms of this rational expression. Describe your strategy.
3(x  5)(x  9)
, x  0, x  9, x  1
2x(x  9)(x  1)
38. Determine the sum of the first five terms of this series:
1
2
3
4
5
 4  6  8  10  . . .
2
2b
3b
4b
5b
6b
Describe your strategy.
.
x 2  7x  10
as the sum or difference of two rational expressions with different denominators. Show
2x 2  50
your work.
39. Write
.
40. A natural number, N, is 4 less than another natural number, M. The sum of the reciprocals of M and N is 5
times the reciprocal of twice the value of M. What are the two numbers? Describe your strategy.
.
41. A cyclist rode from town A to town B and back, a distance of about 4 km each way. On the trip out, there was
a 6-km/h tailwind. On the return trip, there was a 7-km/h headwind. The total riding time was 3 h. To the
nearest tenth of a kilometre per hour, what is the cyclist’s average speed when there is no wind? Explain your
solution.
8