ALGEBRA 1 UNIT 8 RATIONAL EXPRESSION AND EQUATIONS
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PRACTICE QUIZ 1B
NO TI-nSPIRE allowed. Scientific calculator only.
Round to 2 decimal places where appropriate.
Useful formulas: y = kx, xy = k
1. Determine whether each equation or table represents an inverse or a direct variation or neither. Circle your
answer and give a reason for your answer.
A)
B)
C)
D)
u
x
56
DIRECT
y  2 x  1
y
1.2
x
x
2
3
4
5
DIRECT
DIRECT
y
6
4
3
2.4
DIRECT
INVERSE
INVERSE
INVERSE
INVERSE
NEITHER
NEITHER
NEITHER
NEITHER
E)
2. State the excluded values for the following.
A)
y
x2
x
x 2  81
y 2
2 x  17 x  9
C)
B)
D)
EXPLAIN:
EXPLAIN:
EXPLAIN:
EXPLAIN:
m
x2
x 2  5 x  14
y
1
x  64
4
3. Simplify the following expressions.
2r  4
A) r  2
x4
2
C) 3 x  12 x
45
B) 10a  10
v 5
v  10v  25
2
D)
v 2  7v  30
v 2  5v  24
v 5
v  10v  25
2
v 2  7v  30
v 2  5v  24
E)
b 2  3b  28
b 2  49
F)
x 3  x 2  42 x
2
G) 2 x  20 x  42
3r 2  39 r  90
2
H) r  3r  70
4. Given: y varies inversely as x and y= 24 when x = -4.
A) Complete the following table identifying six other ordered pairs that are part of this situation.
B) Graph your equation from part A on the grid.
x
y
5. Given the function
y
1
x2
A) Identify the asymptotes:__________________________
B) Identify the domain:_______________________________
C) Identify the range:_________________________________
D) Fill in the table and graph the function.
x
-2
y
6. y is inversely proportional to x. When y = 2, x = 3.Work out the value of y when x = 18.
7. F is inversely proportional to the square of r. When F=50,r=3. Calculate the value of F when r = 12 to 2
decimal places.
8. The amount of money earned by Sasha, M, is directly proportional to the number of hours she works, h. After
working for 9.5 hours she earns £155.80.
a) Express M in terms of h.
b) Using the equation formed in part a), or otherwise, find out how many hours it would take for her to earn
£688.80.
9.
b is directly proportional to w3 . If b = 10240 when w = 8, find an equation relating b and w.
10. The weight of a piece of wire is directly proportional to its length. A piece of wire is 25 cm long and has a
weight of 6 grams. Another piece of the same wire is 30 cm long. Calculate the weight of the 30 cm piece of wire.
11. A ball falls vertically after being dropped. The ball falls a distance d metres in a time of t seconds. d is directly
proportional to the square of t. The ball falls 20 metres in a time of 2 seconds.
A) Find a formula for d in terms of t.
B) Calculate the distance the ball falls in 3 seconds.
C) Calculate the time the ball takes to fall 605 m.
12. Given that y is inversely proportional to x, complete the following table.
x
y
4
7.5
60
12
13. Write a rational expression with excluded values -2 and 8. Explain how you find the expression.
1
14. Explain why there is no excluded value for the rational expression: x  4 .
2
15. Write a rational expression with no excluded value.
16. The function
given information.
y
a
x  b has an excluded value of 5. and when x = 7, y =-4. find the value of a and b with the