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Practice Test
Question 1
• Expand and simplify
x  5 x  5
2
Question 1
• Expand and simplify
x  5  x  5 
2
Using difference of 2 squares
x  5 x  25 
2
x  5x  25x  125
3
2
Question 2
• Write as the log of a single expression
2 log a  log12  log 2a
Question 2
• Write as the log of a single expression
2 log a  log12  log 2a
 a 2  12 
 log 

log
6a



 2a 
Question 3
• Simplify
3
2
15x y 5xy

2
14wz
7wz
Question 3
• Simplify
3
2
15x y 7wz 3x


2
2
14wz
5xy
2zy
Question 4a
• Solve the following equations
2x  11x
2
3
2
Question 4a
• Solve the following equations
2x  11x
2
3
2x 2  11x  6
2
2x 2  11x  6  0
x  0.5, 6
Question 4b
• Solve the following equations
5 2x  7  4 6  x 

3
9
Question 4b
• Solve the following equations
5 2x  7  4 6  x 

3
9
15 2x  7   4 6  x 
30x  105  24  4 x
34 x  129
129
x
34
Question 5
• For his birthday, Catherine bought Doug
7 white and 14 red roses for a total of
$66.50.
• She noted that one red rose cost 40%
more than one white rose.
• By forming at least one equation,
determine the cost of one white rose.
Question 5
• For his birthday, Catherine bought Doug
7 white and 14 red roses for a total of
$66.50. 7w  14r  66.50
• She noted that one red rose cost 40%
more than one white rose. r  1.4w
• By forming at least one equation,
determine the cost of one white rose.
7w  14 1.4w   66.50
Question 5
26.6w  66.50
w  $2.50
Question 6
• The difference between two positive
numbers is 27.
• The sum of their squares is 13977.
• Find the two numbers
Question 6
• The difference between two positive
numbers is 27. x  y  27
• The sum of their squares is 13977.
x 2  y2  13977
• Find the two numbers
x  27  y
y 2  27  y   13977
2
65, 96 - cannot have a
negative number
2y 2  54 y  729  13977  0
2y 2  54 y  13248  0
y  65,  96
Question 7
• The height, h m, of a helium filled
balloon after it is released is given by
h  0.38t 2  17.7t  1
• Where t is the time since the balloon
was released in seconds.
• Calculate how long it takes the balloon
to first reach a height of 100 m.
Question 7
• Calculate how long it takes the balloon
to first reach a height of 100 m.
h  0.38t 2  17.7t  1  100
0.38t 2  17.7t  99  0
t  6.5 sec s
Question 8
• The height, h m, of a flying fox wire above the
ground x metres horizontally from the release
point is given by
0.05 x
h  8e
• The flying fox finishes when it is 2 metres
above the ground.
• Calculate how far horizontally the flying fox
runs.
Question 8
• The flying fox finishes when it is 2 metres
above the ground.
• Calculate how far horizontally the flying fox
runs.
0.05 x
h  8e
2
1
e

4
0.05 x  ln 0.25
x  27.7m
0.05 x
Question 9
• For what values of p does the line
y px
• Not intersect with the hyperbola
xy  8
Question 9
y  p  2x
xy  8
x  p  2x   8
2x  xp  8  0
2
2x  xp  8  0
2
Question 9
For no intersection
b  4ac  0
2
p 4280
2
-8
8
p  64  0
2
 p  8  p  8   0
8  x  8