PART I
Total Value: 50%
Answer all items. Shade the letter of the correct answer on the computer scorable answer
sheet.
1.
What is the common difference between successive terms generated by the sequence
tn = 23 n + 4 ?
(A)
(B)
(C)
(D)
2.
3.
4.
−4
2
3
3
2
4
Which represents a quadratic relationship?
(A)
x
y
0
–3
1
1
2
5
3
9
4
13
(B)
x
y
0
0
1
4
2
16
3
64
4
256
(C)
x
y
0
3
1
4
2
7
3
12
4
19
(D)
x
y
0
–2
1
–1
2
6
3
25
4
62
Which generates the sequence {4,1, −2, −5, −8,...} ?
(A)
tn = −3n + 1
(B)
(C)
tn = −3n + 7
tn = 3n + 1
(D)
tn = 3n + 7
What is the range of the function provided?
y
5
4
3
(A)
(B)
(C)
(D)
5.
{ y y ≤ −2, y ∈ R}
{ y y ≥ −2, y ∈ R}
{ y y ≤ −1, y ∈ R}
{ y y ≥ −1, y ∈ R}
2
1
–7 –6 –5 –4 –3 –2 –1
–1
1
2
3
4
5
6
7
x
–2
–3
–4
–5
–6
–7
–8
–9
– 10
What is the value of the discriminant for f ( x ) = 0 in the graph provided?
y
(A)
(B)
(C)
(D)
x
−9
−3
0
3
Page 1 of 16
Mathematics 3204 August 2009
6.
What is the axis of symmetry for y = 3 x 2 − 12 x + 11 ?
(A)
(B)
(C)
(D)
7.
8.
Which has the smallest vertical stretch factor when compared to y = x 2 ?
(A)
−2( y + 1) = ( x − 3) 2
(B)
− 34 ( y + 1) = ( x − 3) 2
(C)
2
7 ( y + 1)
(D)
3( y + 1) = ( x − 3) 2
(B)
(C)
(D)
(B)
(C)
(D)
12.
and 1 unit right
reflected across the x-axis, vertical stretch factor of 2 , translated 3 units up
and 1 unit left
( x, y ) → ( x − 4, 12 y + 3)
( x, y ) → ( x − 4, 2 y + 3)
( x, y ) → ( x + 4, 12 y − 3)
( x, y ) → ( x + 4, 2 y − 3)
What is the y-intercept of the function − 12 ( y − 1) = ( x + 3) 2 ?
(A)
(B)
(C)
(D)
11.
reflected across the x-axis, vertical stretch factor of −2 , translated 3 units down
and 1 unit right
reflected across the x-axis, vertical stretch factor of − 12 , translated 3 units up
and 1 unit left
reflected across the x-axis, vertical stretch factor of 12 , translated 3 units down
What mapping rule transforms y = x 2 into 2( y − 3) = ( x + 4) 2 ?
(A)
10.
= ( x − 3) 2
Which describes the graph of −2( y + 3) = ( x − 1) 2 when compared to y = x 2 ?
(A)
9.
x = −2
x = −1
x=2
x=4
−20
−17
−11
−5
What is the general form of 2( y + 1) = ( x − 4) 2 ?
(A)
y = −2 x 2 + 16 x − 33
(B)
y = 12 x 2 + 7
(C)
y = 12 x 2 − 4 x + 7
(D)
y = 12 x 2 − 4 x + 15
2
What is the value of k if kx 2 + 5 x − 6 = 0 has a root of −2 ?
(A)
(B)
(C)
(D)
−4
−1
1
4
Mathematics 3204 August 2009
Page 2 of 16
13.
What is the quadratic function for the graph provided?
y
5
4
3
2
1
14.
(A)
−3( y − 3) = ( x + 2)2
(B)
−3( y + 3) = ( x − 2)
(C)
− 13 ( y − 3) = ( x + 2)2
–5
(D)
− 13 ( y + 3) = ( x − 2)2
–8
–7 –6 –5 –4 –3 –2 –1
–1
1
2
3
4
5
6
7
x
–2
2
–3
–4
–6
–7
–9
– 10
Which graph represents a quadratic function with zeros 1 ± 5 ?
(A)
y
x
(B)
y
x
(C)
y
x
(D)
y
x
15.
What are the zeros of the function y = (2 x − 1)( x + 4) ?
(A)
{− 4, 12}
(C)
{− 4, 2}
{4, −2}
(D)
{4, − 12}
(B)
Page 3 of 16
Mathematics 3204 August 2009
16.
17.
Solve: −2 x 2 − 36 = 0 .
(A)
±2 3
(B)
±2i 3
(C)
±3 2
(D)
±3i 2
A rectangular garden, measuring 15 m by 20 m, has a uniform strip removed from the
edge of one length and the edge of one width to make a concrete walkway. If the area of
the remaining garden is 200 m2, which equation represents the relationship between the
width, the length, and the area of the new garden?
(A)
(B)
(C)
(D)
18.
(15 − 2 x)(20 − 2 x) = 200
(15 − x)(20 − x) = 200
(15 + x)(20 + x) = 200
(15 + 2 x)(20 + 2 x) = 200
What rate of change is represented by the graph provided?
y
x
(A)
(B)
(C)
(D)
19.
P
negative average
negative instantaneous
positive average
positive instantaneous
The table below shows the height, in metres, of a tree as it grows over time, in months.
What is the average rate of change, in metres per month, between months 1 and 3?
month
height (h)
(A)
(B)
(C)
(D)
20.
0
0
1
0.22
0.66
0.88
1.32
1.52
Which sequence is geometric?
(B)
1, 1, 3, 9
6 2 2 2
9 , 15 , 21 , 27
2 2 2 2
(C)
(D)
5, 5.5, 6, 6.5
1, 1, 2, 3
(A)
2
21.
−1
What is the value of ( 23 ) − 30  ?


(A)
(B)
(C)
(D)
1
4
5
4
9
4
25
9
Mathematics 3204 August 2009
Page 4 of 16
2
1
3
1.54
4
1.78
22.
What is the simplified form of
(A)
(B)
(C)
(D)
23.
y = 54 (3) 4
(B)
y = 54 (4) 3
(C)
y = 5(3) 4
(D)
y = 5(4) 3
–3
5
4
0
5
3
20
6
80
9
320
x
x
x
Solve: 3 x −3 = 81 .
−9
1
9
1
3
3
What is the range of the function y = 20(1.8) x + 3.4 ?
(A)
(B)
(C)
(D)
{ y y > 3.4, y ∈ R}
{ y y ≥ 3.4, y ∈ R}
{ y y > 23.4, y ∈ R}
{ y y ≥ 23.4, y ∈ R}
Solve: 4 −2 x +1 = 8 .
(A)
− 14
(B)
− 12
(C)
1
8
1
2
(D)
27.
?
x
(A)
(C)
(D)
26.
5x
Which equation represents the data in the table provided?
(A)
(B)
25.
( 32 ) ( 2 )
2−19 x −1
2−19 x
2−5 x −1
2 −5 x
x
y
24.
43 x
What is the value of x if f ( x) = 32 for the function f ( x) = 2−2( x − 4) ?
(A)
− 13
2
(B)
− 92
(C)
3
2
13
2
(D)
Page 5 of 16
Mathematics 3204 August 2009
28.
A big screen TV is purchased for $2000 and depreciates by 2.5 % per year. What is the
value, in dollars, of the TV after 3 years?
(A)
(B)
(C)
(D)
29.
30.
843.75
1853.72
1950.00
1983.19
Which represents a decay curve with a y-intercept of 4?
(A)
y = ( 12 ) − 3
(B)
y = ( 12 ) + 3
(C)
y = ( 2) − 3
(D)
y = ( 2) + 3
x
x
x
x
The domain for an exponential function is { x ∈ R} and the range is { y y > 1, y ∈ R} .
What is the equation of the horizontal asymptote for the graph of this function?
(A)
(B)
(C)
(D)
31.
y = −1
y =1
x = −1
x =1
Which is the graph of y = log 5 x ?
(A)
y
x
(B)
y
x
(C)
y
x
y
(D)
x
Mathematics 3204 August 2009
Page 6 of 16
32.
3
What is the logarithmic form of 814 = 27 ?
(A)
log 3 ( 27 ) = 81
4
33.
(B)
log 27 ( 34 ) = 81
(C)
log 27 ( 81) =
(D)
log 81 ( 27 ) =
3
4
3
4
Which equation describes the graph provided?
y
34.
35.
(A)
y = ( 12 ) − 3
(B)
y = ( 12 ) + 3
(C)
y = 2x − 3
(D)
y = 2x + 3
(A)
log a 29
(B)
log a 30
(C)
log a 75
(D)
2 log a 15
x
What is the exact value of x for (1.3) x = 28 ?
(B)
(C)
(D)
log1.3
log 28
 1.3 

 28 
log 
log 28
log1.3
 28 

 1.3 
log 
What is the value of x for log 2 5 + log 2 x = 3 ?
(A)
(B)
(C)
(D)
37.
x
What is the simplified form of 2 log a 5 + log a 6 − 13 log a 8 ?
(A)
36.
x
1
6
5
8
5
3
2
2
What transformation of ( x − 4)2 + ( y − 3) 2 = 1 produces  12 ( x − 4)  +  15 ( y − 3)  = 1 ?
1,
2
1
5
(A)
horizontal stretch of
(B)
(C)
(D)
horizontal stretch of 2 , vertical stretch of 5
horizontal stretch of 2, vertical stretch of 5
horizontal stretch of 4, vertical stretch of 25
vertical stretch of
Page 7 of 16
Mathematics 3204 August 2009
38.
What is the length of the major axis of the ellipse given by the equation
2
2
 13 ( x − 1)  +  15 ( y − 3)  = 1 ?
(A)
(B)
(C)
(D)
39.
3
5
6
10
Which is the graph of
(A)
1 ( x − 2) 2
9
+ 14 ( y + 1)2 = 1 ?
y
x
(B)
y
x
(C)
y
x
(D)
y
x
Mathematics 3204 August 2009
Page 8 of 16
40.
Which is true if point P is rotated through an angle θ from standard position as shown?
y
41.
42.
(A)
cos θ = − 35
(B)
cos θ =
(C)
sin θ = − 34
(D)
sin θ =
θ
x
3
5
P(3,-4)
4
5
Chords AB and CD are equidistant from the centre of a circle. What is the length of
CD if AB has endpoints A(− 4, 3) and B(2, −5) ?
(A)
2 17
(B)
(C)
(D)
4 17
10
100
The circle with centre O shown, has a radius of 12 cm. What is the area of the shaded
region if ∠AOB = 45° ?
O
(A)
(B)
(C)
(D)
32.99
56.55
395.84
508.94
45°
B
A
43.
What is the radius of the circle given by 16 x 2 + 16 y 2 = 64 ?
(A)
(B)
(C)
(D)
44.
2
4
8
64
Which angle of rotation, in degrees, on the unit circle will map (1, 0 ) to
(A)
(B)
(C)
(D)
45.
12 cm
(
3
1
2 ,− 2
)?
210
240
300
330
In the circle shown, GH is tangent to the circle at E and ∠DEG = 95° . What is the
measure, in degrees, of ∠DEF ?
D
35°
(A)
(B)
(C)
(D)
42.5
50
55
72.5
F
95°
G
Page 9 of 16
E
H
Mathematics 3204 August 2009
46.
In the circle with centre O shown, BA and BC are tangent to the circle and ∠ABC = 48° .
What is the measure, in degrees, of ∠AOC ?
A
(A)
(B)
(C)
(D)
48
96
132
138
O
x
B
48°
C
47.
In the circle with centre O shown, ∠DBE = 80° and ∠FBE = 60° . What is the measure,
in degrees, of ∠BEF ?
A
O
(A)
(B)
(C)
(D)
70
90
110
160
F
E
D
80°° 60°°
B
48.
In the circle with centre O shown, QR = RS = 4 and OP = 8 . What is the exact value of
PR ?
P
Q
49.
(A)
8−4 5
(B)
8−4 3
(C)
4 3
(D)
4 5
S
O
A circle with centre ( 2, −1) has a diameter AB. If one endpoint of the diameter is B ( 6, 3) ,
what are the coordinates of the other endpoint?
(A)
(B)
(C)
(D)
50.
R
( −8,1)
( −2, −5 )
( 4,1)
(10, 7 )
A math student finds a broken piece of a circular CD. Which process could be used to
determine the radius of the CD before it was broken?
(A)
(B)
(C)
(D)
constructing the perpendicular bisector of a chord
constructing the perpendicular bisectors of two chords
drawing a tangent to the circle
drawing two tangents to the circle
Mathematics 3204 August 2009
Page 10 of 16
PART II
Total Value: 50%
Answer ALL items in the space provided. Show ALL workings.
Value
4
4
4
3x
=
.
x x −3
51.
Algebraically determine the exact roots in simplest form for
52.
A flower bed is in the shape of a rectangle and its length is twice its width. The
bed is surrounded by a 4 m wide walkway. If the total area of the bed and
walkway is 504 m2, algebraically determine the width of the flower bed.
4
w
4
Page 11 of 16
Mathematics 3204 August 2009
Value
4
4
53.
54.
The flight path of an owl as it dives from a tree is shown below. The height of the
owl above the ground, in metres, t seconds after it begins its dive is approximated
by h(t ) = 25 − 20t + 5t 2 .
start
a)
What is the height of the owl at the start of the dive? ___________
b)
Algebraically determine the minimum height of the owl.
A signal flare is fired from ground level and reaches a maximum height of 245 m
at a time of 7 s. After travelling for 14 s, the flare hits the ground. Algebraically
determine the quadratic function representing the path of the flare, and use it to
determine the approximate height of the flare at 9 s.
Height
245 m
7s
Mathematics 3204 August 2009
Page 12 of 16
14 s
Time
Value
4
55.
The power, P , in Watts, supplied to a circuit by a 9 volt battery is given by the
formula P = 9 I − 0.5 I 2 , where I is the current in amperes. Calculate the
approximate instantaneous rate of change in the power with a current of 5
amperes.
4
56.
Algebraically solve for x:
4
57.
Algebraically solve for x:
125 x = ( 25 ) ( 5−2 x ) .
log(3 − x) =
Page 13 of 16
1
log 4 − log x .
2
Mathematics 3204 August 2009
Value
4
58.
A father invested $500 for his son, who was born in 1990, in an account that paid
8% every 2 years. Another father bought his son a hockey card in 1990 for $250
that appreciated at a rate of 10% per year. Write a function to model each
situation and use the functions to determine which is worth more in 2008.
4
59.
A medication has a half-life of 7.5 days. If 30 mg of the medication is
administered initially, determine the equation of the function and use it to
calculate how long it will take, to the nearest day, for the amount of medication in
the bloodstream to reduce to 6 mg.
Mathematics 3204 August 2009
Page 14 of 16
Value
3
60.
Write the equation 4 x 2 + 9 y 2 − 8 x + 72 y + 112 = 0 in transformational form.
3
61.
In the circle with centre O shown, the equation of tangent line AB is given by
y = 12 x − 92 . Algebraically determine the equation of line CD if it is tangent to the
circle at ( −1,10 ) .
D
(-1,10)
C
O
B
y = 12 x − 92
A
Page 15 of 16
Mathematics 3204 August 2009
Value
4
62.
Using coordinate geometry, prove that the diagonals of the rhombus QUAD
shown are perpendicular bisectors of one another.
y
D(-2,5)
A(3,5)
U(6,1)
Q(1,1)
4
63.
x
Square ABDC is inscribed in the circle with centre O shown. Calculate the total
area of the shaded regions if the diameter of the circle is 10.
A
B
O
C
D
Mathematics 3204 August 2009
Page 16 of 16