Intermediate Mathematics
Provincial Assessment 2006
This Student Work Booklet contains the remaining questions for the
Intermediate Mathematics Provincial Assessment 2006.
You will need a pencil, paper, and a ruler for these questions and you
are also permitted the use of a four-function calculator (or a scientific
calculator). No question requires the use of a calculator but you may
use one if you choose. No graphing calculator is permitted.
Section 2: Calculators Permitted
Section 2 contains 40 multiple-choice questions (items 11-50) all
having A,B,C,D choices. You are to shade the appropriate bubble
(having the same number as the question) on the bubble sheet using
a lead pencil only.
Do not shade more than one bubble or the question is scored as
incorrect. Erase carefully with a good quality soft eraser if you need to
change an answer.
Since the first question in this section is item 11, start with bubble 11.
The last bubble you should shade in this assessment is 50 since the
last multiple choice question you answer is item 50.
Please begin Section 2 now.
Page 2 of 14
11.
(A)
(B)
(C)
(D)
12.
2 90
18.97
6 10
12 5
Which number line represents the inequality { x | −2 ≤ x < 1, x ∈ R} ?
(A)
(B)
(C)
(D)
13.
360 in simplest radical form?
Which represents
-3 -2
-1
0
1
2
3
-3 -2
-1
0
1
2
3
-3 -2
-1
0
1
2
3
-3 -2
-1
0
1
2
3
To which subset of the Real Numbers does − 34 belong?
(A)
(B)
Real
(R)
Q
Q
(C)
W
(D)
I
Irrational
(Q)
Rational
(Q)
Integers (I)
Whole (W)
Natural (N)
Page 3 of 14
14.
Squares with areas 36m2 and 64m2 are shown inside a larger
square. What is the length of line segment XY in metres?
X
(A)
10
Y
15.
(B)
14
(C)
18.4
(D)
19.8
64m
2
2
36m
Which matrix represents the amount of stock on hand after the new
stock was bought at the end of the week?
Stock on Hand
at Start of Week
Red Grey
Mitts ⎡15 12 ⎤
Socks
⎢8
⎣
17 ⎥⎦
(A)
⎡11 9 ⎤
⎢12 23 ⎥
⎣
⎦
(B)
⎡19 15 ⎤
⎢ 4 11⎥
⎣
⎦
(C)
⎡3 7 ⎤
⎢ 1 14 ⎥
⎣
⎦
(D)
⎡35 19 ⎤
⎢26 29 ⎥
⎣
⎦
Sales Made
During Week
⎡12 5 ⎤
⎢ 7 3⎥
⎣
⎦
New Stock Bought at
Week’s End
⎡ 8 2⎤
⎢11 9 ⎥
⎣
⎦
Page 4 of 14
16.
There are about 3.8 L of paint in a gallon. About how many litres are
in 2 21 gallons?
(A)
(B)
(C)
(D)
17.
Small sugar cubes have a mass of 41 g. If there are 3 21 g of sugar in a
container, how many sugar cubes must be added to increase the
mass of the container to 5 41 g?
(A)
(B)
(C)
(D)
18.
1 34
7
8 34
9
Calculate:
(A)
(B)
(C)
(D)
19.
1.3
1.5
6.3
9.5
(7 ) × (7 ) .
3
2
72
79
710
713
2 32
Calculate: −2 × 4 .
2
3
(A)
(B)
(C)
(D)
8
9
1
72
729
2
4
Page 5 of 14
20.
Which tile diagram correctly models the product: ( x − 3)( x + 2) ?
(Note that grey tiles are positive and white are negative.)
(A)
(B)
(C)
(D)
21.
Expand completely: 8 x 2 y (2 x 2 − y ) .
(A)
(B)
(C)
(D)
16 x 2 y − 8 x 2 y 2
16 x 4 − 8 y 2
16 x 4 y − 8 x 2 y
16 x 4 y − 8 x 2 y 2
Page 6 of 14
Which is the product of ( x + 3) and (3 x − 2) ?
(A)
(B)
(C)
(D)
23.
Evaluate 2 x 2 + 3 x − 4 y for x = 2 and y = −3 .
(A)
(B)
(C)
(D)
24.
2
10
26
34
A rectangular rug with dimensions 2 x by (x + 1) is placed in a
rectangular room with dimensions (4 x + 3) by (3 x + 4) . What area of
the floor is left uncovered?
(A)
(B)
(C)
(D)
25.
3x 2 − 6
4x 2 − 6
3x 2 + 7x − 6
4x 2 + 7x − 6
2x
10 x 2 + 23 x + 12
10 x 2 + 25 x + 11
14 x 2 + 25 x + 13
14 x 2 + 27 x + 12
(x+1)
RUG
(3x+4)
(4x+3)
The graph below shows the distance traveled by a vehicle over time.
For which portion of the journey was the vehicle traveling fastest?
(A)
(B)
(C)
(D)
A to B
B to C
C to D
D to E
D
Distance
22.
C
B
A
Time
E
Page 7 of 14
26.
Which type of relationship is represented by the table shown?
(A)
(B)
(C)
(D)
27.
x 0 1 2 3 4
y 1 3 9 27 81
arithmetic
exponential
linear
parabolic
This graph represents profit per unit sold. What is the profit, in dollars,
for sales of 500 units?
(A)
200
(B)
250
(C)
750
(D)
1000
Profit in Dollars
2000
1750
1500
1250
1000
750
500
250
200
28.
400
600
800
1000 Units Sold
The points ( 0, 0 ) , ( 3, 1) , and ( 6, 2 ) , when graphed, lie on a line. What
is the equation of the line containing these points?
y
8
7
6
(A)
y=
− 31
x +1
5
4
3
(B)
y = − 31 x
(C)
y= x
1
3
2
1
– 8– 7– 6– 5– 4– 3– 2– 1
– 1
– 2
– 3
– 4
(D)
y = x +1
1
3
– 5
– 6
– 7
– 8
1
2
3
4
5
6
7
8
x
Page 8 of 14
29.
The table shows how the total number of diagonals a polygon has is
related to the number of sides it has. If a polygon has 20 diagonals,
how many sides would there be?
sides
diagonals
3
0
4
2
(A) 8
5
5
(B) 9
(C) 10
6
9
(D) 11
30.
To print rolls of tickets, a company charges $25 as a set-up fee, and
charges an additional $5 per roll of tickets. How many rolls of tickets
can be printed for $200?
(A)
(B)
(C)
(D)
31.
Solve for x: 2(3 x − 7) − 2 x = −5 x + 4 .
(A)
(B)
(C)
(D)
32.
35
40
125
500
1
2
11
9
2
10
In ∆ABC , AB = x , BC is three more than AB, and AC is twice BC. If
the perimeter of ∆ABC is 93 cm, what is the length of AB in cm?
(A)
(B)
(C)
(D)
21
21.75
22.5
28
Page 9 of 14
33.
A cone and a cylinder have the same height and the same base
radius. If volume of the cylinder is 81 cm3, what is the volume of the
cone in cm3?
(A)
(B)
(C)
(D)
34.
An official basketball has a radius of 12.5 cm and usually has a
leather covering. Approximately how much leather, in cm2, is required
to cover 12 official basketballs?
(A)
(B)
(C)
(D)
35
9
27
78
243
164
682
23 562
98 175
A carnival clown has 75 m3 of helium compressed in a
tank. How many spherical balloons with a radius of
0.25 m can be filled with the tank?
(A)
(B)
(C)
(D)
286
1145
1527
4583
0.
m
25
Page 10 of 14
36.
The triangles shown are congruent by which condition?
B
(A)
(B)
(C)
(D)
SAS
ASA
AAS
SSA
C
F
7
5
5
30°
E
A
37.
7
Given ∆ABE ∼ ∆DCE as shown, which statement is true?
A
(A)
38.
30°
D
B
AB DC
=
BE DE
(B)
AB CE
=
BE DC
(C)
BE AB
=
DC CE
(D)
AB BE
=
DC CE
E
D
C
Given the diagram as shown, which statement is true?
J
(A)
(B)
(C)
(D)
CT ≅ UT
RT ≅ UT
∠C ≅ ∠J
∠R ≅ ∠U
C
T
U
R
Page 11 of 14
39.
Given the diagram as shown, determine the length of AB .
A
(A)
(B)
(C)
(D)
3.25
10.5
13
20
F
10
6.5
C
40.
D
B
8
E
4
Chris sights a rock across a river and walks along one of the river
banks making the measurements shown in the diagram. How many
metres wide is the river?
4m
(A)
(B)
(C)
(D)
1
2.25
16
30
1.5 m
6m
R i v e r
Rock
41.
For which transformation must orientation be reversed?
(A)
(B)
(C)
(D)
42.
dilatation
reflection
rotation
translation
Triangle ABC with vertices A ( 4, 2 ) , B (1, 3 ) , and C ( 3, 1) is reflected
in the y-axis. Which mapping describes the transformation?
y
(A)
(B)
(C)
(D)
( x, y ) → ( − y , x )
( x, y ) → ( − x, y )
( x, y ) → ( x, − y )
( x, y ) → ( y , − x )
4
3 B (1,3)
2
A (4,2)
1
– 4 – 3 – 2 – 1
– 1
– 2
– 3
– 4
C (3,1)
1
2
3
4
x
Page 12 of 14
43.
The point ( −2, 3 ) undergoes a reflection in the x-axis followed by a
180° CCW rotation about the origin. What will be the final coordinates
y
of the point? (A grid is provided for your assistance.)
(A)
(B)
(C)
(D)
44.
( −2, − 3 )
( 2, − 3 )
( 2, 3 )
( 3, 2 )
x
Which rule maps ABCD to A'B'C'D' ?
(A)
(B)
(C)
(D)
( x, y ) → ( x + 2, y + 4 )
( x, y ) → ( 2x, y + 4 )
( x, y ) → ( 2x, 2y + 8 )
( x, y ) → ( 2 x + 8, 2y )
D'(0, 16)
A'(-4, 8)
C'(4, 8)
D(0, 4)
A(-2, 0)
B'(0, 0)
C(2, 0)
B(0, -4)
45.
The table shows the heights of several seedlings after various
growing times. Which graph should be used to determine whether
there is a relationship between time and seedling height?
Time(days )
1
3
2
3
3
2
1 2
Height (mm ) 6 13 11 14 15 10 4 7
(A)
(B)
(C)
(D)
box and whisker plot
circle graph
histogram
scatterplot
Page 13 of 14
46.
On which plot does the line/curve drawn best fit the data?
(A)
(B)
(C)
(D)
47
Which scatterplot shows the strongest negative correlation?
A
(A)
(B)
(C)
(D)
B
A
B
C
D
C
D
Page 14 of 14
48.
Which equation best represents the line of best fit that would apply to
y
this scatterplot?
7
(A)
y=
(B)
(C)
(D)
y=
+1
y = x +1
y = 2x + 1
1
4x
1
2x
+1
6
5
4
3
2
1
1
49.
3
4
5
6
7 x
In which situation is the second event dependent on the first event?
(A)
(B)
(C)
(D)
50.
2
driving to school with Mom; then winning the lottery
head on last coin toss; head on next coin toss
6 on last roll of a die; 6 on next roll of a die
waking at 10am; then being late for school
A bag contains 2 green, 1 yellow, and 4 red jelly beans. What is the
probability of picking two red jelly beans in a row from the bag if the
first is not replaced before the second is picked?
(A)
(B)
(C)
(D)
12
42
16
42
12
49
16
49
End of the Assessment