Name: 
 

Math 11 Foundations LG 18 Unit 4 Practice Test #5


Multiple Choice
Identify the choice that best completes the statement or answers the question.
 

 1. 
What are the x- and y-intercepts for the function f(x) = x2 + 5x + 6?
a.
x = –4, x = –2, y = 6
b.
no x-intercepts, y = 6
c.
x = –2.5, y = 6
d.
x = –3, x = –2, y = 6
 

 2. 
Rewrite x2 + x = –x + 3 in standard form. Then solve the equation in standard form by graphing.
a.
x = –3, x = 1
b.
x = 3, x = 1
c.
x = –3, x = –3
d.
x = 3, x = –1
 

 3. 
Which relation is the factored form of f(x) = x2 – 4x + 4?
a.
f(x) = (x – 2)(x + 2)
b.
f(x) = 4(x – 1)2
c.
f(x) = (x + 4)(x – 1)
d.
f(x) = (x – 2)2
 

 4. 
Solve 2x2 = 7x – 6 by factoring.
a.
x = 2, x = 3
b.
x = –2, x = –mc004-1.jpg
c.
x = 2, x = mc004-2.jpg
d.
x = 6, x = –1
 

 5. 
Solve 12w2 + 8w = –7w2 – 3w + 14 by factoring.
a.
w = mc005-1.jpg, w = –mc005-2.jpg
b.
w = mc005-3.jpg, w = mc005-4.jpg
c.
w = –mc005-5.jpg, w = mc005-6.jpg
d.
w = –mc005-7.jpg, w = –mc005-8.jpg
 

 6. 
How many zeros does f(x) = a(x – 2)2 + 5 have if a > 0?
a.
2
b.
0
c.
1
d.
It is impossible to determine.
 

 7. 
Solve –3x2 + 4x + 1 = 0 using the quadratic formula.
a.
x = 1, x = –mc007-1.jpg
b.
x = 1, x = mc007-2.jpg
c.
x = –1, x = mc007-3.jpg
d.
x = –1, x = –mc007-4.jpg
 

 8. 
Ben dives off a 7 m platform. He reaches a maximum height of 7.3 m after 0.27 s. How long does it take him to reach the water?
a.
1.55 s
b.
1.45 s
c.
1.60 s
d.
1.40 s
 

 9. 
The graph shows how a cyclist travels over time.
Over which interval is the cyclist travelling the fastest?

mc009-1.jpg
a.
AB
b.
BC
c.
EF
d.
FG
 

 10. 
The graph shows how a cyclist travels over time.
Over which interval is the cyclist travelling at 0 km/h?

mc010-1.jpg
a.
AB
b.
BC
c.
DE
d.
FG
 

 11. 
Which scale factor(s) will produce an image that is larger than the original?

I. 0.86
II. 116%
III. mc011-1.jpg
a.
I only
b.
I and II only
c.
II and III only
d.
I, II, and III
 

 12. 
Stop signs have a standard width of 60 cm. Measure the scale diagram
of the stop sign to determine which scale factor was used to draw it.

mc012-1.jpg
a.
mc012-2.jpg
b.
8.3%
c.
mc012-3.jpg
d.
7.5%
 

 13. 
A photograph is 6 cm by 11 cm. A copy is made using a scale factor of 140%. What are the dimensions of the copy?
a.
4.3 cm by 7.9 cm
b.
8.4 cm by 15.4 cm
c.
24 cm by 44 cm
d.
43 mm by 79 cm
 

 14. 
The distance between two towns on a map is 5.4 cm. The map was made using a scale of 1 cm to 300 km. What is the actual distance between the two towns?
a.
1600 km
b.
1550 km
c.
1620 km
d.
1520 km
 

 15. 
Data for triangle ABC is shown on the first line of the table.
Triangle ABC is reduced so the height is 1.5 cm.
Which triangle is the reduction of triangle ABC?

Triangle Name
Length of Base (cm)
Height of Triangle (cm)
Scale Factor
Area (cm2)
mc015-1.jpg
ABC
5.0
3.0
1.0
7.5
1.00
DEF
10.0
1.5
2.0
2.5
4.00
GHI
1.5
1.5
0.5
3.0
0.25
JKL
2.5
1.5
0.5
1.875
0.25
MNO
2.5
1.5
0.25
1.75
0.50
a.
DEF
b.
GHI
c.
JKL
d.
MNO
 

 16. 
Data for circle O is shown on the first line of the table.
Circle O is reduced by a scale factor of 0.2.
Which circle is the reduction of circle O?

Circle Name
Radius (cm)
Scale Factor
Area (cm2)
mc016-1.jpg
O
24.0
1  
1809.56   
1    
P
  3.6
0.2
82.73
0.03
Q
  2.3
0.2
62.38
0.04
R
  4.8
0.2
72.38
0.04
S
  2.3
0.2
82.73
0.03
a.
P
b.
Q
c.
R
d.
S
 

 17. 
Data for rectangle ABCD is shown on the first line of the table.
Rectangle ABCD is reduced to an area of 13 cm2.
Which rectangle is the reduction of rectangle ABCD?

Rectangle Name
Length (cm)
Width (cm)
Scale Factor
Area (cm2)
mc017-1.jpg
ABCD
9
13 
1
117 
1
EFGH
3
4
mc017-2.jpg
13
mc017-3.jpg
JKLM
4
    mc017-4.jpg
mc017-5.jpg
13
mc017-6.jpg
NOPQ
1
    mc017-7.jpg
mc017-8.jpg
13
mc017-9.jpg
RSTU
3
    mc017-10.jpg
mc017-11.jpg
13
mc017-12.jpg
a.
EFGH
b.
JKLM
c.
NOPQ
d.
RSTU
 

 18. 
Which one of the following cylinders is similar to a cylinder that is 8 cm long and 2.5 cm in diameter? Choose the best answer.
a.
a cylinder 4 cm long and 1.5 cm in diameter
b.
a cylinder 12 cm long and 3.5 cm in diameter
c.
a cylinder 16 cm long and 5 cm in diameter
d.
all of the above
 

 19. 
A 1:25 scale model of a garbage truck is 0.5 ft tall, 0.32 ft wide, and 1.4 ft long. What are the dimensions of the actual garbage truck?
a.
25 ft by 12.5 ft by 50 ft
b.
9 ft by 6.4 ft by 25 ft
c.
15 ft by 7.4 ft by 33.5 ft
d.
12.5 ft by 8 ft by 35 ft
 

 20. 
Cylinder A has a radius of 5 mm and a height of 30 mm.
Cylinder B has a radius of 20 mm and a height of 120 mm.
These two cylinders are similar.
By what factor is the volume of cylinder B greater than the volume of cylinder A?
a.
64
b.
8
c.
16
d.
32
 

Short Answer
 

 21. 
Fill in the table for the relation y = –x2 – 3x.
Maximum or minimum 
Axis of symmetry 
Vertex 
 

 22. 
Solve x2 + 6x + 4 = 0 using the quadratic formula. Verify by graphing.
 

 23. 
Anna reduces this figure by a scale factor of sa023-1.jpg.
Determine the area of the reduced figure, to the nearest tenth of a square unit.

sa023-2.jpg
 

 24. 
Jamia reduces this figure by a scale factor of sa024-1.jpg.
Determine the area of the figure, to the nearest tenth of a square unit.

sa024-2.jpg
 

 25. 
The giant statue of a white fox in White Fox, SK, is 2.7 m long and 1.4 m tall.
Suppose the town council wants to create scale models of the statue that are 15 cm long to sell to tourists.
What scale factor should they use?
 

Problem
 

 26. 
a) Solve 3x2 + 5x – 2 = 0 using the quadratic formula.
b) Solve the equation by factoring.
 

 27. 
A company manufactures aluminum cans. One customer places an order for cans that must be 19 cm high, with a volume of 3358 cm3.
a) Use a method of your choice to determine the radius that the company should use to manufacture these cans.
b) Explain why you choose this method.
 

 28. 
The following table shows the attendance for the Calgary Stampede over several years.
a) If you were to graph this data, would you use exact or rounded figures? Explain.
b) What scale would you use?
c) Draw a graph of the data.

Year
Attendance
2004
1 221 182
2005
1 242 928
2006
1 262 518
2007
1 251 105
2008
1 236 351
2009
1 186 636
2010
1 145 394
 

 29. 
A window in a clothing store is 6.00 ft high and 15.00 ft long. Lee has been asked to paint a mural on the window. The mural must be pr029-1.jpg the area of the window and the mural and window must be similar. The mural must also be centred on the window. Draw a scale diagram that shows the dimensions of the window, the dimensions of the mural, and where the mural should be placed.
 

 30. 
Yield signs on city, town, and rural roads are equilateral triangles pointing downward. Describe how you would create a similar yield sign that is one-ninth the area of a typical yield sign to use as a collectable novelty.
 



 
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