Name: 
 

Math 10F LG 20 Practice Final #9


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

 1. 
Calculate mc001-1.jpg.
a.
mc001-2.jpg
c.
mc001-4.jpg
b.
mc001-3.jpg
d.
mc001-5.jpg
 

 2. 
What is the value of mc002-1.jpg?
a.
mc002-2.jpg
c.
mc002-4.jpg
b.
mc002-3.jpg
d.
mc002-5.jpg
 

 3. 
Which expression cannot be evaluated?
a.
mc003-1.jpg
c.
mc003-3.jpg
b.
mc003-2.jpg
d.
mc003-4.jpg
 

 4. 
Express mc004-1.jpg as an equivalent radical.
a.
mc004-2.jpg
c.
mc004-4.jpg
b.
mc004-3.jpg
d.
mc004-5.jpg
 

 5. 
Determine the product (x + 8)(x + 11).
a.
x2 + 88x + 88
c.
x2 + 19x + 88
b.
x2 + 8x + 88
d.
x2 + 88x + 19
 

 6. 
Multiply and simplify (6x + 7)2.
a.
36x2 + 84x + 42
c.
36x2 + 42x + 49
b.
36x2 + 84x + 49
d.
36x2 + 49
 

 7. 
What is the factored form of the expression –3x2 + 15?
a.
–3x2(x – 5)
c.
–3x(x2 – 5)
b.
–3x(x – 5)
d.
–3(x2 – 5)
 

 8. 
The area of a rectangular picture frame is represented by the equation A = 12x2 – 18x. When the expression is factored fully, the factors are the dimensions of the frame. What are the dimensions of the frame?
a.
6 by 2x2 – 3
c.
6x by 2x – 3
b.
6 by 2x – 3
d.
6x2 by 2x – 3
 

 9. 
Which of the following pairs of integers has a product of –21 and a sum of 4?
a.
7 and 3
c.
7 and –3
b.
–7 and –3
d.
–7 and 3
 

 10. 
Identify the factored form of x2 – 10x + 16.
a.
(x – 5)(x – 5)
c.
(x – 2)(x – 8)
b.
(x – 4)(x + 4)
d.
(x + 2)(x + 5)
 

 11. 
Which of the following values of k makes the trinomial 4x2 + kx + 100 a perfect square?
a.
20
c.
400
b.
0
d.
40
 

 12. 
Which expression is equivalent to 81m2 + 108m + 36?
a.
(9m – 6)2
c.
(9m – 1296)2
b.
(9m + 6m)2
d.
(9m + 6)2
 
 
Use the graph to answer the question(s) that follow.

The graph shows how the speed of a skier changes over time as she goes down the slope of a mountain.

nar001-1.jpg
 

 13. 
Which statement describes what is happening to the skier as she moves from point D to point A on the graph?
a.
The skier is slowing down and has stopped.
b.
The skier is travelling at a constant speed.
c.
The skier has reached her maximum speed.
d.
The skier is increasing speed at a constant rate.
 

 14. 
Which of the following represent(s) a linear relation?

A {(2, 5), (3, 8), (5, 14), (6, 17)}

B
mc014-1.jpg

C mc014-2.jpg

D
mc014-3.jpg
a.
A
c.
C
b.
A and B
d.
C and D
 

 15. 
Use the table of values to determine the slope of the relation.

mc015-1.jpg
a.
–4
c.
mc015-5.jpg
b.
mc015-4.jpg
d.
4
 

 16. 
Which line segment(s) in the graph has (have) a positive slope?

mc016-1.jpg
a.
line segment AB
c.
line segments EF, IJ, and KL
b.
line segments AB, EF, and CD
d.
line segments IJ, KL, and GH
 

 17. 
What is the y-intercept of the line y = mc017-1.jpgx?
a.
mc017-2.jpg
c.
1
b.
0
d.
mc017-3.jpg
 

 18. 
The equation y = –5x – mc018-1.jpg written in general form is:
a.
15x + 3y + 2 = 0
c.
–5x – y – mc018-3.jpg = 0
b.
5x + y + mc018-2.jpg = 0
d.
–15x – 3y – 2 = 0
 

 19. 
What is the equation of the line that passes through point G(–4, 6) and has a slope of -3?
a.
y = –3x – 6
c.
y = 3x – 6
b.
y = –3x + 6
d.
y = 3x + 6
 

 20. 
Which two lines are parallel?
a.
y = 3x + 2
y = 2x + 2
c.
y = x
y = 5
b.
y = 3x – 4
y = x + 5
d.
y = 0
y = 2
 

 21. 
Which ordered pair is a solution to the linear system y = –x and y = 2x?
a.
(0, 0)
c.
(1, 0)
b.
(0, 1)
d.
(1, 1)
 

 22. 
Determine the ordered pair that solves the linear system 3(x – 1) – 2(y – 3) = 0 and 3(x + 4) – 4(y – 1) – 1 = 0.
a.
(1, 1)
c.
(3, 6)
b.
(2, –3)
d.
(5, 4)
 

 23. 
Which of the following linear systems shows equivalent equations?
a.
4x + y = 6
3x – 6y = 9
c.
3x – 6y = 9
2y = 4x – 6
b.
4y = 2x – 6
4x + y = 6
d.
x – 2y = 3
4y = 2x – 6
 

 24. 
If two lines in a linear system are coincident, how many solutions does the linear system have?
a.
0
c.
indeterminate
b.
1
d.
an infinite number
 

 25. 
Which of the following ordered pairs represents the solution to the linear system y = 2x + 16 and 9x + y = –94?
a.
(–4, –10)
c.
(10, –4)
b.
(–10, –4)
d.
(4, –10)
 

 26. 
What is the solution to the linear system 4x – y = 5 and –x + y = 1?
a.
(–2, –1)
c.
mc026-2.jpg
b.
mc026-1.jpg
d.
(2, 3)
 

 27. 
Brian paints pictures at the town dock and sells them to tourists. He spends $135 for paint supplies plus $5 for each canvas. If he charges $20 per painting, how many paintings must he sell to make a profit?
a.
9
c.
7
b.
25
d.
27
 

 28. 
Deborah babysits for a fee of $98.00 for one evening plus $1.40 per diaper change. Cindy charges $78.40 for one evening plus $2.80 per diaper change. How many diapers does each girl have to change in order to charge the same total fee?
a.
14
c.
15
b.
13
d.
28
 

 29. 
In mc029-1.jpg, AB = 8 cm and BC = 11 cm. Determine the tangent ratio of mc029-2.jpgA, to the nearest thousandth.

mc029-3.jpg
a.
0.520
c.
1.375
b.
0.728
d.
1.536
 

 30. 
In mc030-1.jpg, AC = 8 cm and BC = 11 cm. Determine the sine ratio of mc030-2.jpgB, rounded to the nearest thousandth.

mc030-3.jpg
a.
0.588
c.
0.809
b.
0.728
d.
1.375
 

 31. 
Determine the value of cos 0°.
a.
–1
c.
1
b.
0
d.
undefined
 

 32. 
In mc032-1.jpg, AB = 10 cm, mc032-2.jpg, and mc032-3.jpg. Determine the length of AC to the nearest centimetre.
a.
9 cm
c.
11 cm
b.
10 cm
d.
12 cm
 

 33. 
The imperial unit that has approximately the same length as a metre is the
a.
foot
c.
mile
b.
inch
d.
yard
 

 34. 
A non-standard measuring unit that you choose to use is called a(n)
a.
caliper
c.
metre
b.
instrument
d.
referent
 

 35. 
This quarter is approximately 2.5 cm wide. Estimate how long the line is using the quarter as a referent.

mc035-1.jpg
________________________________
a.
5.0 cm
c.
10.0 cm
b.
7.5 cm
d.
12.5 cm
 

 36. 
A tire has a diameter of 1 ft. How many times will it rotate in order to roll across a field that is 75 yd long? Round your answer to the nearest tenth, if necessary.
a.
75
c.
23.9
b.
25
d.
8
 

 37. 
The base of a right prism has an area of 32.5 ft2. If the prism has a volume of 572 ft3, what is its height?
a.
5.9 ft
c.
35.2 ft
b.
17.6 ft
d.
52.8 ft
 

 38. 
Determine the volume of a right prism that has a base area of 110 mm2 and a height of 2 cm.
a.
2.2 mm3
c.
220 mm3
b.
22 mm3
d.
2200 mm3
 

 39. 
What is the slant height of a right cone with surface area 275.7 m2 and radius 4.5 m?
a.
11 m
c.
15 m
b.
13 m
d.
30 m
 

 40. 
What is the height of a right cone with volume 47.8 mm3 and radius 2.5 mm? Express the answer to the nearest tenth of a millimetre.
a.
2.4 mm
c.
18.3 mm
b.
7.3 mm
d.
22.9 mm
 

Short Answer
 

 1. 
Evaluate using a calculator. Express the answer to four decimal places, where necessary.
a) (62)(62.3)
b) sa001-1.jpg
c) sa001-2.jpg
 

 2. 
Use the graph to answer parts a) to d).

sa002-1.jpg
a) Identify the coordinates of points C and D.
b) Identify the rise from point C to point D.
c) Identify the run from point C to point D.
d) Identify the slope of the line through points C and D.
 

 3. 
Solve the following system of equations graphically.
y = 3x + 4
sa003-1.jpg
 

 4. 
A roof is shaped like an isosceles triangle. The slope of the roof makes an angle of 24sa004-1.jpg with the horizontal, and has an altitude of 3.5 m. Determine the width of the roof, to the nearest tenth of a metre.

sa004-2.jpg
 

 5. 
Calculate the following areas in the indicated unit. Express your answers to the nearest hundredth of a square unit.

Use the table of conversion factors.
Imperial Unit
SI Unit
1 in.
2.54 cm
1 ft
0.3048 m
1 yd
0.9144 m
1 mi
1.609 km

a) What is the area of a rectangle that measures15 mi by 13 mi., in square kilometres?
b) What is the area of a rectangle that measures 5 ft by 6 ft, in square metres?
 

Problem
 

 1. 
A field has a width of x m. Its length is 5 m more than its width. Write an algebraic expression, in simplified form, for the area of the field.
 

 2. 
Jim likes to rock climb in his spare time. Recently, he climbed down from the top of a cliff to the bottom. At the top, where Jim started, he was 2500 ft above the ground. He moved down the cliff at a speed of 20 ft/min.
a) Write an equation to represent the height, h, in feet, that Jim was above the ground after t minutes.
b) Make a table of values for Jim’s height above the ground for values of t from 0 to 4.
c) What was Jim’s height above the ground after 40 min?
d) How many minutes did it take Jim to reach the ground?
 

 3. 
A houseboat on a river travelled 48 km upstream in 6 h. It took the houseboat only 4 h to make the same trip downstream.
a) How fast would the houseboat have travelled in still water?
b) How fast was the river’s current?
 

 4. 
Martha bought 12 ft of fabric to make some clothing. The fabric comes in rolls that are 45 in. wide.
a) What is the area of the piece of fabric, in square feet? in square yards?
b) The cloth cost $3.75/yd. How much did Martha pay for the fabric?
 



 
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