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Math 10F LG 20 Practice Final #2



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

 1. 

What is the volume of a cube with edges of length 9 m?
a.
2187 m3
c.
81 m3
b.
486 m3
d.
729 m3
 

 2. 

Which description about the number 3375 is correct?
a.
a perfect cube
b.
a perfect square
c.
both a perfect cube and a perfect square
d.
neither a perfect cube nor a perfect square
 

 3. 

Which expression represents the volume of a cube of edge length 5x?
a.
(5x)(5x)(5x)
c.
6(5x)2
b.
5x + 5x + 5x
d.
125x2
 

 4. 

Which power is equivalent to mc004-1.jpg?
a.
2643
c.
mc004-3.jpg
b.
mc004-2.jpg
d.
mc004-4.jpg
 

 5. 

Melanie’s bedroom floor has a width equal to 3x + 6 and a length equal to 4x – 7. What equation represents the area of the floor?
a.
A = 12x2 + 45x – 42
c.
A = 12x2 – 45x – 42
b.
A = 12x2 + 3x – 42
d.
A = 12x2 – 3x – 42
 

 6. 

Multiply and simplify (5x + 2)2.
a.
25x2 + 20x + 10
c.
25x2 + 10x + 4
b.
25x2 + 20x + 4
d.
25x2 + 4
 

 7. 

The greatest common factor (GCF) for the set of terms 30x, 45x, 60x2, and 30x2 is
a.
5x
c.
15x
b.
5x2
d.
15x2
 

 8. 

The area of a classroom door is represented by the equation A = 36z2 + 3600z. When the expression is factored fully, the factors are the dimensions of the door. What are the actual height and width of the door if z = 5 cm?
a.
180 cm by 105 cm
c.
160 cm by 120 cm
b.
170 cm by 100 cm
d.
150 cm by 110 cm
 

 9. 

The area, in metres, of a rectangle is x2 – 10x – 75. When the expression is factored fully, the factors are the dimensions of the rectangle. Determine the actual dimensions, in metres, of the rectangle when x = 25.
a.
10 m by 30 m
c.
25 m by 35 m
b.
20 m by 40 m
d.
30 m by 45 m
 

 10. 

What is the factored form of 72 + 27x + x2?
a.
(x + 12)(x + 6)
c.
(x + 3)(x + 24)
b.
(x + 9)(x + 8)
d.
(x + 2)(x + 3)
 

 11. 

Which expression is an example of a difference of squares?
a.
x2 – 21
c.
9x – 64
b.
4x + 16
d.
25x2 – 81
 

 12. 

Which value of k makes the trinomial x2 + 12x + k a perfect square?
a.
mc012-1.jpg
c.
36
b.
144
d.
18
 

 13. 

A swimming pool is being drained. The table shows the volume of water, in kilolitres, remaining after an elapsed time, in minutes. Which graph represents this data?

Time (min)
0
40
120
180
Volume of Water (kL)
50
40
20
5
a.

mc013-1.jpg
c.

mc013-3.jpg
b.

mc013-2.jpg
d.

mc013-4.jpg
 

 14. 

Which of the following represents the domain of the function mc014-1.jpg?
a.
mc014-2.jpg
c.
mc014-4.jpg
b.
mc014-3.jpg
d.
mc014-5.jpg
 

 15. 

Identify the slope of a line with run –5 and rise –15.
a.
3
c.
mc015-3.jpg
b.
mc015-2.jpg
d.
–3
 

 16. 

Points A(5, 0) and B(–4, 2) are on a line. What is the rise from point A to point B?
a.
–2
c.
1
b.
–1
d.
2
 

 17. 

Taylor invested $200 in an account that pays 5% simple interest per year. The equation representing Taylor’s investment is A = P + Prt, where A is the value of the investment, in dollars, P is the starting principal amount, in dollars, r is the interest rate written as a decimal, and t is the number of years the money is invested. What is the value of the investment after 10 years?
a.
$2000
c.
$400
b.
$1000
d.
$300
 

 18. 

When a linear equation is written in the form Ax + By + C = 0, A and B cannot both be
a.
fractions
c.
one
b.
integers
d.
zero
 

 19. 

For the line 4x – 3y – 12 = 0, which statement is true?
a.
The x-intercept is 3 and the y-intercept is –4.
b.
The x-intercept is 3 and the y-intercept is 4.
c.
The x-intercept is 4 and the y-intercept is –3.
d.
The x-intercept is 4 and the y-intercept is 3.
 

 20. 

Identify the equation of the line in general form when the slope is 0.6 and the y-intercept is 0.4.
a.
3x + 5y + 2 = 0
c.
3x – 5y + 2 = 0
b.
3x + 5y – 2 = 0
d.
3x – 5y – 2 = 0
 

 21. 

Identify the ordered pair that is the solution to the linear system 2xy = 2 and 2x + y = 6.
a.
(1, 1)
c.
(3, 3)
b.
(2, 2)
d.
(4, 4)
 

 22. 

Translate the following into an algebraic equation: “Three times a number subtracted from ten is five more than seven times the number.”
a.
3x – 10 = 7x + 5
c.
10 – 3x = 7x + 5
b.
3x – 10 = 7x – 5
d.
10 – 3x = 5 – 7x
 
 
Answer the the following question(s) using the information from the scenario below.

KC Fitness Club charges a flat fee of $25 per month plus $5 per visit. Workout Zone charges a flat fee of $35 per month plus $3 per visit. Let x represent the number of visits per month and let y represent the total cost per month, in dollars.
 

 23. 

Identify the graph that represents this situation.
a.

mc023-1.jpg
c.

mc023-3.jpg
b.

mc023-2.jpg
d.

mc023-4.jpg
 

 24. 

Determine which of the following linear systems shows coincident lines.
a.
6xy = 2
2x + y = 6
c.
3y = 18 – 6x
2x + y = 6
b.
4x + y = 5
6xy = 2
d.
3y = 18 – 6x
4x + y = 5
 

 25. 

Use the substitution method to determine the solution to the linear system y = 4x + 34 and y = –2x – 26.
a.
(–10, –6)
c.
(–10, 6)
b.
(–6, –10)
d.
(10, –6)
 

 26. 

Raoul and Kourosh run a buffet-style restaurant. It costs them $4200.00 for rent and utilities each month, plus an average of $8.00 per person for food. If they charge their customers $20.00 each, what are the costs at the point where the costs equal the revenue?
a.
$7000.00
c.
$4200.00
b.
$4228.00
d.
$4550.00
 

 27. 

Marie had $40 000.00 to invest. She invested part of it in bonds paying 1.2% per annum and the remainder in a second mortgage paying 2.8% per annum. If the total interest after 1 year was $960.00, how much did Marie invest at each rate?
a.
$39 040.00 at 1.2% and $960.00 at 2.8%
b.
$30 000.00 at 1.2% and $10 000.00 at 2.8%
c.
$10 000.00 at 1.2% and $30 000.00 at 2.8%
d.
$960.00 at 1.2% and $39 040.00 at 2.8%
 

 28. 

Let mc028-1.jpg and mc028-2.jpg, and then solve the following system of equations for x and y.
mc028-3.jpg
mc028-4.jpg
a.
(6, 4)
c.
mc028-5.jpg
b.
(4, 6)
d.
mc028-6.jpg
 

 29. 

If cos A = 0.9903, then the measure of mc029-1.jpgA, to the nearest degree, is
a.
45°
c.
b.
82°
d.
 

 30. 

Write the cosine ratio of mc030-1.jpg.

mc030-2.jpg
a.
mc030-3.jpg
c.
mc030-5.jpg
b.
mc030-4.jpg
d.
mc030-6.jpg
 

 31. 

In mc031-1.jpg, AB = 10 cm, mc031-2.jpg, and mc031-3.jpg. Determine the length of AC to the nearest centimetre.
a.
9 cm
c.
11 cm
b.
10 cm
d.
12 cm
 

 32. 

Which statement is incorrect?
a.
You can solve for the unknown side in any triangle, if you know the lengths of the other two sides, by using the Pythagorean theorem.
b.
The hypotenuse is the longest side in a right triangle.
c.
The hypotenuse is always opposite the 90° angle in a right triangle.
d.
The Pythagorean theorem applies to all right triangles.
 

 33. 

What is the most appropriate SI measurement unit to use when estimating the perimeter of this figure?

mc033-1.jpg
a.
centimetre
c.
metre
b.
kilometre
d.
millimetre
 

 34. 

The flying distance from Dawson City to Whitehorse is 540 km. The distance shown on the map is 4 cm. What is the scale of the map as a ratio in lowest terms?

mc034-1.jpg
a.
mc034-2.jpg
c.
mc034-4.jpg
b.
mc034-3.jpg
d.
mc034-5.jpg
 

 35. 

A florist requires 12 in. of ribbon for each bouquet of flowers he creates. How many bouquets will he be able to create from 10 yd of ribbon?
a.
120
c.
22
b.
10
d.
30
 

 36. 

A low bridge has a posted height of 7 ft 6 in. If your truck is 2.3 m high, how many centimetres over or under the bridge height will it be?
a.
1.4 cm over
c.
2.36 cm over
b.
1.4 cm under
d.
2.36 cm under
 

 37. 

Calculate the surface area of the right pyramid, to the nearest tenth of a square foot.

mc037-1.jpg
a.
27.6 ft2
c.
53.4 ft2
b.
34.7 ft2
d.
54.7 ft2
 

 38. 

Calculate the surface area of the right cylinder, to the nearest square foot.

mc038-1.jpg
a.
93 ft2
c.
48 ft2
b.
68 ft2
d.
23 ft2
 

 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. 

Determine the volume of a right cone with diameter 3.4 in. and height 10.8 in. Express the answer to the nearest cubic inch.
a.
33 in.3
c.
131 in.3
b.
98 in.3
d.
523 in.3
 

Problem
 

 1. 

There are 6 bacteria in a dish at the beginning of an experiment. The number of bacteria doubles every 2 h. How many bacteria are there after 9 days? Express your answer in both exponential and simplified form.
 

 2. 

Greg works as a caretaker at a park. In the fall, he rakes all the leaves in the rectangular park. The length of the park is (3x + 1) m. The width of the park is (2x + 4) m.
a) Develop an expression that represents the area of the park.
b) Calculate the actual area that Greg has to rake if x = 5 m.
 

 3. 

Jill earns $8 per hour working at a fast-food restaurant. She takes the bus to and from work for a total of $4 a day. Jill’s daily net earnings can be represented by the function E(t) = 8t – 4.
a) Make a table of values of Jill’s net earnings for values of t from 0 to 4.
b) Graph the relation.
c) How much does Jill earn if she works for 8 h?
 

 4. 

The equation F = pr004-1.jpgC + 32 gives the temperature, in degrees Fahrenheit for a given temperature, in degrees Celsius.
a) Identify the slope and the F-intercept and explain what they mean.
b) What temperature in degrees Fahrenheit corresponds to -40 °C?
 

 5. 

Lee has $200 and would like to buy ten books as gifts. A paperback book costs $14 and a hardcover costs $24. Using a graph, determine the number of each kind of book that Lee should buy to spend all of his $200.
 

 6. 

A spa is offering two deals. Clients can get five facials and three manicures for $128, or two facials and three manicures for $62. What are the special prices of a facial and a manicure?
 

 7. 

Max’s dog is lying on the ground 1.2 m away from him. The angle of elevation from the dog to the top of Max’s head is 48°. How tall is Max, to the nearest tenth of a metre?

pr007-1.jpg
 

 8. 

You are buying a sport bike that you would like to store in your garden shed. The sport bike has a total length of 210 cm. Your garden shed is 6 ft by 8 ft. Will the sport bike fit in the shed? Show how you know.
 
 
Use the table of conversion factors to help answer the following questions.

Imperial Unit
SI Unit
1 in.
2.54 cm
1 ft
0.3048 m
1 yd
0.9144 m
1 mi
1.609 km
 

 9. 

Determine the volume of a right prism with dimensions 2 ft by 3 ft by 6 ft, to the nearest hundredth of a cubic metre.
 



 
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