Download Multiple Choice

Multiple Choice: Choose the best answer and write it on your ANSWER SHEET (in
second booklet)
1. Which of the following expressions is not equal to
36  36
a.
36  2
b.
2. The completely simplified form of
a. 2 5
a. 23 5
9 8
c.
d. 6 2
80 is:
b. 2 10
3. The completely simplified form of
72 ?
3
c. 4 5
d. 8 10
c. 43 5
d. 83 5
40 is:
b. 2 5
3
4. Express 5 2 in radical form.
a.
b.
5
3
5
c.
53
d.
1000
d.
3
52
5. Which of the following is equivalent to 2.53 4 ?
a.
3
6. Express
62.5
 x
4
7
b.
62.5
3
1000
as an exponent.
4
7
a. x 7
b. x 4
7. Express
c.
c.
x4
7
d.
4x
7
6480 as an equivalent mixed radical in simplest form.
a. 6 80
b. 9 80
c. 12 45
d. 36 5
c. whole
d. irrational
c. rational
d. real
8. Which number set does  belong to?
a. natural
b. rational
9. Which number set does -5 not belong to?
a. natural
b. integer
Intro to Applied and Pre-Calculus Mathematics
Page
1
10. Which of the following numbers is not both a perfect square and a perfect cube?
a. 64
b. 729
11. What is y

3
2

b.
12. Express  8
a.  8
d. 4096
expressed in radical form?
a.  y 3

c. 1000
y
3

2
1
c.
3
d.
y2
1
y3
 as a power with a single exponent.
8 5
40
b.  8
13
c.  8 
d.  64 
3
5
13. What is the next number in the sequence 33 , 32 , 31 , 30 , ... ?
a.  1
b. 3 2
1
3
d. 1
c. 0
d. 1
c.
14. Determine the value of  1  7 0 .
0
a. –8
b. –2
15. Which expression is not equal to 4?
27
a. 5
2
  
1
b. 2 2
1
16. Which value of x satisfies the equation x  2 
a. 18
b. 9
c. 2  2 
0
1
d.  
4
1
1
?
9
c. 4.5
d. 3
17. The root of a number can be represented by
a. an integral exponent
c. a rational exponent
b. a negative exponent
d. all exponents
18. Jean invests $800 in a fund. The investment doubles in value each year. The formula
n
A  8002  models the total value of the investment, A, in dollars, after n years. What is the
value of her investment after 4 years?
a. $12 800
b. $6400
Intro to Applied and Pre-Calculus Mathematics
c. $3200
d. $800
Page
2
19. Which of the following referents is not appropriate to estimate the specified measurement
unit?
a.
b.
c.
d.
one rotation of a mountain bike wheel, foot
height at waist level, metre
width of paper clip, millimetre
width of pinky finger, half an inch
Use the figure to the right to answer questions 20 and 21.
20. What is the most appropriate SI measurement unit to use when
estimating the perimeter of this figure?
a. centimetre
b. kilometre
c. metre
d. millimetre
21. Estimate the imperial measurement of the perimeter of the figure shown.
a. 7 ft
b. 7 in
c. 7 mi
d. 7 yd
22. Brenda states that her bedroom is 4.5 _____ wide. What unit is most appropriate for
this measurement?
a. centimeter
b. meter
c. kilometer
d. millimeter
23. Ben measures the length of the street he lives on to be 90,000 cm. Which of the
following measurements is the same length?
a. 0.9 km
b. 0.9 m
c. 90 km
d. 90 m
24. Find the volume of the figure at the right.
a. 18 un3
b. 32 un3
c. 48 un3
d. 72 un3
e. 144 un3
f. 1728 un3
4
25. Find the surface area of the figure at the right.
a. 48 un2
b. 51 un2
c. 60 un2
d. 66 un2
e. 84 un2
f. 96 un2
Intro to Applied and Pre-Calculus Mathematics
6
6
6
6
Page
3
26. Find the volume of this sphere with height 10 units.
a. 79 un3
b. 314 un3
c. 524 un3
d. 628 un3
e. 1257 un3
f. 4189 un3
10
27. Find the surface area of this sphere with height 10 units.
a. 79 un2
b. 314 un2
c. 524 un2
d. 628 un2
e. 1257 un2
f. 4189 un2
28. A cylinder and a cone each have a radius of 3 in. and a height of 8 in. What is the
ratio of the volume of the cone to the volume of the cylinder?
a. Vcone : Vcylinder = 1 : 2
b. Vcone : Vcylinder = 1 : 3
c. Vcone : Vcylinder = 1 :
c. Vcone : Vcylinder = 1 : 1
29. If the base is a square with a side length of 10 and the slant height is 15, find the
surface area of the pyramid.
a. 85
b. 220
c. 310
d. 400
30. Find the volume, to the nearest cubic inch, of a cone whose radius is 12 inches and
whose height is 15 inches.
a. 2827 in 3
b. 2262 in 3
c. 565 in 3
d. 188 in 3
31. Find the volume of a hemisphere whose radius is 10 feet. Round answer to the
nearest cubic foot.
a. 419 ft 3
b. 1047 ft 3
c. 2094 ft 3
d. 4189 ft 3
32. Find the volume of the figure at the right.
a. 300 ft 3
b. 110 ft 3
c. 80 ft 3
d. 100 ft 3
Intro to Applied and Pre-Calculus Mathematics
Page
4
33. Find the volume of each solid. Round to the nearest tenth if necessary.
cone: radius 5.1 km; height 8.5 km
a. 45.4 km3
b. 231.5 km3
c. 289.4 km3
d. 57.9 km3
34. Find the volume of each solid. Round to the nearest tenth if necessary.
triangular pyramid: triangle base, 8.6 km; triangle height, 7.5 km; pyramid height,
13.7 km
a. 441.8 km3
b. 294.6 km3
c. 110.5 km3
d. 147.3 km3
35. Find the surface area of the figure at the right. Round to the nearest tenth if
necessary.
a. 500.7 km2
b. 479 km2
c. 638.6 km2
d. 1161.1 km2
36. Trigonometry is the study of ________.
a. triangles
b. angles
c. trigonometric functions
d. all of these
37. Which trigonometric function can be used to determine the length of the hypotenuse
if the angle theta and the length of the opposite side are known?
a. tangent
b. cosine
c. sine
d. cosine inverse
38. Which trigonometric function can be used to determine the angle theta when the
length of the opposite and adjacent sides are known?
a. tangent
b. sine inverse
c. sine
d. tangent inverse
39. Which trigonometric function can be used to determine the length of the adjacent
side when the angle theta and the length of the hypotenuse are known?
a. cosine
b. cosine inverse
Intro to Applied and Pre-Calculus Mathematics
c. sine
d. sine inverse
Page
5
40. Solve for x in the right triangle pictured.
a. 4.8
b. 5.2
c. 6.03
d. 10.02
e. 10.6
f. 13.3
Use for questions 40 and 41
y
8
37º
41. Solve for y in the right triangle pictured.
x
a. 4.8
b. 5.2
c. 6.03
d. 10.02
e. 10.6
f. 13.3
42. Solve for  in the right triangle pictured.
a. 53º
b. 51 º
c. 39º
d. 37º
e. 22º
f. 14º
Use for questions 42 and 43

5

43. Solve for  in the right triangle pictured.
a. 53º
b. 51 º
c. 39º
d. 37º
e. 22º
f. 14º
44. Determine the length of x in the figure below, to
nearest tenth of a metre.
a. 5.7 m
b. 7.0 m
c. 6.3 m
d. 8.2 m
4
Use for questions 44 and 45
45. Determine the length of y in the figure, to the
nearest tenth of a metre.
a. 5.7 m
b. 7.0 m
c. 6.3 m
d. 8.2 m
Intro to Applied and Pre-Calculus Mathematics
Page
6
For questions 46-50 use the right triangle pictured.
46. Which of the following is equivalent to sin B ?
a.
20
12
b.
20
16
c.
16
12
d.
12
20
e.
16
20
f.
12
16
47. Which of the following is equivalent to tan C ?
a.
20
12
b.
20
16
c.
16
12
d.
12
20
e.
16
20
f.
12
16
C
20
48. Which of the following is equivalent to cos B ?
a.
20
12
b.
20
16
c.
16
12
d.
12
20
e.
16
20
f.
12
16
A
B
12
49. Which of the following is equivalent to cos C ?
a.
20
12
b.
20
16
c.
16
12
d.
12
20
e.
16
20
f.
12
16
50. Which of the following is equivalent to sin C ?
a.
20
12
b.
20
16
c.
16
12
d.
12
20
e.
16
20
f.
12
16
Intro to Applied and Pre-Calculus Mathematics
Page
7
Match each statement to its corresponding term. A term may be used more than once or
not at all. Please place your answers on the corresponding ANSWER SHEET!
1. all linear SI units are derived from this
2. based on British units of measure
a. angle of elevation
3. a personal item used to approximate a measurement
b. angle of depression
4. a system of measurement in which all units are based
on multiples of ten
c. base
5. the angle between the horizontal and the line of sight
looking down to an object
e. cosine ratio
d. caliper
f. cube root
g. entire radical
6.
h. exponent
i. hypotenuse
7.
j. imperial system
k. inch
8. the side opposite the right angle in a right triangle
l. index
9. the angle between the horizontal and the line of sight
up to an object
m. irrational number
10. a number that can be expressed as the product of two
equal factors
o. mixed radical
11. a number that can be expressed as the product of
three equal factors
q. perfect square
12. one of two equal factors of a number
s. Pythagorean theorem
13. one of three equal factors of a number
n. metre
p. perfect cube
r. prime factorization
t. radical
u. radicand
14. a number that cannot be expressed as a terminating
or repeating decimal
v. referent
w. sine ratio
15. the number 3 in the expression
16. the number 25 in the expression
17. the product of 1 and a radical
x. square root
y. Système International
d’Unités
z. tangent ratio
18. the product of a rational number and a radical
19. consists of a root symbol, an index, and a radicand
Intro to Applied and Pre-Calculus Mathematics
Page
8
Answer Sheet
Multiple Choice
Matching
1. _____
20. _____
39. _____
1. _____
2. _____
21. _____
40. _____
2. _____
3. _____
22. _____
41. _____
3. _____
4. _____
23. _____
42. _____
4. _____
5. _____
24. _____
43. _____
5. _____
6. _____
25. _____
44. _____
6. _____
7. _____
26. _____
45. _____
7. _____
8. _____
27. _____
46. _____
8. _____
9. _____
28. _____
47. _____
9. _____
10. _____
29. _____
48. _____
10. _____
11. _____
30. _____
49. _____
11. _____
12. _____
31. _____
50. _____
12. _____
13. _____
32. _____
13. _____
14. _____
33. _____
14. _____
15. _____
34. _____
15. _____
16. _____
35. _____
16. _____
17. _____
36. _____
17. _____
18. _____
37. _____
18. _____
19. _____
38. _____
19. _____
Intro to Applied and Pre-Calculus Mathematics
Page
9
Written Response: Show all of your work for full marks.
Round answers to the nearest tenth unless otherwise specified.
1. Write equivalent expressions using rational exponents.
Negative exponents ARE allowed. (4 marks)
a.
9
114
b.
c.
x
1
7
w3
2. Write equivalent expressions in radical form. (2 marks)
x  3
2
a.
c. 8 3
1
3. Write each of the following terms in simplest mixed radical form. (4 marks)
a.
75
b.
c.
96
c.
Intro to Applied and Pre-Calculus Mathematics
27
3
54
Page
10
4. Without using a calculator, arrange the following in order from least to greatest.
Must show your work for full marks. (3 marks)
4 3, 6 2 , 5 6, 3 7, 5
5. Simplify each expression. Express answer using positive exponents. (10 marks)

3
c.  9 x y
4
4
2
9 
2 0
a. 12 x y  6 x y
2
b.
 4x y 
3
4
Intro to Applied and Pre-Calculus Mathematics
9
4
 93

1
 12a 3 b 2
d. 
2 5
 4a b



3
Page
11
6. Simplify each expression. Express answer using positive exponents. (5 marks)
2
 3  1 
a.  5 2  5 3 
 
  
 23 
y 
 
b.    4
 12 
y 
 
 
6
7. Without using a calculator, solve: (3 marks)
4  19  36
8. A radioactive element has a half-life of one month. The formula for the amount of the
n
1
element remaining is A  m  , where m is the mass of the element, in grams, and n is the
2
number of months. How much of a 740-g sample of the element
a. remains after 6 months? Express your answer to two decimal places. (1 mark)
b. was there 4 months ago? Express your answer to the nearest gram. (1 mark)
Intro to Applied and Pre-Calculus Mathematics
Page
12
9. Convert each of the following measurements. Show the conversions factors as a part
of your work. Round to the nearest tenth when necessary. (15 marks)
Imperial
1 in.
1 ft
1 yd
1 mi
Metric
2.54 cm (0.0254 m)
0.3048 m (30.48 cm)
0.9144 m
1.609 km
Metric
1 mm
1 cm
1m
1 km
Imperial
0.0394 in.
0.3937 in.
3.281 ft (39.37 in. or 1.094 yd)
0.6214 mi (3 280.84 ft)
a. 5 yd to ft
b. 3 yd to inches
c. 574 in to yd, ft, in
d. 19 m to ft
e. 6 ft 2 in to cm
f. 5 km to mi and yd
Intro to Applied and Pre-Calculus Mathematics
Page
13
10. Find the surface area AND volume for each solid.
a.
(8 marks)
b. radius of 3 in. (4 marks)
Intro to Applied and Pre-Calculus Mathematics
Page
14
c.
(6 marks)
6
12
11. Solve for x in each of the following triangles. (4 marks)
a.
b.
12
11
x
24
x
7
Intro to Applied and Pre-Calculus Mathematics
Page
15
12. Solve the triangle using only the given information. (5 marks)
c
x
7
y
4.5
13. A pilot starts his takeoff and climbs steadily at an angle of 12.2 . Determine the
horizontal distance the plane has travelled when it has climbed 5.4 km along its flight
path. (3 marks)
14. A ladder is leaning against a building. It makes a 65 angle with the ground when
placed 6 feet away from the base of the building. How long is the ladder? (3 marks)
Intro to Applied and Pre-Calculus Mathematics
Page
16
15. You are in a lighthouse that is 50 m above sea level. You can see a ship in the bay at
an angle of depression of 20 . Further out into the bay you can see a yacht, which is
directly in line with the ship. The yacht has an angle of depression of 17 . (6 marks)
a. Draw a diagram of the situation
b. How far off shore is the ship?
c. How far off shore is the yacht?
d. How far apart are the ship and the yacht?
Intro to Applied and Pre-Calculus Mathematics
Page
17