Unit 3 Review
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Write the prime factorization of 630.
A)
____
B)
B) 616
B) 6
B) 60 days
B) 4
D) 7956
C) 2 days
D) 40 days
C) 8
D) 16
6. A cube has volume 15 625 cm3. What is the surface area of the cube?
A) 132 893.3 cm2
____
C) 2652
5. There are 16 male students and 20 female students in a Grade 10 math class. The teacher wants to
divide the class into groups with the same number of males and the same number of females in each
group. What is the greatest number of groups the teacher can make?
A) 12
____
D) 8
4. One neighbour cuts his lawn every 8 days. Another neighbour cuts her lawn every 10 days. Suppose
both neighbours cut their lawns today. How many days will pass before both neighbours cut their
lawns on the same day again?
A) 80 days
____
C) 7
3. Determine the least common multiple of 78 and 102.
A) 1326
____
D)
2. Determine the greatest common factor of 56 and 88.
A) 77
____
C)
B) 3750 cm2
C) 25 cm2
D) 10 416.7 cm2
C) 992.25 cm
D) 441 cm
C) 6.71 cm
D) 3375 cm
7. Determine the side length of this square.
Area = 3969 cm2
|
|
|
|
A) 63 cm
____
B) 15.83 cm
8. Determine the edge length of this cube.
Volume
= 91 125 cm 3
A) 301.87 cm
____
B) 45 cm
9. A cube has surface area 3750 square feet. What is its volume?
A) 5625 cubic feet
B) 25 cubic feet
C) 1448 cubic feet
D) 15 625 cubic feet
____ 10. Identify the index of
A)
.
B) 3
C) 7
D) 2
B)
C) 6
D) 8
B) impossible
C) –12.8
D) 4
B)
C)
D)
C)
D)
C)
D)
____ 11. Identify the radicand of
A) 4
____ 12. Evaluate
.
.
A) –4
____ 13. Evaluate
.
A)
____ 14. Which of these numbers is rational?
A)
B)
____ 15. Which of these numbers is irrational?
A)
B)
____ 16. Order these numbers from least to greatest:
A)
,
B)
,
,
,
,
,
,
,
,
,
C)
D)
,
,
,
,
,
,
,
,
,
,
____ 17. Which of these numbers is a natural number?
A) 9
B) 0
C)
D) –1
____ 18. Which of these numbers is a whole number, but not a natural number?
0, –3, 1,
A)
B) 1
____ 19. To which set(s) of numbers does
C) 0
D) –3
belong?
I
Natural
II Integer
III Rational
IV Irrational
A) II and III only
____ 20. Write
A)
____ 21. Write
A)
B) III only
C) I, II and III only D) IV only
in simplest form.
B) 6 3
C)
D)
C)
D)
in simplest form.
B)
____ 22. Write
in simplest form.
A)
B)
C)
D)
C)
D)
C)
D)
C)
D)
C)
D)
C)
D)
C)
D)
____ 23. Write 6 5 as an entire radical.
A)
B)
____ 24. Write
as an entire radical.
A)
B)
____ 25. Write
as an entire radical.
A)
B)
____ 26. Write
in simplest form.
A)
B) 7 2
____ 27. Write
in simplest form.
A)
B)
____ 28. Write
in simplest form.
A)
B)
____ 29. A square has an area of 12 square inches. Determine the side length of the square as a radical in
simplest form.
A)
____ 30. Evaluate
A) 0.05
____ 31. Evaluate
A) –3
____ 32. Evaluate
A)
____ 33. Write
A)
in.
B)
in.
C)
in.
D) 2 3 in.
without using a calculator.
B) 0.125
C) 0.5
D) 0.29
C) 9
D) does not exist
without sing a calculator.
B) 3
without using a calculator.
B)
C)
D)
C)
D)
as a radical.
B)
____ 34. Write
as a power.
A)
B)
C)
D)
____ 35. Evaluate
A) 18
B) 32
C) 1.741 101...
D) 40
____ 36. Evaluate
A)
C)
B)
...
____ 37. Evaluate
A)
3
D)
without using a calculator.
B) 1
C) 1
6
9
D) 9
____ 38. Evaluate
A)
–
____ 39. Evaluate
A)
1
256
____ 40. Evaluate
A)
____ 41. Evaluate
A)
____ 42. Evaluate
A)
B)
C)
D)
–
1
6
without using a calculator.
B)
3
256
C)
–
1
256
D) –256
without using a calculator.
B)
C)
D)
without using a calculator.
B)
C)
D)
C)
D)
without using a calculator.
B)
____ 43. Simplify
A)
–
by writing as a single power.
B)
C)
D)
____ 44. Simplify
A)
____ 45. Simplify
A)
____ 46. Simplify
A)
. Write using powers with positive exponents.
B)
D)
. Write using powers with positive exponents.
B)
C)
D)
C)
D)
B)
C)
D)
B)
C)
D)
B)
C)
D)
B)
C)
D)
B)
C)
D)
B)
C)
D)
.
B)
____ 47. Simplify
A)
C)
.
____ 48. Simplify
A)
____ 49. Evaluate
A)
____ 50. Simplify
A)
____ 51. Simplify
A)
____ 52. Simplify
A)
53. Evaluate
54. Evaluate
55. Evaluate
56. Simplify
.
without using a calculator.
without using a calculator.
Write using powers with positive exponents.
57. Simplify
58. A cube has surface area 2646 m2. What is its volume?
59. Germaine wants to paint a cube with volume 2744 m3. Each tub of paint covers 79 m2. How many
tubs of paint does Germaine need to paint the cube?
60. The height, h metres, of a Douglas fir tree can be estimated from the formula
, where d
metres is the diameter at the base. Use this formula to determine the approximate height of a
Douglas fir tree with base diameter 4.1 m. Write the answer to the nearest metre.
61. At a distance of 1 m from a light source, the intensity of the light is 2 mW/m2 (milliwatts per square
metre). The intensity, I, at a distance d metres from the source is given by the formula: I = 2d–2 .
Determine the intensity of the light 2.5 m from the source.
62. Here is a student’s solution for evaluating a power:
Identify any errors in the solution. Write a correct solution.
63. Identify any errors in each simplification. Write a correct solution.
a)
b)
Unit 3 Review
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
C
D
A
D
B
B
A
B
D
B
B
A
A
D
B
B
A
C
A
B
B
A
C
A
C
B
D
A
D
C
A
C
B
B
B
C
C
C
A
D
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
51.
52.
D
B
A
B
D
A
A
B
B
B
B
D
53. 16
9
54.
4
1
55.
27
56.
57.
58. To calculate the volume, first determine the edge length of the cube.
The surface area of a cube is the sum of the areas of its 6 congruent square faces.
So, the area, A, of one face is:
The edge length, e, of the cube is the square root of the area of one square face.
So, the volume, V, of the cube is the cube of its edge length.
The volume of the cube is 9261 m3.
59. To calculate how many tubs of paint are needed, first determine the surface area of the cube.
The edge length, e, of a cube is equal to the cube root of its volume.
The surface area, SA, of a cube is the sum of the areas of its 6 congruent square faces.
Calculate how many tubs of paint are needed:
Germaine needs 15 tubs of paint to paint the cube.
60. Substitute d = 4.1 in the formula:
So, the height of a Douglas fir with a base diameter of 4.1 m is approximately 90 m.
61. Use the formula
. Substitute: d = 2.5
0.32
At a distance of 2.5 m, the intensity of light is 0.32 mW/m2.
62.
In the first line of the solution, to write the power with a positive exponent, the student wrote the fraction
inside the brackets as a negative fraction instead of taking the reciprocal of the original fraction.
In the second line, the student wrote the index of the radical as 2 instead of 3. The radicand should have been
positive and should have been written as the reciprocal of the fraction.
A correct solution is:
63. a) There is an error in the second line. When multiplying powers with the same base, the exponents should
have been added, not multiplied.
A correct solution:
b) There are two errors in the first line. The coefficient 2 was incorrectly multiplied by the exponent –4.
And, the exponent of the variable n was added to –4 instead of being multiplied by –4.
A correct solution: