Download Mid Term Review

Midterm Review #1
Ch.1-3
(Ver.01-11-MB)
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Which referent could you use for 1 km?
a.
The distance equal to
laps on an oval running track
b. The length of an iPod
c. The length of a snowboard
d. The length of your arm span
____
2. Which referent could you use for 1 yd.?
a. The width of your shortest finger
b. The length of a screwdriver
c. The height of the kitchen counter above the floor
d. The length of a football field
____
3. Which referent could you use for 1 in.?
a. The distance from where you are now to the nearest restaurant
b. The diameter of a bicycle wheel
c. The length of your calculator
d. The width of your largest toe
____
4. Determine tan A and tan C.
C
8
A
B
10
a. tan A = 1.25; tan C = 0.8
b. tan A = 0.8; tan C = 0.7809...
____
5. Calculate the angle of inclination, to the nearest tenth of a degree, of a road with a grade of 22%.
a. 77.3°
____
c. tan A = 0.8; tan C = 1.25
d. tan A = 0.6247...; tan C = 1.25
b. 77.6°
c. 12.4°
d. 12.7°
6. Determine the length of side z to the nearest tenth of a centimetre.
X
4.7 cm
z
61°
Z
a. 9.7 cm
Y
b. 2.6 cm
c. 5.4 cm
d. 8.5 cm
____
7. A helicopter is ascending vertically. On the ground, a searchlight is 125 m from the point where the helicopter
lifted off the ground. It shines on the helicopter and the angle the beam makes with the ground is 48. How high
is the helicopter at this point, to the nearest metre?
a. 187 m
____
b. 93 m
d. 139 m
8. From a point 18 ft. from the base of a flagpole, Seema used a clinometer to sight the top of the flagpole. Seema
held the clinometer 5 ft. 3 in. above the ground. The angle between the horizontal and the line of sight was 52.
Determine the height of the flagpole to the nearest foot.
a. 28 ft.
____
c. 113 m
b. 34 ft.
c. 19 ft.
d. 23 ft.
9. A helicopter is hovering 200 m above a road. A car stopped on the side of the road is 300 m from the helicopter.
What is the angle of elevation of the helicopter measured from the car, to the nearest degree?
a. 56°
b. 48°
c. 42°
d. 34°
____ 10. Determine the length of RS to the nearest tenth of a metre.
R
17°
T
a. 19.7 m
18.8 m
S
b. 5.7 m
c. 18.0 m
d. 64.3 m
____ 11. Determine the length of this wheelchair ramp to the nearest hundredth of a metre.
0.60 m
4.50 m
a. 4.60 m
b. 7.50 m
c. 4.46 m
d. 4.54 m
____ 12. The front of a tent has the shape of an isosceles triangle with equal sides 163 cm long. The measure of the angle
at the peak of the tent is 105. Calculate the maximum headroom in the tent to the nearest centimetre.
105°
163 cm
163 cm
a. 129 cm
b. 125 cm
c. 99 cm
d. 231 cm
____ 13. Determine the length of QR to the nearest metre.
Q
44°
T
R
15 m
83°
S
a. 85 m
b. 170 m
c. 127 m
d. 118 m
____ 14. From the top of a 25-m lookout tower, a fire ranger observes one fire due east of the tower at an angle of
depression of 7. She sees another fire due north of the tower at an angle of depression of 3. How far apart are
the fires to the nearest metre?
a. 205 m
b. 681 m
c. 477 m
d. 519 m
____ 15. Determine the greatest common factor of 84, 210, and 336.
a. 14
b. 1680
c. 21
d. 42
____ 16. Determine the least common multiple of 78 and 102.
a. 1326
b. 6
c. 2652
d. 7956
c. 207.1
d. 35
____ 17. Determine the cube root of 42 875.
a. 1225
b. 4763.9
____ 18. A cube has volume 15 625 cm3. What is the surface area of the cube?
a. 132 893.3 cm2
b. 3750 cm2
c. 25 cm2
d. 10 416.7 cm2
____ 19. A cube has surface area 3750 square feet. What is its volume?
a. 5625 cubic feet
b. 25 cubic feet
____ 20. Factor the binomial
a.
b.
c. 1448 cubic feet
d. 15 625 cubic feet
.
c.
d.
____ 21. Simplify the expression
a.
b.
, then factor.
c.
d.
____ 22. Which of the following trinomials can be represented by a rectangle? Use algebra tiles to check.
a.
b.
c.
d.
____ 23. Expand and simplify:
a.
b.
c.
d.
____ 24. Factor:
a.
b.
c.
d.
____ 25. Factor:
a.
b.
c.
d.
____ 26. Expand and simplify:
a.
b.
c.
d.
____ 27. Factor:
a.
b.
c.
d.
____ 28. Expand and simplify:
a.
c.
b.
d.
____ 29. Which polynomial, written in simplified form, represents the area of this rectangle?
8x – 4y
x + 5y
a.
b.
c.
d.
____ 30. Expand and simplify:
a.
b.
c.
d.
____ 31. Factor:
a.
b.
c.
d.
____ 32. Factor:
a.
b.
c.
d.
____ 33. Determine the area of the shaded region in factored form.
x–5
2x + 7
a.
b.
Short Answer
34. Convert 6 ft. 5 in. to inches.
c.
d.
35. Convert 358 in. to yards, feet, and inches.
36. A cruise ship is 790 ft. long. Convert this length to the nearest metre.
37. On a map of British Columbia, the distance between Vancouver and Squamish is 52 km. Convert this distance
to the nearest mile.
38. A window is 35 in. high. Convert this height to the nearest centimetre.
39. A right cone has a slant height of 14 in. and a base diameter of 10 in. Determine the surface area of the cone to
the nearest square inch.
40. A regular tetrahedron has an edge length of 9.0 m and a slant height of 7.8 m. Calculate the surface area of the
tetrahedron to the nearest tenth of a square metre.
41. In 2008, the Queen Sesheshet Pyramid was discovered in Egypt. Archeologists determined that the original
height of this right square pyramid was about 14 m and the original base side length was about 22 m. Determine
its original volume to the nearest cubic metre.
42. A regular tetrahedron has base area 98.9 m2 and height 8.6 m. Determine its volume to the nearest tenth of a
cubic metre.
43. A right rectangular pyramid has base dimensions 11 cm by 7 cm and height 9 cm. Determine the volume of the
pyramid to the nearest cubic centimetre.
44. A right cone has a volume of 871 cubic inches. The radius of the cone is 8 in. Determine the height of the cone
to the nearest inch.
45. Determine the surface area of this sphere to the nearest square centimetre. Determine its volume to the nearest
cubic centimetre.
19 cm
46. A hemisphere has radius 7 ft. Determine the surface area of the hemisphere to the nearest square foot.
47. A hemisphere has radius 12 m. Determine the volume of the hemisphere to the nearest tenth of a cubic metre.
48. The volume of a length of cylindrical cable is 150 cm3. Calculate the length of the cable, l, to the nearest
centimetre.
4 cm
l
49. Determine the volume of this composite object, which is a right square prism and a right rectangular pyramid, to
the nearest tenth of a cubic metre.
/
2.1 m
|
5m
5m
13 m
50. Each layer of a three-layer wedding cake is a cylinder with height 8 cm. The bottom layer has diameter 24 cm,
the middle layer has diameter 19 cm, and the top layer has diameter 14 cm. The cake is covered in frosting.
Determine the area of frosting to the nearest square centimetre.
51. Factor the binomial
.
52. Factor:
53. Find and correct the errors in this factorization.
54. Find an integer to replace  so that this trinomial can be factored.
55. Factor:
56. Factor:
57. Expand and simplify:
58. Expand and simplify:
59. Find and correct the errors in this solution.
60. Factor:
61. Find an integer to replace  so that the trinomial is a perfect square.
62. Determine the area of this triangle to the nearest tenth of a square centimetre.
129°
22.1 cm
|
|
63. a) Here are a student’s solutions for factoring polynomials. Identify the errors in each solution. Write a correct
solution.
i) Factor:
Solution:
ii) Factor:
Solution:
b) What should the student have done to check her work?
Midterm Review #1
Answer Section
Ch.1-3
(Ver.01-11-MB)
MULTIPLE CHOICE
1. ANS:
LOC:
2. ANS:
LOC:
3. ANS:
LOC:
4. ANS:
LOC:
5. ANS:
LOC:
6. ANS:
REF:
TOP:
7. ANS:
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8. ANS:
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9. ANS:
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10. ANS:
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11. ANS:
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12. ANS:
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13. ANS:
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14. ANS:
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LOC:
15. ANS:
REF:
TOP:
16. ANS:
REF:
TOP:
A
PTS: 1
DIF: Easy
REF: 1.2 Measuring Length and Distance
10.M1
TOP: Measurement
KEY: Conceptual Understanding
C
PTS: 1
DIF: Easy
REF: 1.2 Measuring Length and Distance
10.M1
TOP: Measurement
KEY: Conceptual Understanding
D
PTS: 1
DIF: Easy
REF: 1.2 Measuring Length and Distance
10.M1
TOP: Measurement
KEY: Conceptual Understanding
C
PTS: 1
DIF: Easy
REF: 2.1 The Tangent Ratio
10.M4
TOP: Measurement
KEY: Procedural Knowledge
C
PTS: 1
DIF: Moderate
REF: 2.1 The Tangent Ratio
10.M4
TOP: Measurement
KEY: Procedural Knowledge
D
PTS: 1
DIF: Easy
2.2 Using the Tangent Ratio to Calculate Lengths
LOC: 10.M4
Measurement
KEY: Procedural Knowledge
D
PTS: 1
DIF: Moderate
2.2 Using the Tangent Ratio to Calculate Lengths
LOC: 10.M4
Measurement
KEY: Procedural Knowledge
A
PTS: 1
DIF: Moderate
2.3 Math Lab: Measuring an Inaccessible Height
LOC: 10.M4
Measurement
KEY: Procedural Knowledge
C
PTS: 1
DIF: Moderate
REF: 2.4 The Sine and Cosine Ratios
10.M4
TOP: Measurement
KEY: Procedural Knowledge
A
PTS: 1
DIF: Moderate
2.5 Using the Sine and Cosine Ratios to Calculate Lengths
10.M4
TOP: Measurement
KEY: Procedural Knowledge
D
PTS: 1
DIF: Easy
2.6 Applying the Trigonometric Ratios
LOC: 10.M4
Measurement
KEY: Procedural Knowledge
C
PTS: 1
DIF: Moderate
2.6 Applying the Trigonometric Ratios
LOC: 10.M4
Measurement
KEY: Procedural Knowledge
D
PTS: 1
DIF: Easy
2.7 Solving Problems Involving More than One Right Triangle
10.M4
TOP: Measurement
KEY: Procedural Knowledge
D
PTS: 1
DIF: Moderate
2.7 Solving Problems Involving More than One Right Triangle
10.M4
TOP: Measurement
KEY: Procedural Knowledge
D
PTS: 1
DIF: Moderate
3.1 Factors and Multiples of Whole Numbers
LOC: 10.AN1
Algebra and Number
KEY: Procedural Knowledge
A
PTS: 1
DIF: Easy
3.1 Factors and Multiples of Whole Numbers
LOC: 10.AN1
Algebra and Number
KEY: Procedural Knowledge
17. ANS:
REF:
TOP:
18. ANS:
REF:
TOP:
19. ANS:
REF:
TOP:
20. ANS:
REF:
TOP:
21. ANS:
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TOP:
22. ANS:
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23. ANS:
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24. ANS:
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25. ANS:
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TOP:
26. ANS:
REF:
TOP:
27. ANS:
REF:
TOP:
28. ANS:
LOC:
29. ANS:
LOC:
30. ANS:
LOC:
31. ANS:
LOC:
32. ANS:
LOC:
33. ANS:
LOC:
KEY:
D
PTS: 1
DIF: Easy
3.2 Perfect Squares, Perfect Cubes, and Their Roots
LOC: 10.AN1
Algebra and Number
KEY: Procedural Knowledge
B
PTS: 1
DIF: Moderate
3.2 Perfect Squares, Perfect Cubes, and Their Roots
LOC: 10.AN1
Algebra and Number
KEY: Procedural Knowledge
D
PTS: 1
DIF: Moderate
3.2 Perfect Squares, Perfect Cubes, and Their Roots
LOC: 10.AN1
Algebra and Number
KEY: Procedural Knowledge
A
PTS: 1
DIF: Easy
3.3 Common Factors of a Polynomial
LOC: 10.AN5
Algebra and Number
KEY: Procedural Knowledge
B
PTS: 1
DIF: Moderate
3.3 Common Factors of a Polynomial
LOC: 10.AN5
Algebra and Number
KEY: Procedural Knowledge
C
PTS: 1
DIF: Easy
3.4 Modelling Trinomials as Binomial Products
LOC: 10.AN5
Algebra and Number
KEY: Procedural Knowledge
A
PTS: 1
DIF: Easy
3.5 Polynomials of the Form x^2 + bx + c
LOC: 10.AN4
Algebra and Number
KEY: Procedural Knowledge
D
PTS: 1
DIF: Moderate
3.5 Polynomials of the Form x^2 + bx + c
LOC: 10.AN5
Algebra and Number
KEY: Procedural Knowledge
B
PTS: 1
DIF: Easy
3.6 Polynomials of the Form ax^2 + bx + c
LOC: 10.AN5
Algebra and Number
KEY: Procedural Knowledge
D
PTS: 1
DIF: Moderate
3.6 Polynomials of the Form ax^2 + bx + c
LOC: 10.AN4
Algebra and Number
KEY: Procedural Knowledge
A
PTS: 1
DIF: Easy
3.6 Polynomials of the Form ax^2 + bx + c
LOC: 10.AN5
Algebra and Number
KEY: Procedural Knowledge
C
PTS: 1
DIF: Easy
REF: 3.7 Multiplying Polynomials
10.AN4
TOP: Algebra and Number
KEY: Procedural Knowledge
D
PTS: 1
DIF: Moderate
REF: 3.7 Multiplying Polynomials
10.AN4
TOP: Algebra and Number
KEY: Procedural Knowledge
C
PTS: 1
DIF: Moderate
REF: 3.7 Multiplying Polynomials
10.AN4
TOP: Algebra and Number
KEY: Procedural Knowledge
D
PTS: 1
DIF: Easy
REF: 3.8 Factoring Special Polynomials
10.AN5
TOP: Algebra and Number
KEY: Procedural Knowledge
C
PTS: 1
DIF: Moderate
REF: 3.8 Factoring Special Polynomials
10.AN5
TOP: Algebra and Number
KEY: Procedural Knowledge
B
PTS: 1
DIF: Difficult
REF: 3.8 Factoring Special Polynomials
10.AN4 | 10.AN5
TOP: Algebra and Number
Procedural Knowledge
SHORT ANSWER
34. ANS:
77 in.
PTS: 1
LOC: 10.M2
35. ANS:
9 yd. 2 ft. 10 in.
DIF: Easy
REF: 1.1 Imperial Measures of Length
TOP: Measurement
KEY: Procedural Knowledge
PTS: 1
LOC: 10.M2
36. ANS:
237 m
DIF: Easy
REF: 1.1 Imperial Measures of Length
TOP: Measurement
KEY: Procedural Knowledge
PTS: 1
LOC: 10.M2
37. ANS:
31 mi.
DIF: Easy
REF: 1.3 Relating SI and Imperial Units
TOP: Measurement
KEY: Procedural Knowledge
PTS: 1
LOC: 10.M2
38. ANS:
88 cm
DIF: Easy
REF: 1.3 Relating SI and Imperial Units
TOP: Measurement
KEY: Procedural Knowledge
PTS: 1
LOC: 10.M2
39. ANS:
298 square inches
DIF: Easy
REF: 1.3 Relating SI and Imperial Units
TOP: Measurement
KEY: Procedural Knowledge
PTS: 1
LOC: 10.M3
40. ANS:
140.4 m2
DIF: Moderate
REF: 1.4 Surface Areas of Right Pyramids and Right Cones
TOP: Measurement
KEY: Procedural Knowledge
PTS: 1
LOC: 10.M3
41. ANS:
2259 m3
DIF: Easy
REF: 1.4 Surface Areas of Right Pyramids and Right Cones
TOP: Measurement
KEY: Procedural Knowledge
PTS: 1
LOC: 10.M3
42. ANS:
283.5 m3
DIF: Easy
REF: 1.5 Volumes of Right Pyramids and Right Cones
TOP: Measurement
KEY: Procedural Knowledge
PTS: 1
LOC: 10.M3
43. ANS:
231 cm3
DIF: Easy
REF: 1.5 Volumes of Right Pyramids and Right Cones
TOP: Measurement
KEY: Procedural Knowledge
PTS: 1
LOC: 10.M3
DIF: Easy
REF: 1.5 Volumes of Right Pyramids and Right Cones
TOP: Measurement
KEY: Procedural Knowledge
44. ANS:
13 in.
PTS: 1
LOC: 10.M3
45. ANS:
SA = 1134 cm2
V = 3591 cm3
DIF: Moderate
REF: 1.5 Volumes of Right Pyramids and Right Cones
TOP: Measurement
KEY: Procedural Knowledge
PTS: 1
LOC: 10.M3
46. ANS:
462 square feet
DIF: Moderate
REF: 1.6 Surface Area and Volume of a Sphere
TOP: Measurement
KEY: Procedural Knowledge
PTS: 1
LOC: 10.M3
47. ANS:
3619.1 m3
DIF: Easy
REF: 1.6 Surface Area and Volume of a Sphere
TOP: Measurement
KEY: Procedural Knowledge
PTS: 1
LOC: 10.M3
48. ANS:
12 cm
DIF: Easy
REF: 1.6 Surface Area and Volume of a Sphere
TOP: Measurement
KEY: Procedural Knowledge
PTS: 1
LOC: 10.M3
49. ANS:
370.5 m3
DIF: Moderate
REF: 1.7 Solving Problems Involving Objects
TOP: Measurement
KEY: Procedural Knowledge
PTS: 1
LOC: 10.M3
50. ANS:
1885 cm2
DIF: Easy
REF: 1.7 Solving Problems Involving Objects
TOP: Measurement
KEY: Procedural Knowledge
PTS: 1
LOC: 10.M3
51. ANS:
DIF: Difficult
REF: 1.7 Solving Problems Involving Objects
TOP: Measurement
KEY: Procedural Knowledge
PTS: 1
LOC: 10.AN5
52. ANS:
DIF: Easy
REF: 3.3 Common Factors of a Polynomial
TOP: Algebra and Number
KEY: Procedural Knowledge
PTS: 1
LOC: 10.AN5
53. ANS:
DIF: Easy
REF: 3.5 Polynomials of the Form x^2 + bx + c
TOP: Algebra and Number
KEY: Procedural Knowledge
PTS: 1
LOC: 10.AN5
54. ANS:
Sample answers:
DIF: Moderate
REF: 3.5 Polynomials of the Form x^2 + bx + c
TOP: Algebra and Number
KEY: Procedural Knowledge
PTS: 1
LOC: 10.AN5
55. ANS:
DIF: Moderate
REF: 3.5 Polynomials of the Form x^2 + bx + c
TOP: Algebra and Number
KEY: Procedural Knowledge
PTS: 1
LOC: 10.AN5
56. ANS:
DIF: Easy
REF: 3.6 Polynomials of the Form ax^2 + bx + c
TOP: Algebra and Number
KEY: Procedural Knowledge
PTS: 1
LOC: 10.AN5
57. ANS:
DIF: Moderate
REF: 3.6 Polynomials of the Form ax^2 + bx + c
TOP: Algebra and Number
KEY: Procedural Knowledge
PTS: 1
LOC: 10.AN4
58. ANS:
DIF: Easy
REF: 3.7 Multiplying Polynomials
TOP: Algebra and Number
KEY: Procedural Knowledge
PTS: 1
LOC: 10.AN4
59. ANS:
DIF: Moderate
REF: 3.7 Multiplying Polynomials
TOP: Algebra and Number
KEY: Procedural Knowledge
PTS: 1
LOC: 10.AN4
60. ANS:
DIF: Moderate
REF: 3.7 Multiplying Polynomials
TOP: Algebra and Number
KEY: Procedural Knowledge
PTS: 1
LOC: 10.AN5
61. ANS:
DIF: Easy
REF: 3.8 Factoring Special Polynomials
TOP: Algebra and Number
KEY: Procedural Knowledge
PTS: 1
LOC: 10.AN5
DIF: Moderate
REF: 3.8 Factoring Special Polynomials
TOP: Algebra and Number
KEY: Procedural Knowledge
PROBLEM
62. ANS:
...
Label a diagram.
ABD is an isosceles triangle, so each base
angle is:
A
129°
22.1 cm
B
|
25.5°
Determine the height, AC, of the triangle.
In right ABC, AC is opposite B and AB is
the hypotenuse.
So, use the sine ratio in ABC.
Determine the length of the base, BD, of ABD
BD = 2(BC)
In right ABC, BC is adjacent to B and AB is the hypotenuse.
So, use the cosine ratio in ACB.
The base, BD, is:
The formula for Area, A, of a triangle is:
|
25.5°
C
D
The area of the triangle is approximately 189.8 cm2.
PTS: 1
DIF: Difficult
REF: 2.7 Solving Problems Involving More than One Right Triangle
LOC: 10.M4
TOP: Measurement
KEY: Problem-Solving Skills
63. ANS:
a) i) Correction:
The student did not remove the common factor from the third term correctly. When the common factor is
the same as the term, a factor of 1 remains. This must be written as a term in the factored polynomial.
ii) Correction:
When the student removed the common factor from the third term, she made a sign error. The sign should
be negative, not positive.
b) The student should have expanded her solutions to check that the trinomial was the same as the original
trinomial each time.
PTS: 1
DIF: Moderate
REF: 3.3 Common Factors of a Polynomial
LOC: 10.AN5
TOP: Algebra and Number
KEY: Communication | Problem-Solving Skills