Review for Grade 9 Math Exam - Unit 7 - Similarity and Transformations
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
C
B
C
B
C
B
D
B
D
D
C
C
B
B
D
D
A
SHORT ANSWER
18. The scale factor is 3.5.
19. x = 20.4
y° = 31°
20. y = 6
x° = 66°
21. BD = 6
22. CD = 4.5
CE = 2.5
23. 8.1 m
24.
y
6
5
4
3
2
25.
1
1
2
3
4
5
26. Quadrilateral B is the reflection image of quadrilateral A in the oblique line through (0, 8) and (8, 0).
Quadrilateral C is the reflection image of quadrilateral A in the vertical line through 4 on the x-axis.
Quadrilateral D is the reflection image of quadrilateral A in the oblique line through (0, 0) and (8, 8).
y
27.
6
S
5
R
S'
4
3
Q
2
1
P
P'
1
2
3
4
5
6
7
8
9 10
x
6 x
The shape PSS'P'Q has coordinates: P(0,1), S(2,5), S'(8, 5), P'(10, 1), Q(5, 3)
28.Rotational symmetry of order 2 about the centre; no line symmetry
29. R
PROBLEM
30.
31. a)
Solve for x.
Solve for y.
So, x = 27 cm.
So, y = 45 cm.
b) Let z represent the length.
The length is 115.2 cm.
Review for Grade 9 Math Exam - Unit 8 - Circle Geometry
MULTIPLE CHOICE
1. ANS: D
2. ANS: D
3. ANS: C
4. ANS: B
5. ANS: C
6. ANS: B
7. ANS: A
8. ANS: C
9. ANS: A
10. ANS: D
11. ANS: D
12. ANS: D
SHORT ANSWER
13. ANS: AC
14. ANS: 90°
15. ANS:
Yes.
V
U
O
16. ANS:
v° = 58°, w° = 30°
17. ANS:
m = 63.4, n° = 60°
18. ANS: DE
19. ANS:
Answers may vary. For example:
W
4
3
s
6
X
O
4
Y
20.
D
Minor arc CD
Major arc CD
C
21. ANS: Inscribed angle
22. ANS: Inscribed angle:
Central angle:
23. ANS: 180°
24. ANS: y° = 68°, z° = 136°
25. ANS: y° = 38°, z° = 52°
PROBLEM
26. ANS:
V
H
6411 km
Use the Pythagorean Theorem in
solve for HV.
to
6400 km
O
The vulture was about 375 kilometres from the horizon.
27. ANS:
The distance from the centre of the mirror to the hook is: OT
So, the distance from the top of the mirror to the hook is: OT – 28 cm
Solve for OT.
So,
OT – 28 cm
= 36.8781... cm – 28 cm
= 8.8781... cm
So, the hook is about 8.9 cm above the mirror.
28.
ANS:
O
I know that the centre of the circle lies along the perpendicular bisector of a chord. So, when two different
perpendicular bisectors are drawn, the centre of the circle is the point where they intersect.
29. ANS:
a) No. A chord joins two points on a circle. Given one point on a circle, the point farthest from that point
is on the opposite side of the circle. The line connecting these two points passes through the centre of
the circle, so it is a diameter.
b) Yes. For example, in this circle, chord AB is shorter than radius OC.
A
B
O
C
30. ANS:
Draw two chords.
Construct the perpendicular bisectors of the chords.
The intersection of the perpendicular bisectors is the centre of the circle.
31. ANS:
Sketch a diagram.
P
Let d represent the distance from the chord to
the centre of the circle.
Draw a radius from the centre to one end of
the chord.
26 cm
R
Q
d
S
O
38 cm
T
Label the known lengths.
PR is a chord of the circle, and OQ is perpendicular to the chord, passing through
the centre of the circle, so PQ = QR and QR is
of PR:
ST is a diameter of the circle, and OR is a radius of the circle, so OR is
Use the Pythagorean Theorem in
of ST:
.
Q
13 cm
d
R
19 cm
O
So, the chord is approximately 14 cm from the centre of the circle.
32. ANS:
The sum of the central angles in a circle is 360°.
is an inscribed angle and
angle subtended by the same arc.
is a central
B
So,
A
z°
120°
O
133° 107°
y°
OA and OB are radii, so
is isosceles with
.
The sum of the angles in a triangle is 180°, so in
C
:
Review for Grade 9 June Exam - Unit 9 - Probability and Statistics
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
D
B
A
A
A
B
A
D
B
C
C
A
A
D
B
C
A
PROBLEM
18. ANS:
Answers will vary. For example:
The proportion of men and women at a game is the same for a regular game as for a playoff game.
The proportion of men and women at a game does not depend on the day or the time of day
The proportion of men and women at a game does not depend on the weather.
The proportion of men and women who watch boys’ soccer is the same as for girls’ soccer
19. ANS:
Answers will vary. For example:
a) The principal has assumed:
• The students at his school are similar to the teenagers in the study.
• Students who do not currently consume enough dairy products will consume more if it’s free and
easily available.
b) Students may be unwilling to change their eating habits.
Not all students eat in the cafeteria.
Students may not see the need to consume more dairy products.
20. ANS:
Answers will vary. For example:
a) The line up would be shorter at 1 pm than at 10 am.
The tickets would not be sold out by 1 pm.
The ticket office would still be open at 1 pm.
Good seats would still be available at 1 pm.
b) Tickets might be sold out before 1 pm.
The ticket office may close before 1 pm.
The line up may not be shorter.
The seats they wanted may not be available.
21. ANS:
Answers will vary. For example:
a) Cultural Sensitivity - Students may not have access to the Internet outside of school
Use of Language - The wording of the question leads students to answer “Yes” because it presents the
technology in an attractive way as being “cutting-edge.”
Timing - Student responses may differ depending on whether they’ve already used the technology in
another class.
b) A better set of questions might be:
Do you have Internet access at home? Y / N
How likely are you:
- to do research on the Internet? Unlikely / Somewhat Likely / Likely
- to contribute to a class web page? Unlikely / Somewhat Likely / Likely
- to participate in an online discussion board? Unlikely / Somewhat Likely / Likely
22. ANS:
Answers will vary. For example:
a) Privacy - Students may not want to disclose information about their spending habits.
Ethics - Students may want to know why they are being asked such a question.
Language - Students may not be sure whether “food” also includes snacks.
Timing - At the end of the month students may have less cash, so their responses may be lower than
earlier in the month.
b) Privacy - Josh could use an anonymous questionnaire.
Ethics - Josh could explain why he is collecting the data and how he will use it.
Language - Josh could clarify what is being asked: whether “food” mean snacks only, snacks and
lunches, or the total cost of all meals.
Timing - Josh could have students respond in the middle of the month.
23. ANS:
Answers will vary. For example:
Personal interviews are time-consuming.
Students may not answer honestly since there would be a lack of privacy.
Chin Chu could bias the questions by the tone of her voice, body language, or hints.
24. ANS:
a) The population is all the students in the school.
b) I would survey a sample. It would likely be very difficult and time-consuming to get survey responses
from every student.
c) I would make sure my sample included males and females from each grade, and students in different
cliques.
25. ANS:
Answers may vary. For example:
a) Put the names of all grade 9 students in a hat and select 25-30% of the names.
Select every 10th student from an alphabetical list of all grade 9 students.
Randomly select 5 students from each grade 9 class.
b) Use a computer to randomly select employee numbers.
Select every 15th person in the company directory.