Homework Answers for the Textbook Questions
7.6
1. a) AB and EC
b) BD and AC
c) ∠ABC and ∠ECD
d) ∠BAC and ∠ACE
e) ∠ACE and ∠ECD
f) x = 35°, y = 35°, z = 55°
3. a) ∆PQS and ∆RQS
b) ∠PQS and ∠RQS,
∠PSQ and ∠RSQ
c) x = 110°, Y = 70°
4) x = 55°, y = 30°, z = 25°, w = 65°, t = 60°, s = 65°
5) Ask me in class.
8) AB is parallel to CE.
So, ∠ABC and ∠BCE are alternate angles.
So, ∠ABC = ∠BCE = 90°
AD is a straight angle.
So, ∠BCA + ∠ BCE + ∠ECD = 180°
∠BCA + 90° + ∠ECD = 180°
∠BCA + ∠ECD = 180° – 90° = 90°
So, ∠BCA and ∠ECD are complementary angles.
1. a) AB and EC
b) BD and AC
c) ∠ABC and ∠ECD
d) ∠BAC and ∠ACE
e) ∠ACE and ∠ECD
f) x = 35°, y = 35°, z = 55°
3. a) ∆PQS and ∆RQS
b) ∠PQS and ∠RQS,
∠PSQ and ∠RSQ
c) x = 110°, Y = 70°
4) x = 55°, y = 30°, z = 25°, w = 65°, t = 60°, s = 65°
5) Ask me in class.
8) AB is parallel to CE.
So, ∠ABC and ∠BCE are alternate angles.
So, ∠ABC = ∠BCE = 90°
AD is a straight angle.
So, ∠BCA + ∠ BCE + ∠ECD = 180°
∠BCA + 90° + ∠ECD = 180°
∠BCA + ∠ECD = 180° – 90° = 90°
So, ∠BCA and ∠ECD are complementary angles.
7.5
1) Ask me in class.
2. a) 45° b) Bisect an angle of 90°
3. a) Ask me in class.
b) The method in the example is easier because instead of constructing two angles we only need to construct one angle of 60° and the supplement of this angle is 120°.
4) The answers may vary. I will clarify in class if needed.
5) 360° - 60° = 300°,
180° + 90° + 30° = 300°
6) 360° - 120° = 240°,
180° + 60° = 240°
1) Ask me in class.
2. a) 45° b) Bisect an angle of 90°
3. a) Ask me in class.
b) The method in the example is easier because instead of constructing two angles we only need to construct one angle of 60° and the supplement of this angle is 120°.
4) The answers may vary. I will clarify in class if needed.
5) 360° - 60° = 300°,
180° + 90° + 30° = 300°
6) 360° - 120° = 240°,
180° + 60° = 240°
7.3
2. a) b and h, c and g, a and e, d and f
b) c and e, d and h
c) c and h, d and e
3. a) AB and EC
b) BD and AC
c) ∠ABC and ∠ECD
d) ∠BAC and ∠ACE
e) 50°, 65°, 65°
5. a) 145°, 35° b) 145°, 35°, 145°
7. a) ∠DBG=60°, ∠BDF=120°, ∠CBD=50°, ∠BCD=70°, ∠BCE=110°
b) Ask me in class
8) 125°, 55°, 55°, 35°
10. a) Ask me in class b) Ask me in class
12) The corresponding and alternate angles are not equal, and the interior angles are not supplementary.
2. a) b and h, c and g, a and e, d and f
b) c and e, d and h
c) c and h, d and e
3. a) AB and EC
b) BD and AC
c) ∠ABC and ∠ECD
d) ∠BAC and ∠ACE
e) 50°, 65°, 65°
5. a) 145°, 35° b) 145°, 35°, 145°
7. a) ∠DBG=60°, ∠BDF=120°, ∠CBD=50°, ∠BCD=70°, ∠BCE=110°
b) Ask me in class
8) 125°, 55°, 55°, 35°
10. a) Ask me in class b) Ask me in class
12) The corresponding and alternate angles are not equal, and the interior angles are not supplementary.
7.2
2) ∠K=120°, =∠M=30°
3. a) 60° because it is an equilateral
b) ∠A=∠B=∠C = 60°
5. a) 110° b) 50° c) 45°
6. a) No b) Yes
8) Ask me in class.
10. a) No, No b) No, No
11) 108°
2) ∠K=120°, =∠M=30°
3. a) 60° because it is an equilateral
b) ∠A=∠B=∠C = 60°
5. a) 110° b) 50° c) 45°
6. a) No b) Yes
8) Ask me in class.
10. a) No, No b) No, No
11) 108°
7.1
2. a) ∠TWR b) ∠TWS c) ∠PWQ and ∠TWR d) ∠PWS
3. a) 146° b) 34° c) 124°
4. a) 80° b) 55° c) 152°
6) Ask me in class.
7) ∠EBD=∠DBC=55°
2. a) ∠TWR b) ∠TWS c) ∠PWQ and ∠TWR d) ∠PWS
3. a) 146° b) 34° c) 124°
4. a) 80° b) 55° c) 152°
6) Ask me in class.
7) ∠EBD=∠DBC=55°
5.2
1. Elise
2. a) Not True b) 7 out of 10 cats ate it. 30% were either not hungry or disliked the food.
5. a) No b) A convincing argument could be that one-third of the students wanted extended library hours.
7. a) This is self-evident if you look closely at the chart in your textbook.
b)i) More females eat 5-10 fruits and vegetables per day.
ii) Almost twice as many men aged 25-34 eat 5 to 10 servings of fruits and vegetables per day.
c)i) This group eats the least number of fruits and vegetables per day.
ii) These groups eat 5-10 fruits and vegetables per day.
d)i) Again self-evident if you if you look closely at the chart in your textbook.
ii) No
1. Elise
2. a) Not True b) 7 out of 10 cats ate it. 30% were either not hungry or disliked the food.
5. a) No b) A convincing argument could be that one-third of the students wanted extended library hours.
7. a) This is self-evident if you look closely at the chart in your textbook.
b)i) More females eat 5-10 fruits and vegetables per day.
ii) Almost twice as many men aged 25-34 eat 5 to 10 servings of fruits and vegetables per day.
c)i) This group eats the least number of fruits and vegetables per day.
ii) These groups eat 5-10 fruits and vegetables per day.
d)i) Again self-evident if you if you look closely at the chart in your textbook.
ii) No
5.1
1. a) Sample b) Census c) Sample
2. a) Biased b) Reliable c) Biased d) Biased
4) Ask me in class.
6. i) Yes ii) Yes iii) Yes iv) Yes
8. Method 1: Census
Method 2: Reliable Sample
1. a) Sample b) Census c) Sample
2. a) Biased b) Reliable c) Biased d) Biased
4) Ask me in class.
6. i) Yes ii) Yes iii) Yes iv) Yes
8. Method 1: Census
Method 2: Reliable Sample
4.9
1) If you are having trouble with this question, then ask me for help in class.
3. a) 1 b) 10 c) 0.01 d) 0.1 e) 0.1 f) 0.01 g) 0.01 h) 0.1 i) 0.01
4. a) 2340 b) 3.45 c) 0.1223 d) 12 e) 13.2 f) 0.05 g) 0.0725 h) 7.25 i) 14.56
5.) No. It is only true as long as the divisor is greater than 1.
6. a) 1781 b) 4250 c) 1.12 d) 10.5 e) 1060 f) 30200
7. a) L= 1.55 cm, P= 23.1 cm
b) L= 15.5 cm, P= 33 cm
c) L= 155 cm, P= 310.2 cm
d) L= 1550 cm, P= 1300.02 cm
e) L= 15500 cm, P= 31000.002 cm
1) If you are having trouble with this question, then ask me for help in class.
3. a) 1 b) 10 c) 0.01 d) 0.1 e) 0.1 f) 0.01 g) 0.01 h) 0.1 i) 0.01
4. a) 2340 b) 3.45 c) 0.1223 d) 12 e) 13.2 f) 0.05 g) 0.0725 h) 7.25 i) 14.56
5.) No. It is only true as long as the divisor is greater than 1.
6. a) 1781 b) 4250 c) 1.12 d) 10.5 e) 1060 f) 30200
7. a) L= 1.55 cm, P= 23.1 cm
b) L= 15.5 cm, P= 33 cm
c) L= 155 cm, P= 310.2 cm
d) L= 1550 cm, P= 1300.02 cm
e) L= 15500 cm, P= 31000.002 cm
4.4
2. a) 15/32 b) 8/45 c) ½ d) 4/7 e) 2/9 f) 16/25
4. a) i) 3/10 ii) 3/10 iii) 3/32 iv) 3/32 v) 2/5 vi) 2/5
b) Ask me in class.
5) Ask me in class
2. a) 15/32 b) 8/45 c) ½ d) 4/7 e) 2/9 f) 16/25
4. a) i) 3/10 ii) 3/10 iii) 3/32 iv) 3/32 v) 2/5 vi) 2/5
b) Ask me in class.
5) Ask me in class
4.1
1. a) ½ b) 5/6 c) 2/3 d) ¾ e) 1/3 f) ¾ g) ¾ h) 2/5
2. a) 3/8, ½, 4/5 b) 3/5, 7/10, 6/8 c) 7/4, 6/3, 5/2 d) 7/5, 13/6, 10/3
5. a) ½ b) 3/2 c) ¼ d) ¾ e) 5/4 f) 7/4
7. a) Some examples could be: 16/3, 17/3, 21/4, 22/4, 23/4 etc.
b) No, because we can go on forever.
8. a) 3/3, ¾, 3/5, 3/6, 4/3, 4/4, 4/5, 4/6, 5/3, 5/4, 5/5, 5/6, 6/3, 6/4, 6/5, 6/6
b) 3/6, 3/5, 4/6, ¾, 4/5, 5/6, 3/3, 4/4, 5/5, 6/6, 6/5, 5/4, 4/3, 6/4, 5/3, 6/3
c) i) none ii) 3/5, 4/6, ¾, 4/5, 5/6 iii) 6/5, 5/4, 4/3, 6/4, 5/3, 6/3
1. a) ½ b) 5/6 c) 2/3 d) ¾ e) 1/3 f) ¾ g) ¾ h) 2/5
2. a) 3/8, ½, 4/5 b) 3/5, 7/10, 6/8 c) 7/4, 6/3, 5/2 d) 7/5, 13/6, 10/3
5. a) ½ b) 3/2 c) ¼ d) ¾ e) 5/4 f) 7/4
7. a) Some examples could be: 16/3, 17/3, 21/4, 22/4, 23/4 etc.
b) No, because we can go on forever.
8. a) 3/3, ¾, 3/5, 3/6, 4/3, 4/4, 4/5, 4/6, 5/3, 5/4, 5/5, 5/6, 6/3, 6/4, 6/5, 6/6
b) 3/6, 3/5, 4/6, ¾, 4/5, 5/6, 3/3, 4/4, 5/5, 6/6, 6/5, 5/4, 4/3, 6/4, 5/3, 6/3
c) i) none ii) 3/5, 4/6, ¾, 4/5, 5/6 iii) 6/5, 5/4, 4/3, 6/4, 5/3, 6/3
2.7
1. a) 0.05 b) 0.07 c) 0.03 d) 0.0125 e) 0.035 f) 0.0325 g) 0.0575 h) 0.025
3. a) $840 b) $1800 c) $740
4. a) I = $75, Amount = $2575
b) I = $1080 , Amount = $7080
c) I = $14 , Amount = $714
5. a) $560 b) About $53.33
7. $3489.58
8. Answers may vary.
1. a) 0.05 b) 0.07 c) 0.03 d) 0.0125 e) 0.035 f) 0.0325 g) 0.0575 h) 0.025
3. a) $840 b) $1800 c) $740
4. a) I = $75, Amount = $2575
b) I = $1080 , Amount = $7080
c) I = $14 , Amount = $714
5. a) $560 b) About $53.33
7. $3489.58
8. Answers may vary.
2.6
1. a) i) PST = $2.00, GST = $1.75 ii) PST = $12.00, GST = $10.50
b) i) PST is about $2.08, GST is about $1.82 ii) PST is about $12.20, GST is about $10.67
c) i) $29.89 ii) $175.32
2. i) a) About $20 b) About $18 c) $71.99 d) About $82.70
ii) a) About $60 b) $54 c) $66 d) $75.90
3. a) About 40% b) $13.10
4. Choice B
7. $389120
8. a) $150 b) About $167.80
9. Store B’s offer
1. a) i) PST = $2.00, GST = $1.75 ii) PST = $12.00, GST = $10.50
b) i) PST is about $2.08, GST is about $1.82 ii) PST is about $12.20, GST is about $10.67
c) i) $29.89 ii) $175.32
2. i) a) About $20 b) About $18 c) $71.99 d) About $82.70
ii) a) About $60 b) $54 c) $66 d) $75.90
3. a) About 40% b) $13.10
4. Choice B
7. $389120
8. a) $150 b) About $167.80
9. Store B’s offer
2.5
1. a) 20 b) 24 c) 800 d) 40
2. a) 833.3g b) 500 cm c) 1500g
3. a) About 7.1% b) 30%
5. a) About 5% b) About 5.3%
8. a) 36 b) About 36 min
9. a) About 167 cm b) About 180 cm
1. a) 20 b) 24 c) 800 d) 40
2. a) 833.3g b) 500 cm c) 1500g
3. a) About 7.1% b) 30%
5. a) About 5% b) About 5.3%
8. a) 36 b) About 36 min
9. a) About 167 cm b) About 180 cm
2.4
1. a) 1.2 b) 2.5 c) 4.75 d) 0.003 e) 0.0053 f) 0.0075
3. a) i) 720 ii) 72 iii) 7.2 iv) 0.72
b) The decimal point in the answer moves one place to the left each time.
c) i) 7200 ii) 0.072
5. a) 168 b) 180
6. About 84 percent
7. a) 1% of 2000 = 20. Since 0.75 % is less than 1%, the population was less than 20.
b) 15 people
c) 1985 people
1. a) 1.2 b) 2.5 c) 4.75 d) 0.003 e) 0.0053 f) 0.0075
3. a) i) 720 ii) 72 iii) 7.2 iv) 0.72
b) The decimal point in the answer moves one place to the left each time.
c) i) 7200 ii) 0.072
5. a) 168 b) 180
6. About 84 percent
7. a) 1% of 2000 = 20. Since 0.75 % is less than 1%, the population was less than 20.
b) 15 people
c) 1985 people
2.3
1. a) $133/week b) 85 km/h c) About $0.29/bottle d) $0.33/can
2. a) 8 grapefruit for $2.99 b) 125g for $0.79 c) 150 mL of toothpaste for $2.19 d) 2L of orange juice for $4.49
4. a) 87.5 km
b) The average speed is the mean distance travelled in 1 h.
c) 8 h
5. a) i) 60 km in 3 h
b) Ask me at school if you need help on this question
7. About 4.9 cm
9. About 520.8 kg or about 205.3 bags
10. a) i) About 17 min ii) About 31 min
b) i) Swimming, 52 min ii) Cycling for 1 h then walking for 1 h this would approximately be equal to the number of calories from the ice cream and donut.
1. a) $133/week b) 85 km/h c) About $0.29/bottle d) $0.33/can
2. a) 8 grapefruit for $2.99 b) 125g for $0.79 c) 150 mL of toothpaste for $2.19 d) 2L of orange juice for $4.49
4. a) 87.5 km
b) The average speed is the mean distance travelled in 1 h.
c) 8 h
5. a) i) 60 km in 3 h
b) Ask me at school if you need help on this question
7. About 4.9 cm
9. About 520.8 kg or about 205.3 bags
10. a) i) About 17 min ii) About 31 min
b) i) Swimming, 52 min ii) Cycling for 1 h then walking for 1 h this would approximately be equal to the number of calories from the ice cream and donut.
2.2
2. Answers may vary based on the scale you choose.
5. a) 105 km b) 6 cm
6. a) 9.6 cm by 12.8 cm b) 6.2 cm by 8.4 cm
7. The answers may vary based on the size of the page. For example, if the page is 25cm long then the scale of the photo would be 1:212.
2. Answers may vary based on the scale you choose.
5. a) 105 km b) 6 cm
6. a) 9.6 cm by 12.8 cm b) 6.2 cm by 8.4 cm
7. The answers may vary based on the size of the page. For example, if the page is 25cm long then the scale of the photo would be 1:212.
2.1
1. a) 36 b) 18 c) 10 d) 3 e) 15 f) 20
3. a) 10
b) Logical reasoning and equivalent ratios could also have been used.
4. 148
6. 64
7. a) No b) 15
8. 24
9. a) 39 b) 26 c) 1111.50
1. a) 36 b) 18 c) 10 d) 3 e) 15 f) 20
3. a) 10
b) Logical reasoning and equivalent ratios could also have been used.
4. 148
6. 64
7. a) No b) 15
8. 24
9. a) 39 b) 26 c) 1111.50