Practice Homework Book (Answers)
7.6
1) Alternate angles: ∠CBD and ∠DBE
Corresponding angles: ∠DCB and ∠EBA
Supplementary angles: ∠DBE and ∠EBA
Complementary angles: ∠ CBE and ∠EBA
2) ∠ACB = 70°
∠BAC = 40°
∠ACD = ∠BAC = 40°
∠D = 50° (complementary angles)
3) ∠PQT = ∠SRQ (corresponding angles) = 65°
∠SQT = ∠PQT = 65° (equal angles)
∠S = ∠SQT = 65° (alternate angles)
∠S = ∠R = 65°
So, ∆QRS is isosceles and QR = QS (base angles are equal)
4) ∠E = 30° (alternate angles)
CF = CE (radii of circle)
∆CEF is isosceles.
So, ∠CFE = ∠E = 30° (base angles)
∠CFB and ∠CFE are complementary.
So, ∠CFB = 60°
5) ∠CAB and ∠B are complementary
So, ∠CAB = 90° – 58° = 32°
∠ACD = ∠CAB = 32° (alternate angles)
∆ADC is isosceles.
So, ∠DAC = ∠ACD = 32° (base angles)
∠D + ∠ACD + ∠DAC = 180° (angle sum of a triangle)
So, ∠D = 180° – 32° – 32° = 116°
6) ∠LQP = ∠QLM = 35° (alternate angles)
PLQ = 80° (angle sum of a triangle)
KPL = 80° (alternate angles, KP parallel to LQ)
PLK = 65° (alternate angles)
PKL = 35° (corresponding angles)
7) x = 35° (angle sum of a triangle)
y = 55° (alternate angles)
z = x = 35° (corresponding angles)
w = 60° + 55° (corresponding angles)
w = 115°
t + w + z = 180° (angle sum of a triangle)
t = 180° - 115° - 35° = 30°
1) Alternate angles: ∠CBD and ∠DBE
Corresponding angles: ∠DCB and ∠EBA
Supplementary angles: ∠DBE and ∠EBA
Complementary angles: ∠ CBE and ∠EBA
2) ∠ACB = 70°
∠BAC = 40°
∠ACD = ∠BAC = 40°
∠D = 50° (complementary angles)
3) ∠PQT = ∠SRQ (corresponding angles) = 65°
∠SQT = ∠PQT = 65° (equal angles)
∠S = ∠SQT = 65° (alternate angles)
∠S = ∠R = 65°
So, ∆QRS is isosceles and QR = QS (base angles are equal)
4) ∠E = 30° (alternate angles)
CF = CE (radii of circle)
∆CEF is isosceles.
So, ∠CFE = ∠E = 30° (base angles)
∠CFB and ∠CFE are complementary.
So, ∠CFB = 60°
5) ∠CAB and ∠B are complementary
So, ∠CAB = 90° – 58° = 32°
∠ACD = ∠CAB = 32° (alternate angles)
∆ADC is isosceles.
So, ∠DAC = ∠ACD = 32° (base angles)
∠D + ∠ACD + ∠DAC = 180° (angle sum of a triangle)
So, ∠D = 180° – 32° – 32° = 116°
6) ∠LQP = ∠QLM = 35° (alternate angles)
PLQ = 80° (angle sum of a triangle)
KPL = 80° (alternate angles, KP parallel to LQ)
PLK = 65° (alternate angles)
PKL = 35° (corresponding angles)
7) x = 35° (angle sum of a triangle)
y = 55° (alternate angles)
z = x = 35° (corresponding angles)
w = 60° + 55° (corresponding angles)
w = 115°
t + w + z = 180° (angle sum of a triangle)
t = 180° - 115° - 35° = 30°
7.3
1. a) ∠p b) ∠d c) ∠p d) ∠p e) ∠c
2. a) 65° b) 65° c) 115° d) 65° e) 65° f) 115°
3. a) 62° b) 28° c) 28° d) 62°
4. a) ∠F=115°, ∠C=75°
b) 360°
5) ∠Q=117°, ∠R=63°
6) ∠P=38°
1. a) ∠p b) ∠d c) ∠p d) ∠p e) ∠c
2. a) 65° b) 65° c) 115° d) 65° e) 65° f) 115°
3. a) 62° b) 28° c) 28° d) 62°
4. a) ∠F=115°, ∠C=75°
b) 360°
5) ∠Q=117°, ∠R=63°
6) ∠P=38°
7.2
1. a) ∠B=70°, ∠C=70° b) ∠B=120°, ∠C=30°
2. a) ∠L=65°, ∠K=50° b) ∠VST=20°, ∠V=125°
3) ∠CBD=65°, ∠ABD=25°, ∠A=65°
4) ∠R=45°, ∠QTS=110°, ∠QST=40°
5) ∠R=65°, ∠T=30°
6) ∠F=135°
7) Ask me in class
1. a) ∠B=70°, ∠C=70° b) ∠B=120°, ∠C=30°
2. a) ∠L=65°, ∠K=50° b) ∠VST=20°, ∠V=125°
3) ∠CBD=65°, ∠ABD=25°, ∠A=65°
4) ∠R=45°, ∠QTS=110°, ∠QST=40°
5) ∠R=65°, ∠T=30°
6) ∠F=135°
7) Ask me in class
7.1
1. a) ∠PQL or ∠KQR b) ∠TQR c) ∠PQK d) ∠LQR e) ∠PQL
2. a) 55° b) 55° c) 125° d) 125°
3. a) ∠SKR
b) ∠PKT
c) ∠PKS or ∠QKR
d) ∠PKT
e) ∠PKS or ∠QKR
4) Ask me in class
1. a) ∠PQL or ∠KQR b) ∠TQR c) ∠PQK d) ∠LQR e) ∠PQL
2. a) 55° b) 55° c) 125° d) 125°
3. a) ∠SKR
b) ∠PKT
c) ∠PKS or ∠QKR
d) ∠PKT
e) ∠PKS or ∠QKR
4) Ask me in class
5.4
1) Mean = 7 cm; Median = 5 cm; Mode = 3 cm
2) Data without the outlier: 3 cm, 3 cm, 4 cm, 5 cm, 6 cm, 7 cm
Mean = 4.7 cm; Median = 4.5 cm; Mode = 3 cm
3) This means that the size sold most often last week was medium, or more jeans of that size were sold last week.
4) Scores with the outliers: Mean = 81.6; Median = 82.5; Mode = 78
Scores without the outliers: Mean = 82.75; Median = 82.5; Mode = 78
Therefore, Sophie should choose the mean score without the outliers for her mid-term report because it is the highest score among all the averages.
5) For her 6ht tryout race Celia should aim for less than 5 min 46 s.
This is possible for Celia because 2 of her tryout times are less than 5 min 46 s.
6. a) 8 A: 121 cm, 169 cm, 175 cm, and 186 cm
8 B: 118 cm, 123 cm, 178 cm, and 187 cm
b) 8 A: Mean = 146.1 cm; Median = 148 cm; Mode = 149 cm
8 B: Mean = 147 cm; Median = 146.5 cm; Mode = 158 cm
c) With the outliers, the girls in 8A are taller because their mean and median heights are greater than those of 8B.
Without the outliers, the girls in 8B are taller because their mean and mode heights are greater than those of 8A.
1) Mean = 7 cm; Median = 5 cm; Mode = 3 cm
2) Data without the outlier: 3 cm, 3 cm, 4 cm, 5 cm, 6 cm, 7 cm
Mean = 4.7 cm; Median = 4.5 cm; Mode = 3 cm
3) This means that the size sold most often last week was medium, or more jeans of that size were sold last week.
4) Scores with the outliers: Mean = 81.6; Median = 82.5; Mode = 78
Scores without the outliers: Mean = 82.75; Median = 82.5; Mode = 78
Therefore, Sophie should choose the mean score without the outliers for her mid-term report because it is the highest score among all the averages.
5) For her 6ht tryout race Celia should aim for less than 5 min 46 s.
This is possible for Celia because 2 of her tryout times are less than 5 min 46 s.
6. a) 8 A: 121 cm, 169 cm, 175 cm, and 186 cm
8 B: 118 cm, 123 cm, 178 cm, and 187 cm
b) 8 A: Mean = 146.1 cm; Median = 148 cm; Mode = 149 cm
8 B: Mean = 147 cm; Median = 146.5 cm; Mode = 158 cm
c) With the outliers, the girls in 8A are taller because their mean and median heights are greater than those of 8B.
Without the outliers, the girls in 8B are taller because their mean and mode heights are greater than those of 8A.
5.2
1. a) It shows the number of adults that go to the movies on Friday, Saturday and Sunday
b)i) Most youth go on Saturday
ii) Most adults go on Fridays
c)i) When the two bars for each day are stacked on top of each other then the height of the bars for Saturday is the greatest.
ii) When the bars for each age group are stacked up together then the height of the stacked bars for each age group is about the same.
2. a) No
b) - Most people drive vans and SUVs.
- Very few people drive sports cars.
3. a) Self-Evident if you look at the graph in your PHB carefully.
b) ‘B’ is the most valid argument.
c) ‘C’ is the most valid argument.
4. a) Self-Evident if you look at the graph in your PHB carefully.
b) The taller a person is, the longer the person’s foot.
c) 19cm
1. a) It shows the number of adults that go to the movies on Friday, Saturday and Sunday
b)i) Most youth go on Saturday
ii) Most adults go on Fridays
c)i) When the two bars for each day are stacked on top of each other then the height of the bars for Saturday is the greatest.
ii) When the bars for each age group are stacked up together then the height of the stacked bars for each age group is about the same.
2. a) No
b) - Most people drive vans and SUVs.
- Very few people drive sports cars.
3. a) Self-Evident if you look at the graph in your PHB carefully.
b) ‘B’ is the most valid argument.
c) ‘C’ is the most valid argument.
4. a) Self-Evident if you look at the graph in your PHB carefully.
b) The taller a person is, the longer the person’s foot.
c) 19cm
5.1
1. a) Census b) Sample c) Sample d) Census
2. a) Continuous b) Qualitative c) Discrete d) Continuous
3. a) The population is all hotel guests.
b) The population is all teachers in the school.
c) The population is all customers of the lawn-care company.
4. a) Biased b) Reliable c) Biased
5. a) Biased because only 10 students are surveyed
b) Biased because it does not represent people who use the centre in the afternoons, evenings, or on the weekends.
6. a) Sample survey
b) Census Survey
1. a) Census b) Sample c) Sample d) Census
2. a) Continuous b) Qualitative c) Discrete d) Continuous
3. a) The population is all hotel guests.
b) The population is all teachers in the school.
c) The population is all customers of the lawn-care company.
4. a) Biased b) Reliable c) Biased
5. a) Biased because only 10 students are surveyed
b) Biased because it does not represent people who use the centre in the afternoons, evenings, or on the weekends.
6. a) Sample survey
b) Census Survey
4.6
1. a) 6 b) 4
2. a) 6 b) 5
3) 9
4. a) ¼ b) 3/10
5. a) 2/7 b) 5/6
6) 1/6
1. a) 6 b) 4
2. a) 6 b) 5
3) 9
4. a) ¼ b) 3/10
5. a) 2/7 b) 5/6
6) 1/6
4.4
1. a) 2/3 x 1/2 = 1/3 b) 1/4 x 2/5 = 1/10 c) 1/3 x 1/3 = 1/9 d) 1/2 x 5/6 = 5/12
2. a) 3/16 b) 1/3
3) 3/8
4) 1/20, 6/20, 3/20, 1/10, 3/10
1. a) 2/3 x 1/2 = 1/3 b) 1/4 x 2/5 = 1/10 c) 1/3 x 1/3 = 1/9 d) 1/2 x 5/6 = 5/12
2. a) 3/16 b) 1/3
3) 3/8
4) 1/20, 6/20, 3/20, 1/10, 3/10
4.1
1. a) 8 b) 18 c) 21
2. a) 2/5 b) ¾ c) 2/3 d) 3/7
3. a) 5/2 b) 9/20
4.) 1/6, 2/9, ¼
5. a) 5/6, 7/9, ¾, 2/3
b) Sumy, Ed, Lucy, Maria
1. a) 8 b) 18 c) 21
2. a) 2/5 b) ¾ c) 2/3 d) 3/7
3. a) 5/2 b) 9/20
4.) 1/6, 2/9, ¼
5. a) 5/6, 7/9, ¾, 2/3
b) Sumy, Ed, Lucy, Maria
2.7
1. a) 0.07 b) 0.049 c) 0.035 d) 0.0475
2. a) ½ b) ¾ c) 5/4
3.) $140
4.) $150 (For the $500 Deposit), $207 (For the $1150 Deposit), $437.50 (For the $5000 Deposit)
5. a) $960 b) $3960 c) $82.50
6.) $876
7.) $2651.20
8.) 10%
1. a) 0.07 b) 0.049 c) 0.035 d) 0.0475
2. a) ½ b) ¾ c) 5/4
3.) $140
4.) $150 (For the $500 Deposit), $207 (For the $1150 Deposit), $437.50 (For the $5000 Deposit)
5. a) $960 b) $3960 c) $82.50
6.) $876
7.) $2651.20
8.) 10%
2.6
1. a) $40.32 b) $5.11 c) $21.00
2. a) $2.76 b) $3942.20 c) $148.11
3. a) Discount = $27.60, Sale Price = $64.40 b) Discount = $71.40, Sale Price = $404.60
4.) $4300
5. a) 12% b) $430 100
6.) $180
7.) Store A
8. a) $220.80 b) $220.80
1. a) $40.32 b) $5.11 c) $21.00
2. a) $2.76 b) $3942.20 c) $148.11
3. a) Discount = $27.60, Sale Price = $64.40 b) Discount = $71.40, Sale Price = $404.60
4.) $4300
5. a) 12% b) $430 100
6.) $180
7.) Store A
8. a) $220.80 b) $220.80
2.5
1.a) 1% = 1.5, 100% = 150 b) 28% = 56, 1% = 2, 100% = 200 c) 150% = 36, 1% = 0.24, 100% = 24
2.a) Increase = $23; Increase as a fraction of the original = 0.25; Percent increase = 25
b) 10 c) decrease = 4% d) increase = 16%
3.) 600
4.a) Increases by about 23% b) Decreases by about 9%
5.a) About 7 500 000 b) About 40%
6.) 27 L
7.) 217
8. a) 1008 items/week b) $63
1.a) 1% = 1.5, 100% = 150 b) 28% = 56, 1% = 2, 100% = 200 c) 150% = 36, 1% = 0.24, 100% = 24
2.a) Increase = $23; Increase as a fraction of the original = 0.25; Percent increase = 25
b) 10 c) decrease = 4% d) increase = 16%
3.) 600
4.a) Increases by about 23% b) Decreases by about 9%
5.a) About 7 500 000 b) About 40%
6.) 27 L
7.) 217
8. a) 1008 items/week b) $63
2.4
1.a) 1.75 b) 0.005
2. a) 2.3 b) 1.85 c) 3.24 d) 0.0074 e) 0.007 f) 0.0009
3. a) 50% b) 150% c) 250% d) 1% e) 0.5% f) 1.5%
4.a)i) 360 ii) 36 iii)3.6
b)i) 3600 ii) 0.36
5.) 152
6.) 386 runners completed in under 40 min and there were 59 runners in this group.
7.) 120.3% of $1000 is the greater amount of money.
1.a) 1.75 b) 0.005
2. a) 2.3 b) 1.85 c) 3.24 d) 0.0074 e) 0.007 f) 0.0009
3. a) 50% b) 150% c) 250% d) 1% e) 0.5% f) 1.5%
4.a)i) 360 ii) 36 iii)3.6
b)i) 3600 ii) 0.36
5.) 152
6.) 386 runners completed in under 40 min and there were 59 runners in this group.
7.) 120.3% of $1000 is the greater amount of money.
2.3
1. a) $0.66/bottle b) 70 words/min c) $141/week d) $1.30/100 g
2. a) First one is the better buy. b) First one is the better buy.
3. a) 60.5 km/h b) 62 km/h c) 61.8 km/h
4.) Tasha
5. a) 14.5 points/game b) 377 points
6.) Twenty-four 500mL bottles for $9.18 is the better buy.
7. a) British Colombia b) Saskatchewan c) Ontario d) British Colombia
1. a) $0.66/bottle b) 70 words/min c) $141/week d) $1.30/100 g
2. a) First one is the better buy. b) First one is the better buy.
3. a) 60.5 km/h b) 62 km/h c) 61.8 km/h
4.) Tasha
5. a) 14.5 points/game b) 377 points
6.) Twenty-four 500mL bottles for $9.18 is the better buy.
7. a) British Colombia b) Saskatchewan c) Ontario d) British Colombia
2.2
1. a) 1:10 b) 32 cm
2.) 1.6cm
3.) 1500 km
4.) 66.5 cm
5. a) 17 cm by 11 cm b) 30.5 cm by 18.5 cm
6. a) 1:150 b) 40.8 cm
1. a) 1:10 b) 32 cm
2.) 1.6cm
3.) 1500 km
4.) 66.5 cm
5. a) 17 cm by 11 cm b) 30.5 cm by 18.5 cm
6. a) 1:150 b) 40.8 cm
2.1
1. a) 6 b) 15 c) 3
2. a) 3 b) 10 c) 15
3. a) 8 b) 32 c) 2 d) 8 e) 6 f) 20
4.) 98
5.) 45 cm
6.) 42
7.) 24 boys and 4 teachers
1. a) 6 b) 15 c) 3
2. a) 3 b) 10 c) 15
3. a) 8 b) 32 c) 2 d) 8 e) 6 f) 20
4.) 98
5.) 45 cm
6.) 42
7.) 24 boys and 4 teachers