Bk 2A Chapter 1 Rate and Ratio
1 Rate and Ratio
Review Exercise 1 (p. 1.3)
1. Walking speed of Annie’s grandmother[pic]
2. Average speed of Mr Lee’s car[pic]
3. Distance travelled by the bird[pic]
4. Time needed to travel 425 km[pic]
5. ∵ (ABC ( (PQR
∴ [pic]
[pic]
∴ [pic]
[pic]
6. ∵ (DEF ( (LMN
∴ [pic]
[pic]
∴ [pic]
[pic]
Activity
Activity 1.1 (p. 1.4)
1. (a) Distance that David can cycle in 1 hour
[pic]
(b) Distance that Mark can cycle in 1 hour
[pic]
2. Mark
Classwork
Classwork (p. 1.5)
(a) The required rate[pic]
(b) The required rate [pic]
(c) The required rate[pic]
(d) The required rate[pic]
Quick Practice
Quick Practice 1.1 (p. 1.6)
(a) Speed of the boat[pic]
(b) Speed of the boat[pic]
Quick Practice 1.2 (p. 1.6)
(a) Price of the ribbon[pic]
(b) Amount that Winnie needs to pay[pic]
Quick Practice 1.3 (p. 1.7)
(a) Jill’s rate of folding paper flowers[pic]
(b) Time needed to fold 50 pieces of paper flowers
[pic]
∴ Jill can finish 50 pieces of paper flowers for a party which will start in half an hour’s time.
Alternative Solution
Number of paper flowers folded in half an hour
[pic]
∴ Jill can finish 50 pieces of paper flowers for a party which will start in half an hour’s time.
Quick Practice 1.4 (p. 1.13)
(a) 18 : 24[pic]
(b) 0.36 : 0.9[pic]
(c) [pic][pic]
Alternative Solution
[pic]
(d) 150 g : 2 kg[pic]
Quick Practice 1.5 (p. 1.13)
∵ [pic]
∴ [pic]
Quick Practice 1.6 (p. 1.14)
(a) [pic]
∴ [pic]
(b) [pic]
∴ [pic]
Quick Practice 1.7 (p. 1.14)
(a) Number of red beans : total number of beans
[pic]
(b) Number of green beans[pic]
Number of green beans : total number of beans
[pic]
(c) Number of red beans : number of green beans
[pic]
Quick Practice 1.8 (p. 1.15)
Tom’s monthly expenditure[pic]
Tom’s monthly savings[pic]
Alternative Solution
Tom’s monthly savings[pic]
Quick Practice 1.9 (p. 1.15)
Fraction of the original piece of paper which is the area of the square[pic]
Let y cm2 be the area of the original piece of paper.
[pic]
∴ The area of the original piece of paper is 6 cm2.
Quick Practice 1.10 (p. 1.17)
(a) 0.6 : 0.4 : 1[pic]
(b) [pic]
[pic]
Quick Practice 1.11 (p. 1.17)
|(a) | |x |
|50 : 1 |20 cm |( 0.4 ) cm |
|1 : 25 000 |8 cm |( 2 ) km |
|[pic] |5 cm |( 1.5 ) km |
(b) For length on the scale drawing = 5 cm
and the actual length = 10 m = 1000 cm,
Scale[pic]
For length on the scale drawing = 2 cm
and the actual length = 1 mm = 0.1 cm,
Scale[pic]
For length on the scale drawing = 6 cm
and the actual length = 30 km = 3000 000 cm,
Scale[pic]
Hence,
|Length on the scale drawing |Actual |Scale |
| |length | |
|5 cm |10 m |1 : 200 |
|2 cm |1 mm |20 : 1 |
|6 cm |30 km |1 : 500 000 |
2. (a) Scale of the map
[pic]
(b) Let x cm be the distance between the two cities on the map.
∴ x cm : 18 km = 1 : 250 000
[pic]
∴ The distance between the two cities on the map is 7.2 cm.
(c) Let y km be the actual length of the river.
∴ 4.2 cm : y km = 1 : 250 000
[pic]
∴ The actual length of the river is 10.5 km.
3. (a) Actual length (width) of the study
[pic]
∴ The bench cannot be fit into the study.
(b) Actual area of the study[pic]
∴ Area of the study : area of the whole flat
[pic]
Exercise
Exercise 1A (p. 1.8)
Level 1
1. Eric’s running rate[pic]
2. Ellen’s answering rate[pic]
3. The worker’s wage[pic]
4. Weight of potato chips[pic]
5. Exchange rate for HKD and USD[pic]
6. Price of apples[pic]
7. The rent of the flat[pic]
8. Yvonne’s typing rate[pic]
9. Cost of the fish[pic]
10. The rate that the vehicles arrived at the traffic junction
[pic]
Level 2
11. For a 5 kg-pack of rice, price[pic]
For a 8 kg-pack of rice, price[pic]
∴ The 8 kg-pack of rice is cheaper.
12. (a) (i) Billy’s cycling speed[pic]
(ii) Bill’s cycling speed[pic]
(b) Joey’s cycling speed[pic]
∴ Joey’s cycling speed > Billy’s cycling speed
∴ Joey cycles faster than Billy.
Alternative Solution
Joey’s cycling speed[pic]
> 0.25 km/min
∴ Joey’s cycling speed > Billy’s cycling speed
∴ Joey cycles faster than Billy.
13. (a) (i) Price of barbecued pork in Singapore
[pic]
(ii) Price of barbecued pork in Hong Kong
[pic]
(b) Price of barbecued pork in Singapore
[pic]
∴ It is not cheaper to buy barbecued pork in Singapore.
Alternative Solution
Price of barbecued pork in Hong Kong
[pic]
∴ It is cheaper to buy barbecued pork in Hong Kong.
∴ It is not cheaper to buy barbecued pork in Singapore.
14. (a) Price of orange[pic]
(b) Price of one-and-a-half dozens oranges
[pic]
15. (a) The required exchange rate[pic]
(b) Amount of RMB that we can exchange
[pic]
16. (a) Mary’s reading speed[pic]
(b) Time needed by Mary to finish 66 pages[pic]
17. (a) Mr Fung’s running speed[pic]
(b) Distance ran by Mr Fung in 18 minutes
[pic]
∴ Mr Fung cannot finish a 3-km race in 18 minutes.
Alternative Solution
Time needed by Mr Fung to finish a 3-km race
[pic]
∴ Mr Fung cannot finish a 3-km race in 18 minutes.
18. (a) Henry’s average rate of saving money per month
[pic]
(b) Henry’s total saving between 1st January, 2009 to 31st March, 2009
[pic]
∴ Henry can afford to buy a toy worth $250.
19. (a) Mrs Lee’s hourly wage[pic]
(b) Let h hours be the time that Mrs Lee works per day.
[pic]
∴ Mrs Lee needs to work 10 hours per day.
Alternative Solution
The time that Mrs Lee needs to work per day
[pic]
20. (a) Petrol consumption rate of Peter’s car
[pic]
(b) Total petrol consumption for the whole journey
[pic]
∴ Peter cannot reach city B without refilling his car.
Alternative Solution
Distance travelled by Peter’s car using 20 L of petrol
[pic]
∴ Peter cannot reach city B without refilling his car.
21. (a) Kelvin’s running speed[pic]
(b) Kelvin’s walking speed[pic]
(c) (i) Total distance travelled by Kelvin
[pic]
Total time taken
[pic]
(ii) Kelvin’s average speed[pic]
22. (a) (i) Time taken by Mary[pic]
Time taken by Ann[pic]
(ii) [pic]
(b) (i) Distance travelled by Peter[pic]
Distance travelled by Mary[pic]
(ii) [pic]
∵ [pic]
∴ Peter will meet Mary at 12:24 p.m.
Exercise 1B (p. 1.21)
Level 1
1. (a) 48 : 72[pic]
(b) 0.2 : 0.8[pic]
(c) 1.5 : 0.45[pic]
2. (a) [pic][pic]
(b) [pic]
(c) [pic]
3. (a) 42 days : 2 weeks[pic]
Alternative Solution
42 days : 2 weeks[pic]
(b) 1.8 km : 600 m[pic]
(c) 25 min : 900 s[pic]
4. (a) Number of pencils : number of ball pens
[pic]
(b) Area of the blue regions : area of the yellow regions
[pic]
5. (a) 3 : 9 : 15[pic]
(b) [pic][pic]
6. (a) ∵ [pic]
∴ [pic]
(b) ∵ [pic]
∴ [pic]
7. (a) [pic]
∴ [pic]
(b) [pic]
∴ [pic]
(c) [pic]
∴ [pic]
|8. |(a) | |x |
|3 |1 |6 |4 |
|3 |2 |5 |3 |
|3 |3 |4 |2 |
|3 |4 |3 |1 |
|3 |5 |2 |0 |
|4 |1 |5 |9 |
|4 |2 |4 |8 |
|4 |3 |3 |7 |
|4 |4 |2 |6 |
|4 |5 |1 |5 |
|5 |1 |4 |14 |
|5 |2 |3 |13 |
|5 |3 |2 |12 |
|5 |4 |1 |11 |
|6 |2 |2 |18 |
|6 |3 |1 |17 |
(Accept any two continued ratios from the above table.)
Challenging Questions (p. 1.41)
1. (a) (i) Amount of inheritance obtains by the eldest son
[pic]
(ii) Amount of inheritance obtains by the eldest son
[pic]
(b) Let Mr Chan passes away k years later.
Amount of inheritance obtains by the eldest son
[pic]
Amount of inheritance obtains by the youngest son
[pic]
Hence,
[pic]
∴ The age of the second son when Mr Chan passed away is 21 + 12, that is 33.
2. To complete the job alone,
A’s working rate[pic]
B’s working rate[pic]
C’s working rate[pic]
Besides,
A’s working days : B’s working days[pic]
B’s working days : C’s working days[pic]
A’s working days : B’s working days : C’s working days
[pic]
Let y be the total number of working days for completing the job.
The part of job completed by A[pic]
The part of job completed by B[pic]
The part of job completed by C [pic]
∴ [pic]
∴ It takes 20 working days to complete the job.
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