### June Vacation Chap 9.2 RATE (L4) Self-Paced Learning

1. Mathematics Textbook 1B
(a) Go through Chapter 9 (p9 to p11)
(b) Attempt Exercise 9.2 Q1 to Q10.

2. ACELearning Portal: eLearning Portal
> Subject: Secondary 1 Express
> Ratio, Rate and Speed: Choose Rate

(a) Go through video lessons: Rate, Average Rate, Example 1, Example 2
Note: An email has been sent to all students via the AceLearning

1. Q1:
(a):\$3.50/l (b):72 vases/day
(c):47 words/min (d)\$80/m²
(e):4kg/m (f):60g/egg
Q2:
(a):\$23/h (b)\$920/week
Q3:
(a):9km/l (b)\$1.20/l
Q4:
(a):87.5g/cube (b):0.7g/cm³ of cube
Q5:
(a):\$15/ticket (b):\$150
Q6:
(a):\$22.50/m² (b):\$450
Q7:
(a):45l/min (b):3 min
Q8:
(a):\$26/kg (b):25g (c):3kg and \$78
Q9:
(a):\$201 600 (b):\$4200/m²
Q10:
(a)19.3g/cm³
(b)No,it is not made of pure gold.When we calculate the mass per m³ of the gold cube with side 2cm,the mass is 15g.The mass of the pure gold cube is 19.3g/cm³ thus there's a difference between the pure gold cube and the gold cube,thus this shows that the gold cube with side 2cm is not a pure gold cube.

2. Q1.
(a)\$3.50/l
(b)72 vases/day
(c)376 words/min
(d)\$80/m²
(e)4kg/m
(f)60g/egg

Q2.
(a)\$23/h
(b)\$920/week

Q3.
(a)9km/l
(b)\$1.20/l

Q4.
(a)87.5g/cube
(b)\$1.20/l

Q5.
(a)\$15/ticket
(b)\$150

Q6.
(a)\$22.50/m²
(b)\$450

Q7.
(a)27l
(b)3 min

Q8.
(a)\$26
(b)25g
(c)Mass:3 kg Cost:\$78

Q9.
(a)\$201 600
(b)\$4200/m²

Q10.
(a)19.3g
(b)No, its is not made of pure gold as pure gold's mass per cm³ is 19.3g as calculated using the first block which is a pure gold block, but the second block's mass per cm³ is 15g so it cannot be entirely made of pure gold as the their mass per cm³ are different.

3. Q1. (a) \$3.50/l
(b) 72 vases/day
(c) 47 words/min
(d) \$80/m²
(e) 4kg/m
(f) 60g/egg

Q2. (a) \$23/h
(b) \$920/week

Q3. (a) 9km/l
(b) \$1.20/l

Q4. (a) 87.6g/wooden cube
(b) 0.7g/cm³

Q5. (a) \$15/concert tickets
(b) \$150

Q6. (a) \$22.50/m²
(b) \$450

Q7. (a) 27l/min
(b) 3 min

Q8. (a) \$26/kg
(b) 25g
(c) Mass: 3000g Cost: \$78

Q9. (a) \$201600
(b) \$4200/m²

Q10. (a) 19.3g/cm³
(b) No, it is not made of pure gold. As calculated, the mass of a pure gold cube is 19.3g/cm³but the mass of the another gold cube is 15g/cm³. The masses of the two different cubes are different so the gold cube could not possibly be made of pure gold.

4. 1. (a)\$3.50/litre
(b)72vases/day
(c)47words/min
(d)\$80/m^2
(e)4kg/m
(f)60g/egg

2. (a)\$23/hour
(b)\$920/week

3. (a)9Km/litre
(b)\$1.20/litre

4. (a)87.5g/cube
(b)0.7g/cm^3 of cube

5. (a)\$15/ticket
(b)\$50

6. (a)\$22.50/m^2
(b)\$450

7. (a)27litres/minute
(b)3minutes

8. (a)\$26/Kg
(b)25g
(c)mass=3Kg
cost=\$78

9. (a)\$201000
(b)\$4200/m^2

10.(a)19.3g/cm^3
(b)No because its mass per cm^3 is 15 while the mass of pure gold per cm^3 is 19.3g. Since their mass per cm^3 is different, the second gold cube is not made of pure gold.

5. Q1
a. \$3.50/l
b. 72 vases/day
c. 47 words/min
d. \$80/m^2
e. 4kg/m
f. 60g/egg
Q2.
a. \$23/hr
b. \$920/wk
Q3
a. 9km/l
b. 1.20/l
Q4
a. 87.5g/cube
b. 0.7g/cm^3 of cube
Q5
a \$15/ticket
b \$150
Q6
a. \$22.50/m^2
b. \$450
Q7
a. 27l/min
b. 3 min
Q8
a. \$26
b. 25g
c. 3kg, \$78
Q9
a. \$201 600
b. \$4200/m^2
Q10
a.19.3g
b. Nope, it is not made of pure gold. It is lighter than what pure gold should weigh as its mass of gold per cm^3 is 15g/cm^3 while the mass of pure gold per cm^3 is 19.3g/cm^3.

6. Q1.
(a)\$3.50/l
(b)72 vases/day
(c)47 words/min
(d)\$80/m²
(e)4kg/m
(f)60g/egg

Q2.
(a)\$23/h
(b)\$920/week

Q3.
(a)9km/l
(b)\$1.20/l

Q4.
(a)87.5g/cube
(b)0.7 m/cm3

Q5.
(a)\$15/ticket
(b)\$150

Q6.
(a)\$22.50/m²
(b)\$450

Q7.
(a)27l
(b)3 min

Q8.
(a)\$26
(b)25g
(c)Mass:3 kg Cost:\$78

Q9.
(a)\$201 600
(b)\$4200/m²

Q10.
(a)19.3g
(b)No, its is not made of pure gold as the first block of pure gold is already 120g thus if this block is made of pure gold, it should have lesser mass. Thus, this block is not made of pure gold.

7. Q1.
(a) \$3.50/litre
(b)72 vases/day
(c)47 words/minute
(d)\$80/m^2
(e)4kg/m
(f)60g/egg

Q2.
(a)\$23/hour
(b)\$920/week

Q3.
(a)9km/litre
(b)\$1.20/litre

Q4.
(a)87.5g/cube
(b)0.7g/cm^3 of cube

Q5.
(a)\$15/ticket
(b)\$150

Q6.
(a)\$22.5/m^2
(b)\$450

Q7.
(a)27litres/minute
(b)3 minutes

Q8.
(a)\$26/kg
(b)25g/m^2
(c)3kg

Q9.
(a)\$201,600
(b)\$4,200/m^2

Q10.
(a)19.3g/cm^3
(b)No, it is not made of pure gold as 8cm^2 of pure gold should weigh 154.4g, while this block weighs only 120g. Thus, this block has impurities and is not made of pure gold.

8. Q1-
(a) \$3.50/litre
(b) 72 vases/day
(c) 47 wrods/minute
(d) \$80/m^2
(e) 4kg/m
(f) 60g/egg

Q2-
(a) \$23/hour
(b) \$920/week

Q3-
(a) 9litres/km
(b) \$1.20/litre

Q4-
(a) 87.5g/cube
(b) 0.7g/cm^3 of cube

Q5-
(a) \$15/ticket
(b) \$150

Q6-
(a) \$22.5/m^2
(b) \$450

Q7-
(a) 27litres/min
(b) 3 minutes

Q8-
(a) \$26/kg
(b) 25g/m^2
(c) 3kg, \$78

Q9-
(a) \$201 600
(b) \$4 200/m^2

Q10-
(a) 19.3g/cm^3
(b) No, the god cube would not have been made of pure gold. The volume of that 2cm by 2cm by 2cm cube is 8cm^3. While the mass of pure gold per cm^3 is 19.3g, thus the mass of the 2cm cube should be 8 x 19.3 = 154.4 not 120.

9. 1. a) 4.5/litre
b) 72vases/day
c)47words/min
d)\$80/m^2
e)4kg/m
f)60g/egg

2. a) \$23/hr
b) \$920/wk

3. a) 9km/litre
b)\$1.20/litre

4. a)87.5g/cube
b) 0.7g/cm^3 of a cube

5. a) \$15/ticket
b) \$150

6. a) \$22.50/m^2
b) \$450

7. a) 27litre/min
b) 3 min

8. a) \$26
b) 25g
c) 3kg , \$78

9. a) \$201600
b) \$4200

10. a) 19.3g/m^3
b) No , it is not made of pure gold . real gold has the mass of 19.3g/m^3 but the gold that is not pure has the mass of 15g/m^3

10. 1. a) \$3.50/l
b) 70 vases/ day
c) 47 words/ min
d) \$80/ m^2
e) 4 kg/ m
f) 60 g/ egg

2. a) \$23/ h
b) \$920/ week

3. a) 9km/l
b) \$1.20/l

4. a) 87.5g
b) 0.7g

5. a) \$15
b) \$150

6. a) \$22.50
b) \$450

7. a) 27 litre
b) 3 minute

8. a) \$26
b) 25g
c) Mass: 3kg
Cost: \$78

9. a) \$201 600
b) \$4200

10. a) 19.3g
b) No, it is not. The mass of pure gold per m^3 is supposed to be 19.3g. However, the mass of this gold per m^3 is 15g. Both masses are different when they are supposed to be same if the gold is pure gold.

11. 1.
a) \$3.50/l
b) 72vases/day
c) 47words/day
d) \$80/m^2
e) 4kg/m
f) 60g/egg
2.
a) \$23/h
b) \$920/week
3.
a) 9km/l
b) \$1.20/l
4.
a) 87.5g/cube
b) 0.7g/cm^3
5.
a) \$15
b) \$150
6.
a) \$22.5/m^3
b) \$450
7.
a) 27l/min
b) 3 minutes
8.
a) \$26/kg
b) 25g/m^2
c) 3000g of Fertiliser that costs \$78
9.
a) \$201600
b) \$4200/m^2
10.
a) 19.3g/cm^3
b) No, its density is not the same as Pure Gold.

12. Q1. (a) \$3.50/l
(b) 72 vases/day
(c) 47 words/min
(d) \$140/m^2
(e) 4 kg/m
(f) 60g/egg

Q2. (a) \$23/hour
(b) \$920/week

Q3. (a) 9km/l
(b) \$1.20/litre

Q4. (a) 87.5g/cube
(b) 0.7g/cm^3 of cube

Q5. (a) \$15/ticket
(b) \$150

Q6. (a) \$22.50/m^2
(b) \$450

Q7. (a) 27l/min
(b) 2 days 2 hours

Q8. (a) \$26/kg
(b) 25g/m^2
(c) 3kg, \$78

Q9. (a) \$201 600
(b) \$4200/m^2

Q10.(a) 19.3g/cm^3
(b) No, it is not made of pure gold. The mass of pure gold per cm^3 is 19.3g while this gold cube does not have the same density as this, thus it is not pure gold.

Nina

13. Basic Practice
1.
(a) \$3.5/ℓ
(b) 72 vases/day
(c) 47 words/min
(d) \$80/m²
(e) 4kg/m
(f) 60g/egg

2.
(a) \$23/h
(b) \$920/week

3.
(a) 9km/ℓ
(b) \$1.2/ℓ

4.
(a) 87.5g/cube
(b) 0.7g/cm³ of cube

5.
(a) \$15/ticket
(b) \$150

6.
(a) \$22.50/m²
(b) \$450

7.
(a) 27 ℓ/min
(b) 3 min

Maths@Work
8.
(a) \$26/kg
(b) 25g
(c) Mass: 3kg; Cost: \$78

9.
(a) \$201600
(b) No, it is not made of pure gold. This is because the mass of pure gold per cm³ is 19.3g while the mass of the gold per cm³ is 15g. Thus, the gold cube is not made of pure gold.

14. 1.
(a) \$3.50/ℓ
(b) 72vases/day
(c) 97words/min
(d) \$80//m²
(e) 4kg/m
(f) 60g/egg

2.
(a) \$4.60
(b) \$920

3.
(a) 9km/ℓ
(b) \$1.20/ℓ

4.
(a) 87.5g/cube
(b) 0.7g/cm³ of cube

5.
(a) \$85
(b) \$850

6.
(a) \$22.50/m²
(b) \$450

7.
(a) 27ℓ/min
(b) 3mins

8.
(a) \$26/kg
(b) 25g of fertiliser
(c) 3kg pack of fertiliser and \$78

9.
(a) \$201600
(b) \$4200/m²

10.
(a) 19.3g/cm^3
(b) No, it is not made of pure gold as the density of the gold cube is not the same as the pure gold cube.

15. 1.
(a) \$3.5ℓ
(b) 72 vases/day
(c) 47 words/min
(d) \$80/m^2
(e) 4kg/m
(f) 60g/egg

2.
(a) His hourly wage rate is \$23
(b) His weekly wage rate is \$920

3.
(a) The rate of petrol consumption is 9km/litter
(b) The price of petrol per litter was \$1.20

4.
(a) The mass of per cube is 87.5g
(b) The mass per cm^3

5.
(a) The price per ticket was \$15
(b) The price of 10 tickets was \$150

6.
(a) The price of laying floor tiles per m^2 was \$22.50
(b) The price of laying 20m^2 of floor tiles was \$450

7.
(a) It delivers 27 litres/minute
(b) It will take the pipe 3 minutes to fill the empty tank completely with water.

8.
(a) The cost of fertiliser per kg is \$26
(b) 25g of fertiliser can be applied to 1m^2 of lawn
(c) The mass of the fertiliser required for the lawn is 3kg. The cost of the fertiliser required for the lawn is \$78

9.
(a) Jenny paid \$201 600
(b) The price per m^2 of the apartment was \$4200

10.
(a) The mass of pure gold per cm^3 is 19.3g
(b) No it is not made of pure gold. It's mass per cm^3 is only 15g, whereas the mass of pure gold per cm^3 is 19.3g.

16. 1. a)\$3.50/l
b)72 vases/day
c)47 words/min
d)\$80/m^2
e)4kg/m
f)60g/egg

2.a)\$23/h
b)\$920/week

3.a)9km/l
b)\$1.20/l

4.a)87.5g/cube
b)0.7g/cm^3

5.a)\$15/ticket
b)\$150

6.a)\$22.50/m^2
b)\$450

7.a)27l/min
b)3min

8.a)\$26/kg
b)25g/m^2
c)\$78

9.a)\$201 600
b)\$4200/m^2

10.a)19.3g/cm^2
b)2cm x 2cm x 2cm=8cm^3
120g/8cm^3=15g/cm^3
No it is not solid gold as the average rate of it is 15g/cm^3 while the proper average rate of a solid gold cube is 19.3g/cm^3.

17. ____________________ [ E X E R C I S E 9 . 2 ] ____________________

[1] a) \$3.50/ℓ
[1] b) 72 vases/day
[1] c) 47 words/min
[1] d) \$80/m^2
[1] e) 4kg/m
[1] f) 60g/egg

[2] a) \$23/hr
[2] b) \$920/week

[3] a) 9km/ℓ
[3] b) \$1.2/ℓ

[4] a) 87.5g/cube
[4] b) 525g/cm^3 of cube

[5] a) \$120 ÷ 8 = \$15/ticket
[5] b) \$15 x 10 = \$150
\$150 for 10 tickets

[6] a) \$270 ÷ 12m^2 = \$22.5/m^2
[6] b) \$22.5 x 20m^2 = \$450

[7] a) 1 min = 3 x 20s
9ℓ x 3 = 27ℓ/min

[7] b) 30 x 45 x 60 = 81000 cm^3
81000cm^3 = 81 ℓ
81ℓ ÷ 27ℓ = 3 min

[8] a) 500g = 0.5kg
\$13 ÷ 0.5kg = \$26/kg

[8] b) 500g ÷ 20m^2 = 25g/m^2

[8] c) 15 x 8 = 120
120 ÷ 20 = 6
6 x 800 = 3000
6 x 13 = \$78

[9] a) \$504 000 x 2/3 = \$201 600
[9] b) \$504 000 ÷ 120m^2 = \$4200/m^2

[10] a) 3 x 3 x 3 = 27
521.1 ÷ 27 = 19.3g/cm^2

[10] b) 2 x 2 x 2 = 8
120 ÷ 8 = 15
No, I don't think that it is made of pure gold as the mass doesn't seem to meet the average rate per cm^3.