Chap 9.2 RATE (L4) Self-Paced Learning Materials

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
  • Additional Arithmetic
  • Ratio, Rate and Speed: Choose Rate
(a) Go through video lessons: Rate, Average Rate, Example 1, Example 2
(b) Try Practice Drills on your own to check your understanding
(c) Attempt Acelearning Quiz: Chap 9.2 Rate Quiz 1 (This has been assigned to you on 1 May 2010).
You are expected to complete Chapter 9.2 on your own by 15 May 2010.
As this chapter is not going to be covered in the class, please check/clarify with Ms Loh (Face-to-face or virtually) when you are in doubt or need help.
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Answers to Exercise 9.2

Basic Practice
No. 1
(a) A 2 litre bottle of peanut oil costs $7
The price rate is $3.50 /l

(b) A company produces 360 vases in 5 days
The rate of production is 72 vases/day

(c) Huili typed 376 words in 8 minutes
Her rate of typing is 47 words/min

(d)  A carpet of area 3 m² costs $240.
The price rate is $80/m²

(e) The mass of a 2.5-m metal bar is 10 kg
The rate of mass is 4 kg/m

(f) The mass of 12 eggs is 720g
The rate of mass is 60g/egg

No. 2
Rahman works 5 days a week and 8 hours a day. His daily wage is $184.
(a) Find his hourly wage rate.
Since his daily wage is $184 and he works for 8 hours a day,
His hourly wage rate = $184 ÷ 8 = $23/h

(b) Find his weekly wage rate.
Since he works for 5 days a week,
His weekly wage rate = $184 x 5 = $920/week

No. 3
A car travelled 225 km on 25 litres of petrol. The price of the petrol consumed was $30.
(a) Find the rate of petrol consumption in km/litre
Since the car consumes 25 litres of petrol in 225 km
The rate of consumption (i.e. distance the car could travel with 1 litre of petrol)
= 225 km ÷ 25 litres 
= 9 km/litre

(b) What is the price of petrol per litre?
Since 25 litres of petrol cost $30,
The price of petrol per litre = $30 ÷ 25
= $1.20/litre

No. 4
There are 6 wooden cubes, each of side 5 cm. Their total mass is 525 g. Find the mass per
(a) cube
(b) cm³ of cube.

(a) Mass of each cube = 525g ÷ 6
= 87.5 g
(b) Volume of each cube = 5 x 5 x 5 cm³
= 125 cm³
Hence, mass per cm³ of cube = 87.5g ÷ 125cm³
= 0.7 g/cm³

Further Practice
No. 5
John spent $120 on 8 concert tickets
(a) Find the price per ticket
Price per ticket = $120 ÷ 8
= $15

(b) Find the price of 10 tickets
Price of 10 tickets = $15 x 10
= $150

No. 6
The price of laying 12 m² of floor tiles is $270.
(a) Find the price of laying floor tiles per m².
Price of laying floor tiles per m² = $270 ÷ 12
= $22.50

(b) Find the price of laying 20 m² of floor files.
Price = $22.50 x 20
= $450

No. 7
A pipe delivers 9 litres of water in 20 seconds.
(a) Find the amount of water it delivers per minute.
In 20 seconds, it delivers 9 litres
In 60 seconds (i.e. 20 seconds x 3), it delivers (9 litres x 3 =) 27 litres of water per minute

(b) An empty fish tank is 60 cm long, 45 cm wide and 30 cm high. How long does it take for the pipe to fill the tank completely with water?
Volume of Tank = 60 x 45 x 30 cm³
= 81000 cm³
Since 1 litre = 1000 cm³, then 81000 cm³ is equivalent to 81 litres
Hence, time taken to fill the tank = 81 litres ÷ 27
= 3 minutes

Maths@Work
No. 8
A 500-g pack of fertiliser that costs $13 can be applied to 20 m² of lawn.
(a) What is the cost of the fertiliser per kg?
Since 500g costs $13 and 2x500g makes 1 kg
Hence, cost of fertiliser per kg = $26/kg

(b) Find the mass of the fertiliser that can be applied ot 1 m² of lawn.
Since 20 m² of land requires 500g,
Then 1 m² of land will require (500g ÷ 20 =) 25 g of fertiliser

(c) A rectangular lawn measures 15 m x 8 m. Find the mass and cost of the fertiliser required for the lawn.
Area of lawn = 120 m²
Mass of fertiliser required = 120 m² x 25
= 3000 g = 3 kg

Cost of fertiliser = 3 x $26
= $78

No. 9
The price of an apartment of area 120 m² is $504 000.
Jenny and her mother shared the cost of such apartment in the ratio of 2:3.
(a) How much did Jenny pay?
Since Jenny paid 2 out of 5 parts, amount she paid = $504 000/5 x 2
= $201 600

(b) What was the price per m² of the apartment?
Since 120 m² cost $504 000,
Cost of 1 m² = $504 000 ÷ 120
= $4200/m²

No. 10
A pure gold cube is of side 3 cm. Its mass is 521.1g
(a) Find the mass of pure gold per cm³.
Volume of cube = 3 x 3 x 3 cm³ = 27 cm³
Mass of pure gold per cm³ = 521.1g ÷ 27 cm³
= 19.3 g/cm³ {This is also known as the density, which is the same for all pure elements}

(b) Another gold cube is of side 2 cm. Its mass is 120g.
Is it made of pure gold? Explain briefly.
Volume of cube = 2 x 2 x 2 cm³ = 8 cm³
Density = 120 g ÷ 8 cm³
= 15 g/cm³
In 1 cm³, we could only find 15g of gold instead of 19.3g.
Hence the cube is not made of pure gold.