Sec 1 G2 Maths Ratio, rate and speed worksheet with answers

A free Sec 1 G2 Maths worksheet on ratio, rate and speed: 7 questions, 30 marks, short questions first and then structured ones, in the school exam style. The answers and full worked solutions are on the last page.

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Sec 1 G2 Maths worksheet: Ratio, rate and speed

Total: 30 marksSuggested time: 50 minutes

Name: ______________________________Class: ____________ Date: ____________

Answer all questions. Show all your working. Give non-exact answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless the question says otherwise.

Section A

A camera costs S$189 in Singapore. The same camera costs A$239 overseas, where S$1

=

A$1.15. Where is it cheaper? Show your working.

Answer[2]

A motorcyclist travels from A to B in 35 minutes and then from B to C in 40 minutes. The distances are shown in the diagram. Find the average speed for the whole journey, in km/h.

Answerkm/h[3]

(a)A van travels 135 km at a constant speed of 90 km/h. Find the time taken. Give your answer in hours and minutes.

Answer (a)[2]

(b)A cyclist moves at a constant speed of 4 m/s for 15 minutes. Find the distance covered, in km.

Answer (b)km[2]

Section B

Money changer	Rate
A	S$1 = ¥112.5
B	S$100 = ¥11137.5

(a)Devi wants to change S$200 into Japanese yen. The rates at two money changers are shown in the table. Which money changer gives Devi more Japanese yen?

Answer (a)[2]

(b)A train 150 m long travels at a constant speed of 54 km/h. It passes completely through a tunnel 1200 m long: from the moment its front reaches the tunnel to the moment its back leaves it. Find the time this takes, in seconds.

Answer (b)s[3]

(a)A leaking tap drips 12 ml of water every minute. Find the volume of water, in litres, it wastes in 6 hours.

Answer (a)[2]

(b)The aspect ratio of a rectangle is width : height. A video with an aspect ratio of

16 : 10

is shown on a screen with an aspect ratio of

21 : 9

. It is made as large as possible without being cut off, so it fills the full height of the screen, as shown in the diagram. Find the fraction of the screen that is not covered.

Answer (b)[3]

Packet	A	B
Volume	250 ml	500 ml
Price	$1.60	$3.50

(a)The table shows the sizes and prices of two packets of liquid detergent. Which packet is the best buy?

Answer (a)[2]

(b)Of the beads in a box,

\dfrac{1}{5}

are yellow. The rest are red and blue in the ratio

1 : 2

. There are 48 blue. Find the number of yellow.

Answer (b)[3]

(a)The distance–time graph shows Devi's cycle ride from home. Devi stopped once on the way. Find the length of time, in minutes, for which Devi stopped.

Answer (a)min[1]

(b)A car travels 180 km on 15 litres of petrol. Find its petrol consumption, in km per litre.

Answer (b)[2]

(c)A car travels from A to B and then from B to C, as shown in the diagram. The journey from A to B takes 1.5 hours and the journey from B to C takes 0.5 hours. Find the average speed for the whole journey, in km/h.

Answer (c)km/h[3]

END OF PAPER

Answers and worked solutions

Question 1

Answer: SG[2]

\dfrac{239}{1.15}

= 207.8261\ldots

\approx 207.83

(to the nearest cent)S$207.83 > S$189, so it is cheaper in Singapore.

Question 2

Answer:

\phantom{\text{Average speed}} = 33.6 \text{ km/h}

[3]

\text{Total distance} = 36 + 6

\phantom{\text{Total distance}} = 42 \text{ km}

\text{Total time} = \dfrac{35 + 40}{60}

\phantom{\text{Total time}} = 1.25 \text{ h}

\text{Average speed} = \dfrac{42}{1.25}

\phantom{\text{Average speed}} = 33.6 \text{ km/h}

Question 3

(a)Answer: Time taken

= 1

30

min[2]

\text{Time} = \dfrac{135}{90}

= 1.5

0.5 \text{ h} = 0.5 \times 60 \text{ min}

\phantom{0.5 \text{ h}} = 30 \text{ min}

Time taken

= 1

30

min

(b)Answer:

\dfrac{3600}{1000} = 3.6 \text{ km}

[2]

15 \text{ min} = 15 \times 60 \text{ s}

\phantom{15 \text{ min}} = 900 \text{ s}

\text{Distance} = 4 \times 900

= 3600

\dfrac{3600}{1000} = 3.6 \text{ km}

Question 4

(a)Answer: A[2]

\text{A: } 200 \times 112.5 = 22500

\dfrac{11137.5}{100} = 111.375

\text{B: } 200 \times 111.375 = 22275

Money changer A gives more Japanese yen.

(b)Answer:

\phantom{\text{Time}} = 90 \text{ s}

[3]

54 \text{ km/h} = \dfrac{54}{3.6}

\phantom{54 \text{ km/h}} = 15 \text{ m/s}

\text{Distance} = 1200 + 150

\phantom{\text{Distance}} = 1350 \text{ m}

\text{Time} = \dfrac{1350}{15}

\phantom{\text{Time}} = 90 \text{ s}

Question 5

(a)Answer:

\dfrac{4320}{1000} = 4.32 \text{ litres}

[2]

6 \text{ h} = 6 \times 60 \text{ min}

\phantom{6 \text{ h}} = 360 \text{ min}

12 \times 360 = 4320 \text{ ml}

\dfrac{4320}{1000} = 4.32 \text{ litres}

(b)Answer:

\dfrac{11}{35}

of the screen is not covered.[3]

\text{picture } 16 : 10 = 144 : 90

\text{screen } 21 : 9 = 210 : 90

\text{Covered} = \dfrac{144}{210}

\phantom{\text{Covered}} = \dfrac{24}{35}

1 - \dfrac{24}{35} = \dfrac{11}{35}

\dfrac{11}{35}

of the screen is not covered.

Question 6

(a)Answer: A[2]

\text{A: } \dfrac{1.60}{250} \times 100 = 0.64

\text{B: } \dfrac{3.50}{500} \times 100 = 0.7

Packet A costs the least for 100 ml ($0.64), so it is the best buy.

(b)Answer: There are

18

yellow.[3]

1 - \dfrac{1}{5} = \dfrac{4}{5}

\text{blue} = \dfrac{2}{3} \times \dfrac{4}{5}

\phantom{\text{blue}} = \dfrac{8}{15}

of the whole

\text{Whole} = 48 \div \dfrac{8}{15}

\phantom{\text{Whole}} = 48 \times \dfrac{15}{8}

\phantom{\text{Whole}} = 90

\dfrac{1}{5} \times 90 = 18

There are

18

yellow.

Question 7

(a)Answer:

\phantom{\text{Stop}} = 30 \text{ min}

[1]

The flat stage is AB.

\text{Stop} = 70 - 40

\phantom{\text{Stop}} = 30 \text{ min}

(b)Answer: The rate is

12

km per litre.[2]

\text{Rate} = \dfrac{180}{15}

= 12

The rate is

12

km per litre.

(c)Answer:

\phantom{\text{Average speed}} = 21 \text{ km/h}

[3]

\text{Total distance} = 24 + 18

\phantom{\text{Total distance}} = 42 \text{ km}

\text{Total time} = 1.5 + 0.5

\phantom{\text{Total time}} = 2 \text{ h}

\text{Average speed} = \dfrac{42}{2}

\phantom{\text{Average speed}} = 21 \text{ km/h}

Sec 1 G2 Maths Ratio, rate and speed worksheet with answers

In the print window, choose Save as PDF to download it.

Or practise it online with step-by-step help when you get one wrong.

Section B

Money changer	Rate
A	S$1 = ¥112.5
B	S$100 = ¥11137.5

(a)Devi wants to change S$200 into Japanese yen. The rates at two money changers are shown in the table. Which money changer gives Devi more Japanese yen?

Answer (a)[2]

Answer (b)s[3]

Packet

Volume

250 ml

500 ml

Price

$1.60

$3.50

Answers and worked solutions

Question 1

Answer: SG[2]

\dfrac{239}{1.15}

= 207.8261\ldots

\approx 207.83

(to the nearest cent)S$207.83 > S$189, so it is cheaper in Singapore.

Question 2

Answer:

\phantom{\text{Average speed}} = 33.6 \text{ km/h}

[3]

\text{Total distance} = 36 + 6

\phantom{\text{Total distance}} = 42 \text{ km}

\text{Total time} = \dfrac{35 + 40}{60}

\phantom{\text{Total time}} = 1.25 \text{ h}

\text{Average speed} = \dfrac{42}{1.25}

\phantom{\text{Average speed}} = 33.6 \text{ km/h}

Question 3

(a)Answer: Time taken

= 1

30

min[2]

\text{Time} = \dfrac{135}{90}

= 1.5

0.5 \text{ h} = 0.5 \times 60 \text{ min}

\phantom{0.5 \text{ h}} = 30 \text{ min}

Time taken

= 1

30

min

(b)Answer:

\dfrac{3600}{1000} = 3.6 \text{ km}

[2]

15 \text{ min} = 15 \times 60 \text{ s}

\phantom{15 \text{ min}} = 900 \text{ s}

\text{Distance} = 4 \times 900

= 3600

\dfrac{3600}{1000} = 3.6 \text{ km}

Question 4

(a)Answer: A[2]

\text{A: } 200 \times 112.5 = 22500

\dfrac{11137.5}{100} = 111.375

\text{B: } 200 \times 111.375 = 22275

Money changer A gives more Japanese yen.

(b)Answer:

\phantom{\text{Time}} = 90 \text{ s}

[3]

54 \text{ km/h} = \dfrac{54}{3.6}

\phantom{54 \text{ km/h}} = 15 \text{ m/s}

\text{Distance} = 1200 + 150

\phantom{\text{Distance}} = 1350 \text{ m}

\text{Time} = \dfrac{1350}{15}

\phantom{\text{Time}} = 90 \text{ s}

Question 5

(a)Answer:

\dfrac{4320}{1000} = 4.32 \text{ litres}

[2]

6 \text{ h} = 6 \times 60 \text{ min}

\phantom{6 \text{ h}} = 360 \text{ min}

12 \times 360 = 4320 \text{ ml}

\dfrac{4320}{1000} = 4.32 \text{ litres}

(b)Answer:

\dfrac{11}{35}

of the screen is not covered.[3]

\text{picture } 16 : 10 = 144 : 90

\text{screen } 21 : 9 = 210 : 90

\text{Covered} = \dfrac{144}{210}

\phantom{\text{Covered}} = \dfrac{24}{35}

1 - \dfrac{24}{35} = \dfrac{11}{35}

\dfrac{11}{35}

of the screen is not covered.

Question 6

(a)Answer: A[2]

\text{A: } \dfrac{1.60}{250} \times 100 = 0.64

\text{B: } \dfrac{3.50}{500} \times 100 = 0.7

Packet A costs the least for 100 ml ($0.64), so it is the best buy.

(b)Answer: There are

18

yellow.[3]

1 - \dfrac{1}{5} = \dfrac{4}{5}

\text{blue} = \dfrac{2}{3} \times \dfrac{4}{5}

\phantom{\text{blue}} = \dfrac{8}{15}

of the whole

\text{Whole} = 48 \div \dfrac{8}{15}

\phantom{\text{Whole}} = 48 \times \dfrac{15}{8}

\phantom{\text{Whole}} = 90

\dfrac{1}{5} \times 90 = 18

There are

18

yellow.

Question 7

(a)Answer:

\phantom{\text{Stop}} = 30 \text{ min}

[1]

The flat stage is AB.

\text{Stop} = 70 - 40

\phantom{\text{Stop}} = 30 \text{ min}

(b)Answer: The rate is

12

km per litre.[2]

\text{Rate} = \dfrac{180}{15}

= 12

The rate is

12

km per litre.

(c)Answer:

\phantom{\text{Average speed}} = 21 \text{ km/h}

[3]

\text{Total distance} = 24 + 18

\phantom{\text{Total distance}} = 42 \text{ km}

\text{Total time} = 1.5 + 0.5

\phantom{\text{Total time}} = 2 \text{ h}

\text{Average speed} = \dfrac{42}{2}

\phantom{\text{Average speed}} = 21 \text{ km/h}