Sec 1 Maths Ratio, rate and speed worksheet with answers

A free Sec 1 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 Maths worksheet: Ratio, rate and speed

Total: 30 marksSuggested time: 45 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

Previous meter reading	Current meter reading	Rate
45108 kWh	45460 kWh	30 cents per kWh

The table shows a household's electricity meter readings for a month and the rate charged. Find the cost of the electricity used, in dollars.

Answer$[2]

The distance–time graph shows Jun Jie's drive from Town P. Find Jun Jie's speed from A to B, in km/h.

Answerkm/h[2]

A car travels at a constant speed of 60 km/h for 12 minutes. Find the distance it travels, in km.

Answerkm[2]

(a)Express

1.8 : 2.4

in its simplest form.

Answer (a)[2]

(b)Express the ratio

40

:

1.5

m in its simplest form.

Answer (b)[2]

Section B

Currency	S$1 buys
Thai baht (THB)	26.2
Hong Kong dollars (HK$)	5.85
US dollars (US$)	0.76

(a)The table shows a money changer's exchange rates. Jun Jie changes S$120 into US dollars. Find the amount, in US dollars, that Jun Jie receives. Give your answer correct to 2 decimal places where necessary.

Answer (a)[2]

(b)(i)Express

12 : 18 : 30

in its simplest form.

Answer (b)(i)[2]

(b)(ii)Express

0.35 : 0.7

in its simplest form.

Answer (b)(ii)[2]

Currency	S$1 buys
Japanese yen (¥)	108
Australian dollars (A$)	1.2
US dollars (US$)	0.75

(a)The table shows a money changer's exchange rates. Ravi changes S$120 into Japanese yen. Find the amount, in Japanese yen, that Ravi receives. Give your answer correct to 2 decimal places where necessary.

Answer (a)[1]

(b)Water flows from a tap at 12 litres per minute. Find the volume of water, in litres, that flows out in 8 minutes.

Answer (b)[2]

(c)(i)A go-kart travels at a constant speed of 45 km/h. Each of its wheels has a diameter of 28 cm and turns without slipping. Find the number of complete turns (revolutions) each wheel makes in one minute, correct to the nearest whole number.

Answer (c)(i)[2]

(c)(ii)An electric scooter travels at a constant speed of 20 km/h. Each of its wheels has a diameter of 25 cm and turns without slipping. Find the number of complete turns (revolutions) each wheel makes in one minute, correct to the nearest whole number.

Answer (c)(ii)[2]

Previous meter reading	Current meter reading	Rate
24315 kWh	24725 kWh	27.5 cents per kWh

(a)The table shows a household's electricity meter readings for a month and the rate charged. Find the cost of the electricity used, in dollars.

Answer (a)$[2]

(b)The distance–time graph shows Jun Jie's walk from home and back again. Find Jun Jie's speed on the way back, from A to B, in km/h.

Answer (b)km/h[2]

(c)The ratio of Chen Wei's stamps to Jun Jie's stamps is

4 : 3

. The ratio of Jun Jie's stamps to Ravi's stamps is

2 : 3

. Find the ratio of Chen Wei's stamps to Jun Jie's stamps to Ravi's stamps.

Answer (c)[3]

END OF PAPER

Answers and worked solutions

Question 1

Answer: The electricity costs $105.60.[2]

45460 - 45108 = 352 \text{ kWh}

352 \times 30 = 10560 \text{ cents}

\dfrac{10560}{100} = 105.60

The electricity costs $105.60.

Question 2

Answer:

\phantom{\text{Speed}} = 40 \text{ km/h}

[2]

\text{Distance} = 110 - 40

\phantom{\text{Distance}} = 70 \text{ km}

From 0830 to 1015:

105

min

\text{Speed} = 70 \div \dfrac{105}{60}

\phantom{\text{Speed}} = 40 \text{ km/h}

Question 3

Answer: The distance is

12

km.[2]

12 \text{ min} = \dfrac{12}{60} \text{ h}

\phantom{12 \text{ min}} = 0.2 \text{ h}

\text{Distance} = 60 \times 0.2

= 12

The distance is

12

km.

Question 4

(a)Answer:

\phantom{18 : 24} = 3 : 4

[2]

1.8 : 2.4 = 1.8 \times 10 : 2.4 \times 10

\phantom{1.8 : 2.4} = 18 : 24

\text{HCF of } 18 \text{ and } 24 = 6

18 : 24 = \dfrac{18}{6} : \dfrac{24}{6}

\phantom{18 : 24} = 3 : 4

(b)Answer:

\phantom{40 : 150} = 4 : 15

[2]

1.5 \text{ m} = 1.5 \times 100 \text{ cm}

\phantom{1.5 \text{ m}} = 150 \text{ cm}

\text{HCF of } 40 \text{ and } 150 = 10

40 : 150 = \dfrac{40}{10} : \dfrac{150}{10}

\phantom{40 : 150} = 4 : 15

Question 5

(a)Answer: Jun Jie receives US$91.20.[2]

120 \times 0.76

= 91.20

Jun Jie receives US$91.20.

(b)(i)Answer:

\phantom{12 : 18 : 30} = 2 : 3 : 5

[2]

\text{HCF of } 12, 18 \text{ and } 30 = 6

12 : 18 : 30 = \dfrac{12}{6} : \dfrac{18}{6} : \dfrac{30}{6}

\phantom{12 : 18 : 30} = 2 : 3 : 5

(b)(ii)Answer:

\phantom{35 : 70} = 1 : 2

[2]

0.35 : 0.7 = 0.35 \times 100 : 0.7 \times 100

\phantom{0.35 : 0.7} = 35 : 70

\text{HCF of } 35 \text{ and } 70 = 35

35 : 70 = \dfrac{35}{35} : \dfrac{70}{35}

\phantom{35 : 70} = 1 : 2

Question 6

(a)Answer:

= 12960

[1]

120 \times 108

= 12960

Ravi receives ¥12960.

(b)Answer:

96

litres[2]

12 \times 8

= 96

96

litres

(c)(i)Answer:

\phantom{\text{Turns}} = 852.61\ldots \approx 853

[2]

\dfrac{45 \times 100\,000}{60} = 75000 \text{ cm}

\pi \times 28 = 87.96\ldots \text{ cm}

\text{Turns} = \dfrac{75000}{87.96\ldots}

\phantom{\text{Turns}} = 852.61\ldots \approx 853

(c)(ii)Answer:

\phantom{\text{Turns}} = 424.41\ldots \approx 424

[2]

\dfrac{20 \times 100\,000}{60} = 33333.33\ldots \text{ cm}

\pi \times 25 = 78.53\ldots \text{ cm}

\text{Turns} = \dfrac{33333.33}{78.53\ldots}

\phantom{\text{Turns}} = 424.41\ldots \approx 424

Question 7

(a)Answer: The electricity costs $112.75.[2]

24725 - 24315 = 410 \text{ kWh}

410 \times 27.5 = 11275 \text{ cents}

\dfrac{11275}{100} = 112.75

The electricity costs $112.75.

(b)Answer:

\phantom{\text{Speed}} = 4 \text{ km/h}

[2]

From

2

km to

0

km:

2

kmFrom 0750 to 0820:

30

min

\text{Speed} = 2 \div \dfrac{30}{60}

\phantom{\text{Speed}} = 4 \text{ km/h}

(c)Answer:

\text{Chen Wei} : \text{Jun Jie} : \text{Ravi} = 8 : 6 : 9

[3]

\text{LCM of } 3 \text{ and } 2 = 6

\text{Chen Wei} : \text{Jun Jie} = 4 : 3

\phantom{\text{Chen Wei} : \text{Jun Jie}} = 4 \times 2 : 3 \times 2

\phantom{\text{Chen Wei} : \text{Jun Jie}} = 8 : 6

\text{Jun Jie} : \text{Ravi} = 2 : 3

\phantom{\text{Jun Jie} : \text{Ravi}} = 2 \times 3 : 3 \times 3

\phantom{\text{Jun Jie} : \text{Ravi}} = 6 : 9

\text{Chen Wei} : \text{Jun Jie} : \text{Ravi} = 8 : 6 : 9

Practice questions by skill

Sec 1 Maths Ratio, rate and speed worksheet with answers

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

Need the formulas first? Read the Ratio, rate and speed notes. Or practise it online with step-by-step help when you get one wrong.

Previous meter reading

Current meter reading

Rate

45108 kWh

45460 kWh

30 cents per kWh

Section B

Currency	S$1 buys
Thai baht (THB)	26.2
Hong Kong dollars (HK$)	5.85
US dollars (US$)	0.76

Answer (a)[2]

(b)(i)Express

12 : 18 : 30

in its simplest form.

Answer (b)(i)[2]

(b)(ii)Express

0.35 : 0.7

in its simplest form.

Answer (b)(ii)[2]

Currency

S$1 buys

Japanese yen (¥)

108

Australian dollars (A$)

1.2

US dollars (US$)

0.75

Previous meter reading

Current meter reading

Rate

24315 kWh

24725 kWh

27.5 cents per kWh

Answers and worked solutions

Question 1

Answer: The electricity costs $105.60.[2]

45460 - 45108 = 352 \text{ kWh}

352 \times 30 = 10560 \text{ cents}

\dfrac{10560}{100} = 105.60

The electricity costs $105.60.

Question 2

Answer:

\phantom{\text{Speed}} = 40 \text{ km/h}

[2]

\text{Distance} = 110 - 40

\phantom{\text{Distance}} = 70 \text{ km}

From 0830 to 1015:

105

min

\text{Speed} = 70 \div \dfrac{105}{60}

\phantom{\text{Speed}} = 40 \text{ km/h}

Question 3

Answer: The distance is

12

km.[2]

12 \text{ min} = \dfrac{12}{60} \text{ h}

\phantom{12 \text{ min}} = 0.2 \text{ h}

\text{Distance} = 60 \times 0.2

= 12

The distance is

12

km.

Question 4

(a)Answer:

\phantom{18 : 24} = 3 : 4

[2]

1.8 : 2.4 = 1.8 \times 10 : 2.4 \times 10

\phantom{1.8 : 2.4} = 18 : 24

\text{HCF of } 18 \text{ and } 24 = 6

18 : 24 = \dfrac{18}{6} : \dfrac{24}{6}

\phantom{18 : 24} = 3 : 4

(b)Answer:

\phantom{40 : 150} = 4 : 15

[2]

1.5 \text{ m} = 1.5 \times 100 \text{ cm}

\phantom{1.5 \text{ m}} = 150 \text{ cm}

\text{HCF of } 40 \text{ and } 150 = 10

40 : 150 = \dfrac{40}{10} : \dfrac{150}{10}

\phantom{40 : 150} = 4 : 15

Question 5

(a)Answer: Jun Jie receives US$91.20.[2]

120 \times 0.76

= 91.20

Jun Jie receives US$91.20.

(b)(i)Answer:

\phantom{12 : 18 : 30} = 2 : 3 : 5

[2]

\text{HCF of } 12, 18 \text{ and } 30 = 6

12 : 18 : 30 = \dfrac{12}{6} : \dfrac{18}{6} : \dfrac{30}{6}

\phantom{12 : 18 : 30} = 2 : 3 : 5

(b)(ii)Answer:

\phantom{35 : 70} = 1 : 2

[2]

0.35 : 0.7 = 0.35 \times 100 : 0.7 \times 100

\phantom{0.35 : 0.7} = 35 : 70

\text{HCF of } 35 \text{ and } 70 = 35

35 : 70 = \dfrac{35}{35} : \dfrac{70}{35}

\phantom{35 : 70} = 1 : 2

Question 6

(a)Answer:

= 12960

[1]

120 \times 108

= 12960

Ravi receives ¥12960.

(b)Answer:

96

litres[2]

12 \times 8

= 96

96

litres

(c)(i)Answer:

\phantom{\text{Turns}} = 852.61\ldots \approx 853

[2]

\dfrac{45 \times 100\,000}{60} = 75000 \text{ cm}

\pi \times 28 = 87.96\ldots \text{ cm}

\text{Turns} = \dfrac{75000}{87.96\ldots}

\phantom{\text{Turns}} = 852.61\ldots \approx 853

(c)(ii)Answer:

\phantom{\text{Turns}} = 424.41\ldots \approx 424

[2]

\dfrac{20 \times 100\,000}{60} = 33333.33\ldots \text{ cm}

\pi \times 25 = 78.53\ldots \text{ cm}

\text{Turns} = \dfrac{33333.33}{78.53\ldots}

\phantom{\text{Turns}} = 424.41\ldots \approx 424

Question 7

(a)Answer: The electricity costs $112.75.[2]

24725 - 24315 = 410 \text{ kWh}

410 \times 27.5 = 11275 \text{ cents}

\dfrac{11275}{100} = 112.75

The electricity costs $112.75.

(b)Answer:

\phantom{\text{Speed}} = 4 \text{ km/h}

[2]

From

2

km to

0

km:

2

kmFrom 0750 to 0820:

30

min

\text{Speed} = 2 \div \dfrac{30}{60}

\phantom{\text{Speed}} = 4 \text{ km/h}

(c)Answer:

\text{Chen Wei} : \text{Jun Jie} : \text{Ravi} = 8 : 6 : 9

[3]

\text{LCM of } 3 \text{ and } 2 = 6

\text{Chen Wei} : \text{Jun Jie} = 4 : 3

\phantom{\text{Chen Wei} : \text{Jun Jie}} = 4 \times 2 : 3 \times 2

\phantom{\text{Chen Wei} : \text{Jun Jie}} = 8 : 6

\text{Jun Jie} : \text{Ravi} = 2 : 3

\phantom{\text{Jun Jie} : \text{Ravi}} = 2 \times 3 : 3 \times 3

\phantom{\text{Jun Jie} : \text{Ravi}} = 6 : 9

\text{Chen Wei} : \text{Jun Jie} : \text{Ravi} = 8 : 6 : 9