Sec 4 G1 Maths Problems in real-world contexts worksheet with answers

A free Sec 4 G1 Maths worksheet on problems in real-world contexts: 8 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.

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.

Try a question: Problems in real-world contexts

Free · no sign-up

Answer a real practice question. Get it wrong and MugCorner shows you where it went wrong, with hints and a step-by-step guide.

MugCornerT-Leng Tuition · mugcornersg.com

Sec 4 G1 Maths worksheet: Problems in real-world contexts

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

Bus stop	Bus 1	Bus 2	Bus 3	Bus 4	Bus 5
Ferry Terminal	1830	1844	1900	1917	1935
Community Club	1839	1853	1909	1926	1944
Park	1847	1901	1917	1934	1952
Hospital	1854	1908	1924	1941	1959
Interchange	1911	1925	1941	1958	2016

The table shows part of a bus timetable. Kumar reaches the Ferry Terminal stop at 1857 and takes the first bus that comes. Find the total time, in minutes, that Kumar takes from reaching the Ferry Terminal stop to arriving at the Hospital stop.

Answermin[2]

Hire of one bus	$420 (45 seats)
Entrance ticket	$18 per student (teachers free)

67 students and 5 teachers go on an excursion to the ArtScience Museum. They hire enough buses for everyone, and every student pays for an entrance ticket. The costs are shown in the table. The total cost is shared among the students only, and each student pays the same whole number of dollars, enough to cover the total cost. Find the least amount each student pays.

Answer$[2]

The diagram shows the floor plan of a flat. The bedroom walls are 2.6 m high. The door is 0.9 m wide and 2.1 m high, and there is one window 1.5 m wide and 1.2 m high. The walls (not the door or the window) are given two coats of paint. One tin of paint covers 24 m² for one coat and costs $36.80. Find the least cost of the paint.

Answer$[3]

Engine capacity (EC) in cc	Road tax for 6 months ($)
EC ≤ 600	$200 \times 0.782$
600 < EC ≤ 1000	$[200 + 0.125(\text{EC} - 600)] \times 0.782$
1000 < EC ≤ 1600	$[250 + 0.375(\text{EC} - 1000)] \times 0.782$
1600 < EC ≤ 3000	$[475 + 0.75(\text{EC} - 1600)] \times 0.782$

The table shows the road tax rates for cars. Mei Ling's car has an engine capacity of 1332 cc. Find the road tax Mei Ling pays for 6 months, correct to the nearest cent.

Answer$[3]

Month	January	February	March
Electricity used (kWh)	356	381	402

The table shows the electricity Ali's household used in three months. Retailer A charges a fixed price of 26.12 cents per kWh. Retailer B charges 10% less than the tariff of 28.4 cents per kWh. Both prices are before 9% GST. Which retailer is cheaper for these three months? Find the amount the household would pay that retailer, including GST, correct to the nearest cent.

Answer$[3]

Annual value	Tax rate (%)	Property tax payable ($)
On the first $12,000	0	0
On the next $28,000	4	1,120
On the first $40,000		1,120
On the next $10,000	6	600
On the first $50,000		1,720
On the next $25,000	10	2,500
On the first $75,000		4,220
On the next $10,000	14	1,400
On the first $85,000		5,620
On the next $15,000	20	3,000
On the first $100,000		8,620

Jun Jie's family lives in a flat with an annual value of $66,400. The table shows the property tax rates for owner-occupied homes. Find the property tax payable for the year.

Answer$[3]

Section B

(a)(i)A flight departs at 2350. Write down this time using the 12-hour clock.

Answer (a)(i)[1]

(a)(ii)A charity walk starts at 1015 and ends at 1150 the same day. Find the duration of the charity walk, in hours and minutes.

Answer (a)(ii)[1]

	Adult	Child
Package tour (flights and hotel)	$759	$529
Return flight only	$389	$289

(b)A family of 2 adults and 2 children plans a 3-night holiday in Tokyo. They can buy the package tour in the table, or buy return flights and book a hotel themselves. The hotel costs $212 per room per night, and they need 2 rooms. Which option is cheaper? Find the total cost of the cheaper choice.

Answer (b)$[2]

Ingredient	For 3 servings
rice	270 g
prawns	240 g
frozen peas	90 g
eggs	3 eggs
cooking oil	45 ml

(c)The table shows a recipe for prawn fried rice for 3 servings. Chen Wei has 1.6 kg of rice, 400 g of frozen peas and 22 eggs, and plenty of everything else. Find the greatest number of servings Chen Wei can make.

Answer (c)[2]

	Adult	Child
Package tour (flights and hotel)	$759	$529
Return flight only	$610	$458

(a)A family of 2 adults and 3 children plans a 3-night holiday in Seoul. They can buy the package tour in the table, or buy return flights and book a hotel themselves. The hotel costs $126 per room per night, and they need 2 rooms. Which option is cheaper? Find the total cost of the cheaper choice.

Answer (a)$[2]

Annual value	Tax rate (%)	Property tax payable ($)
On the first $12,000	0	0
On the next $28,000	4	1,120
On the first $40,000		1,120
On the next $10,000	6	600
On the first $50,000		1,720
On the next $25,000	10	2,500
On the first $75,000		4,220
On the next $10,000	14	1,400
On the first $85,000		5,620
On the next $15,000	20	3,000
On the first $100,000		8,620

(b)Chen Wei's family lives in a flat with an annual value of $54,600. The table shows the property tax rates for owner-occupied homes. Find the property tax payable for the year.

Answer (b)$[3]

City	Time zone
Singapore	UTC+8
London	UTC+0
Bangkok	UTC+7
Sydney	UTC+11

(c)The table shows the time zones of some cities. Chen Wei has a meeting in Bangkok at 1000 on 24 December, Bangkok time. The flight from Singapore takes 2 h 25 min, and getting from the airport to the meeting takes 1 h 35 min. Find the latest time and date, in Singapore time, at which the flight can leave Singapore.

Answer (c)[3]

END OF PAPER

Answers and worked solutions

Question 1

Answer:

= 0 \text{ h } 27 \text{ min}

[2]

Bus 3 (at the Ferry Terminal stop at 1900).

19 \text{ h } 24 \text{ min} = 18 \text{ h } 84 \text{ min} \quad (1 \text{ h} = 60 \text{ min})

18 \text{ h } 84 \text{ min} - 18 \text{ h } 57 \text{ min}

= 0 \text{ h } 27 \text{ min}

It takes 27 minutes altogether.

Question 2

Answer: Each student pays $31 (rounding down would not cover the cost).[2]

67 + 5 = 72

\dfrac{72}{45} = 1.6 \rightarrow 2 \text{ buses}

2 \times 420 + 67 \times 18 = 2046

\dfrac{2046}{67} = 30.537\ldots \rightarrow 31

Each student pays $31 (rounding down would not cover the cost).

Question 3

Answer: The paint costs $147.20.[3]

2 \times (3.8 + 5.2) = 18

18 \times 2.6 = 46.8

\text{door: } 0.9 \times 2.1 = 1.89

\text{window: } 1.5 \times 1.2 = 1.8

46.8 - 1.89 - 1.8 = 43.11 \text{ m}^2

43.11 \times 2 = 86.22 \text{ m}^2

\dfrac{86.22}{24} = 3.592\ldots \rightarrow 4 \text{ tins}

4 \times 36.80 = 147.20

The paint costs $147.20.

Question 4

Answer: The road tax for 6 months is $292.86.[3]

1000 < 1332 \leq 1600

\text{EC} - 1000 = 1332 - 1000

\phantom{\text{EC} - 1000} = 332

250 + 0.375(332) = 374.5

374.5 \times 0.782 = 292.859

\approx 292.86

(to the nearest cent)The road tax for 6 months is $292.86.

Question 5

Answer: Retailer B is cheaper: the household would pay $317.33.[3]

356 + 381 + 402 = 1139 \text{ kWh}

\dfrac{1139 \times 26.12}{100} = 297.5068

28.4 \times \dfrac{90}{100} = 25.56 \text{ cents per kWh}

\dfrac{1139 \times 25.56}{100} = 291.1284

291.1284 \times \dfrac{109}{100} = 317.329956

\approx 317.33

(to the nearest cent)Retailer B is cheaper: the household would pay $317.33.

Question 6

Answer: The property tax is $3,360.[3]

\text{Tax on the first } 50000 \rightarrow 1720

\text{Rest} = 66400 - 50000

\phantom{\text{Rest}} = 16400

\dfrac{10}{100} \times 16400 = 1640

1720 + 1640 = 3360

The property tax is $3,360.

Question 7

(a)(i)Answer: 11.50 p.m.[1]

2350 is p.m. (from noon).

23 - 12 = 11

So 2350 is 11.50 p.m..

(a)(ii)Answer:

= 1 \text{ h } 35 \text{ min}

[1]

11 \text{ h } 50 \text{ min} - 10 \text{ h } 15 \text{ min}

= 1 \text{ h } 35 \text{ min}

It takes 1 h 35 min.

(b)Answer: The package tour is cheaper: $2,576 altogether, $52 less.[2]

2 \times 759 + 2 \times 529 = 2576

2 \times 389 + 2 \times 289 = 1356

212 \times 2 \times 3 = 1272

1356 + 1272 = 2628

The package tour is cheaper: $2,576 altogether, $52 less.

(c)Answer:

\text{eggs: } \dfrac{22}{1} = 22 \rightarrow 22

[2]

\text{rice: } \dfrac{1600}{90} = 17.777\ldots \rightarrow 17

\text{frozen peas: } \dfrac{400}{30} = 13.333\ldots \rightarrow 13

\text{eggs: } \dfrac{22}{1} = 22 \rightarrow 22

The frozen peas runs out first: at most 13 servings.

Question 8

(a)Answer: The package tour is cheaper: $3,105 altogether, $245 less.[2]

2 \times 759 + 3 \times 529 = 3105

2 \times 610 + 3 \times 458 = 2594

126 \times 2 \times 3 = 756

2594 + 756 = 3350

The package tour is cheaper: $3,105 altogether, $245 less.

(b)Answer: The property tax is $2,180.[3]

\text{Tax on the first } 50000 \rightarrow 1720

\text{Rest} = 54600 - 50000

\phantom{\text{Rest}} = 4600

\dfrac{10}{100} \times 4600 = 460

1720 + 460 = 2180

The property tax is $2,180.

(c)Answer:

= 7 \text{ h } 0 \text{ min}

[3]

10 \text{ h } 0 \text{ min} = 9 \text{ h } 60 \text{ min} \quad (1 \text{ h} = 60 \text{ min})

9 \text{ h } 60 \text{ min} - 1 \text{ h } 35 \text{ min}

= 8 \text{ h } 25 \text{ min}

It stays on the same day.

8 \text{ h } 25 \text{ min} - 2 \text{ h } 25 \text{ min}

= 6 \text{ h } 0 \text{ min}

8 - 7 = 1

Bangkok is 1 h behind Singapore.

6 \text{ h } 0 \text{ min} + 1 \text{ h}

= 7 \text{ h } 0 \text{ min}

Latest departure, Singapore time: 0700 on 24 December.

Sec 4 G1 Maths Problems in real-world contexts 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.

Try a question: Problems in real-world contexts

Free · no sign-up

Answer a real practice question. Get it wrong and MugCorner shows you where it went wrong, with hints and a step-by-step guide.

MugCornerT-Leng Tuition · mugcornersg.com

Sec 4 G1 Maths worksheet: Problems in real-world contexts

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

Bus stop	Bus 1	Bus 2	Bus 3	Bus 4	Bus 5
Ferry Terminal	1830	1844	1900	1917	1935
Community Club	1839	1853	1909	1926	1944
Park	1847	1901	1917	1934	1952
Hospital	1854	1908	1924	1941	1959
Interchange	1911	1925	1941	1958	2016

Answermin[2]

Hire of one bus	$420 (45 seats)
Entrance ticket	$18 per student (teachers free)

Answer$[2]

Answer$[3]

Engine capacity (EC) in cc	Road tax for 6 months ($)
EC ≤ 600	$200 \times 0.782$
600 < EC ≤ 1000	$[200 + 0.125(\text{EC} - 600)] \times 0.782$
1000 < EC ≤ 1600	$[250 + 0.375(\text{EC} - 1000)] \times 0.782$
1600 < EC ≤ 3000	$[475 + 0.75(\text{EC} - 1600)] \times 0.782$

The table shows the road tax rates for cars. Mei Ling's car has an engine capacity of 1332 cc. Find the road tax Mei Ling pays for 6 months, correct to the nearest cent.

Answer$[3]

Month	January	February	March
Electricity used (kWh)	356	381	402

Answer$[3]

Annual value	Tax rate (%)	Property tax payable ($)
On the first $12,000	0	0
On the next $28,000	4	1,120
On the first $40,000		1,120
On the next $10,000	6	600
On the first $50,000		1,720
On the next $25,000	10	2,500
On the first $75,000		4,220
On the next $10,000	14	1,400
On the first $85,000		5,620
On the next $15,000	20	3,000
On the first $100,000		8,620

Jun Jie's family lives in a flat with an annual value of $66,400. The table shows the property tax rates for owner-occupied homes. Find the property tax payable for the year.

Answer$[3]

Section B

(a)(i)A flight departs at 2350. Write down this time using the 12-hour clock.

Answer (a)(i)[1]

(a)(ii)A charity walk starts at 1015 and ends at 1150 the same day. Find the duration of the charity walk, in hours and minutes.

Answer (a)(ii)[1]

	Adult	Child
Package tour (flights and hotel)	$759	$529
Return flight only	$389	$289

Answer (b)$[2]

Ingredient	For 3 servings
rice	270 g
prawns	240 g
frozen peas	90 g
eggs	3 eggs
cooking oil	45 ml

Answer (c)[2]

	Adult	Child
Package tour (flights and hotel)	$759	$529
Return flight only	$610	$458

Answer (a)$[2]

Annual value	Tax rate (%)	Property tax payable ($)
On the first $12,000	0	0
On the next $28,000	4	1,120
On the first $40,000		1,120
On the next $10,000	6	600
On the first $50,000		1,720
On the next $25,000	10	2,500
On the first $75,000		4,220
On the next $10,000	14	1,400
On the first $85,000		5,620
On the next $15,000	20	3,000
On the first $100,000		8,620

(b)Chen Wei's family lives in a flat with an annual value of $54,600. The table shows the property tax rates for owner-occupied homes. Find the property tax payable for the year.

Answer (b)$[3]

City	Time zone
Singapore	UTC+8
London	UTC+0
Bangkok	UTC+7
Sydney	UTC+11

Answer (c)[3]

END OF PAPER

Answers and worked solutions

Question 1

Answer:

= 0 \text{ h } 27 \text{ min}

[2]

Bus 3 (at the Ferry Terminal stop at 1900).

19 \text{ h } 24 \text{ min} = 18 \text{ h } 84 \text{ min} \quad (1 \text{ h} = 60 \text{ min})

18 \text{ h } 84 \text{ min} - 18 \text{ h } 57 \text{ min}

= 0 \text{ h } 27 \text{ min}

It takes 27 minutes altogether.

Question 2

Answer: Each student pays $31 (rounding down would not cover the cost).[2]

67 + 5 = 72

\dfrac{72}{45} = 1.6 \rightarrow 2 \text{ buses}

2 \times 420 + 67 \times 18 = 2046

\dfrac{2046}{67} = 30.537\ldots \rightarrow 31

Each student pays $31 (rounding down would not cover the cost).

Question 3

Answer: The paint costs $147.20.[3]

2 \times (3.8 + 5.2) = 18

18 \times 2.6 = 46.8

\text{door: } 0.9 \times 2.1 = 1.89

\text{window: } 1.5 \times 1.2 = 1.8

46.8 - 1.89 - 1.8 = 43.11 \text{ m}^2

43.11 \times 2 = 86.22 \text{ m}^2

\dfrac{86.22}{24} = 3.592\ldots \rightarrow 4 \text{ tins}

4 \times 36.80 = 147.20

The paint costs $147.20.

Question 4

Answer: The road tax for 6 months is $292.86.[3]

1000 < 1332 \leq 1600

\text{EC} - 1000 = 1332 - 1000

\phantom{\text{EC} - 1000} = 332

250 + 0.375(332) = 374.5

374.5 \times 0.782 = 292.859

\approx 292.86

(to the nearest cent)The road tax for 6 months is $292.86.

Question 5

Answer: Retailer B is cheaper: the household would pay $317.33.[3]

356 + 381 + 402 = 1139 \text{ kWh}

\dfrac{1139 \times 26.12}{100} = 297.5068

28.4 \times \dfrac{90}{100} = 25.56 \text{ cents per kWh}

\dfrac{1139 \times 25.56}{100} = 291.1284

291.1284 \times \dfrac{109}{100} = 317.329956

\approx 317.33

(to the nearest cent)Retailer B is cheaper: the household would pay $317.33.

Question 6

Answer: The property tax is $3,360.[3]

\text{Tax on the first } 50000 \rightarrow 1720

\text{Rest} = 66400 - 50000

\phantom{\text{Rest}} = 16400

\dfrac{10}{100} \times 16400 = 1640

1720 + 1640 = 3360

The property tax is $3,360.

Question 7

(a)(i)Answer: 11.50 p.m.[1]

2350 is p.m. (from noon).

23 - 12 = 11

So 2350 is 11.50 p.m..

(a)(ii)Answer:

= 1 \text{ h } 35 \text{ min}

[1]

11 \text{ h } 50 \text{ min} - 10 \text{ h } 15 \text{ min}

= 1 \text{ h } 35 \text{ min}

It takes 1 h 35 min.

(b)Answer: The package tour is cheaper: $2,576 altogether, $52 less.[2]

2 \times 759 + 2 \times 529 = 2576

2 \times 389 + 2 \times 289 = 1356

212 \times 2 \times 3 = 1272

1356 + 1272 = 2628

The package tour is cheaper: $2,576 altogether, $52 less.

(c)Answer:

\text{eggs: } \dfrac{22}{1} = 22 \rightarrow 22

[2]

\text{rice: } \dfrac{1600}{90} = 17.777\ldots \rightarrow 17

\text{frozen peas: } \dfrac{400}{30} = 13.333\ldots \rightarrow 13

\text{eggs: } \dfrac{22}{1} = 22 \rightarrow 22

The frozen peas runs out first: at most 13 servings.

Question 8

(a)Answer: The package tour is cheaper: $3,105 altogether, $245 less.[2]

2 \times 759 + 3 \times 529 = 3105

2 \times 610 + 3 \times 458 = 2594

126 \times 2 \times 3 = 756

2594 + 756 = 3350

The package tour is cheaper: $3,105 altogether, $245 less.

(b)Answer: The property tax is $2,180.[3]

\text{Tax on the first } 50000 \rightarrow 1720

\text{Rest} = 54600 - 50000

\phantom{\text{Rest}} = 4600

\dfrac{10}{100} \times 4600 = 460

1720 + 460 = 2180

The property tax is $2,180.

(c)Answer:

= 7 \text{ h } 0 \text{ min}

[3]

10 \text{ h } 0 \text{ min} = 9 \text{ h } 60 \text{ min} \quad (1 \text{ h} = 60 \text{ min})

9 \text{ h } 60 \text{ min} - 1 \text{ h } 35 \text{ min}

= 8 \text{ h } 25 \text{ min}

It stays on the same day.

8 \text{ h } 25 \text{ min} - 2 \text{ h } 25 \text{ min}

= 6 \text{ h } 0 \text{ min}

8 - 7 = 1

Bangkok is 1 h behind Singapore.

6 \text{ h } 0 \text{ min} + 1 \text{ h}

= 7 \text{ h } 0 \text{ min}

Latest departure, Singapore time: 0700 on 24 December.