Sec 4 G2 Maths Problems in real-world contexts worksheet with answers
A free Sec 4 G2 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.
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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
1
City
Time compared with Singapore
Bangkok
1 h behind Singapore
Sydney
3 h ahead of Singapore
The table shows the time differences between Singapore and some cities. Find the local time and date in Bangkok when it is 0635 on 23 March in Singapore.
Answer[1]
2
Adult
Child
Package tour (flights and hotel)
$899
$649
Return flight only
$389
$289
A family of 2 adults and 2 children plans a 4-night holiday in Bangkok. They can buy the package tour in the table, or buy return flights and book a hotel themselves. The hotel costs $212 per room per night, and they need 2 rooms. Which option is cheaper? Find the total cost of the cheaper choice.
Answer$[2]
3
The diagram shows the floor plan of a flat, drawn to a scale of 1 : 40. The lengths marked are measured on the plan. Find the actual floor area of the bedroom, in m².
Answerm²[2]
4
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
The annual value of a home is the rent it could earn in a year. Farah's family lives in a flat that could be rented out for $4,800 a month. The table shows the property tax rates for owner-occupied homes. Find the property tax payable for the year.
Answer$[3]
5
Engine capacity (EC) in cc
Road tax for 6 months ($)
EC ≤ 600
200×0.782
600 < EC ≤ 1000
[200+0.125(EC−600)]×0.782
1000 < EC ≤ 1600
[250+0.375(EC−1000)]×0.782
1600 < EC ≤ 3000
[475+0.75(EC−1600)]×0.782
The table shows the road tax rates for cars. Jun Jie's car has an engine capacity of 1248 cc. Find the road tax Jun Jie pays for 6 months, correct to the nearest cent.
Answer$[3]
6
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
Ben's family lives in a flat with an annual value of $52,300. The table shows the property tax rates for owner-occupied homes. Find the property tax payable for the year.
Answer$[3]
Section B
7
Each month, Ms Rahman and Ms Rahman's employer pay into a savings scheme at the rates in the table. Ms Rahman's monthly salary is $5000 this year, and it will increase by 5% at the start of each of the next two years.
Contributions (rates for this question only)
Percentage of the monthly salary
Employee
20%
Employer
15%
Share of the total paid into the Ordinary Account
62%
(a)Find the total amount paid into the scheme each month this year.
Answer (a)$[1]
(b)Find the total amount paid into the scheme over the three years.
Answer (b)$[3]
(c)Find the amount paid into the Ordinary Account over the three years.
Answer (c)$[1]
(d)After the three years, Ms Rahman wants to buy a flat costing $180 000, with a down payment of 25% of the price paid from the Ordinary Account. Is the amount in part (c) enough? Show your working.
Answer (d)[2]
8
The Pillai family, 3 adults and 3 children, is planning a 4-night holiday in Bangkok. The table shows the costs if they book everything themselves. The exchange rate is S$1 = THB 25.5.
Item
Cost
Return flight
S$420 per adult, S$320 per child
Hotel (one family room)
THB 4,800 per night
Breakfast
THB 340 per person per day
(a)Calculate the cost of the hotel for the 4 nights in Singapore dollars. Give your answer correct to the nearest cent.
Answer (a)S$[2]
(b)Using your answer to part (a), find the total cost of the flights and the hotel if the family books them themselves.
Answer (b)S$[2]
(c)A travel agent sells a package of the same flights and hotel, with breakfast included, at S$748 per adult and S$518 per child. Booking early gives a discount of 8%. Find the cost of the package for the family after the discount.
Answer (c)S$[2]
(d)If the family books everything themselves, they buy breakfast for everyone on each of the 4 days. Find the cost of the breakfasts in Singapore dollars, correct to the nearest cent.
Answer (d)S$[2]
(e)Which option should the family choose to pay less for the holiday?
Answer (e)[1]
END OF PAPER
Answers and worked solutions
Question 1
Answer: =5 h 35 min[1]
Bangkok is 1 h behind Singapore.It stays on the same day.6 h 35 min−1 h=5 h 35 minTime in Bangkok: 0535 on 23 March.
Question 2
Answer: Buying the flights and hotel themselves is cheaper: $3,052 altogether, $44 less.[2]
2×899+2×649=30962×389+2×289=1356212×2×4=16961356+1696=3052Buying the flights and hotel themselves is cheaper: $3,052 altogether, $44 less.
Question 3
Answer: 3.8×5.2=19.76 m2 m²[2]
9.5×40=380 cm13×40=520 cm380 cm=3.8 m520 cm=5.2 m3.8×5.2=19.76 m2The bedroom's floor area is 19.76 m².
Question 4
Answer: The property tax is $2,480.[3]
Annual value=4800×12Annual value=57600Tax on the first 50000→1720Rest=57600−50000Rest=760010010×7600=7601720+760=2480The property tax is $2,480.
Question 5
Answer: The road tax for 6 months is $268.23.[3]
1000<1248≤1600EC−1000=1248−1000EC−1000=248250+0.375(248)=343343×0.782=268.226≈268.23 (to the nearest cent)The road tax for 6 months is $268.23.
Question 6
Answer: The property tax is $1,950.[3]
Tax on the first 50000→1720Rest=52300−50000Rest=230010010×2300=2301720+230=1950The property tax is $1,950.
Question 7
(a)Answer: $1750.00[1]
Each month=10020+15×5000=1750
(b)Answer: $66202.50[3]
Year 1=12×5000=60000Year 2=60000×1.05=63000Year 3=63000×1.05=66150Total paid in=10035×(60000+63000+66150)=66202.50
(c)Answer: $41045.55[1]
Ordinary Account=10062×66202.50=41045.55
(d)Answer: No: the down payment is $45000 against $41045.55[2]
Down payment=10025×180000=4500041045.55<45000, so it is not enough.
Question 8
(a)Answer: $752.94 S$[2]
Hotel in THB: 4×4800=19200Hotel in S$: 25.519200=752.9411…≈752.94 (to the nearest cent)
(b)Answer: $2972.94 S$[2]
Flights=3×420+3×320Flights=2220Flights and hotel=2220+752.94Flights and hotel=2972.94
(c)Answer: $3494.16 S$[2]
Before the discount=3×748+3×518Before the discount=3798After the discount=3798×10092After the discount=3494.16
(d)Answer: $320 S$[2]
Breakfasts in THB: 6×340×4=8160Breakfasts in S$: 25.58160=320
(e)Answer: Book everything themselves: $3292.94 < $3494.16[1]
Themselves, with breakfasts=2972.94+320.00Themselves, with breakfasts=3292.94Package=3494.163292.94<3494.16: booking everything themselves costs less.