Sec 4 E-Math Problems in real-world contexts worksheet with answers
A free Sec 4 E-Math worksheet on problems in real-world contexts: 7 questions, 29 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
(a)A night market opens at 7.45 p.m. Write down this time using the 24-hour clock.
Answer (a)[1]
(b)A night market opens at 1505. Write down this time using the 12-hour clock.
Answer (b)[1]
2
The diagram shows the floor plan of a flat. Skirting board is fixed along the bottom of the bedroom's walls, all the way round except across the doorway, which is 0.9 m wide. Skirting board is sold in 2.5 m lengths at $8.60 each. Find the least cost of the skirting board.
Answer$[2]
3
Plan A (with phone)
Plan B (SIM only)
Monthly fee
$58
$15
Data each month
20 GB
15 GB
Extra data
$4 per GB
$6 per GB
Phone
$98 when you sign up
buy it yourself for $1,059
Hui Min needs a new phone and compares the two plans in the table. Hui Min uses about 35 GB of data a month. Over 24 months, which plan is cheaper? Find the total cost of the cheaper plan over the 24 months.
Answer$[2]
4
The diagram shows the floor plan of a flat, drawn to a scale of 1 : 50. The lengths marked are measured on the plan. Find the actual floor area of the bedroom, in m².
Answerm²[2]
5
Chargeable income
Income tax rate (%)
Gross tax payable ($)
On the first $20,000
0
0
On the next $15,000
2.5
375
On the first $35,000
375
On the next $15,000
5
750
On the first $50,000
1,125
On the next $30,000
8
2,400
On the first $80,000
3,525
On the next $40,000
12
4,800
On the first $120,000
8,325
On the next $40,000
15
6,000
On the first $160,000
14,325
Ben's chargeable income for the year is $153,800. The table shows the income tax rates. Calculate the income tax Ben pays for the year.
Answer$[3]
Section B
6
Mrs Lee buys a flat for $700 000 to rent out. Mrs Lee pays a down payment of 25% of the price in cash, and the buyer's stamp duty and the legal fees in the table. The rest of the price is a loan at a flat rate of 2.4% per annum simple interest for 20 years, paid back in equal monthly instalments.
Charge
Rate (for this question only)
Buyer's stamp duty
1% of the first $180 000, 2% of the next $180 000, 3% of the next $640 000, 4% of the rest of the price
Property tax, each year
10% of the first $30 000 of the annual value, 15% of the rest
Legal fees
$3300
(a)Calculate the buyer's stamp duty.
Answer (a)$[2]
(b)Find the total amount of cash Mrs Lee pays when buying the flat.
Answer (b)$[1]
(c)Calculate the monthly instalment.
Answer (c)$[2]
(d)Mrs Lee rents the flat out at $2900 a month. Each year, an agent's fee of one month's rent is paid, and property tax is charged on an annual value equal to the rent for the year. Find the rent Mrs Lee keeps in a year after the agent's fee and the property tax.
Answer (d)$[3]
(e)Mrs Lee says, "The rent I keep pays for all the loan instalments each year." Is Mrs Lee correct? Show your working.
Answer (e)[1]
7
The Ong family, 2 adults and 1 child, is planning a 3-night holiday in Hong Kong. The table shows the costs if they book everything themselves. The exchange rate is S$1 = HK$ 6.
Item
Cost
Return flight
S$460 per adult, S$350 per child
Hotel (one family room)
HK$ 1,100 per night
Breakfast
HK$ 88 per person per day
(a)Calculate the cost of the hotel for the 3 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$838 per adult and S$588 per child. Booking early gives a discount of 8%. Find the cost of the package for the family after the discount.
Answer (c)S$[2]
(d)If the family books everything themselves, they buy breakfast for everyone on each of the 3 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
(a)Answer: 7+12=19[1]
7+12=19So 7.45 p.m. is 1945, with 4 digits (45 minutes).
(b)Answer: 3.05 p.m.[1]
1505 is p.m. (from noon).15−12=3So 1505 is 3.05 p.m..