Sec 4 E-Math Real-World Problems topical questions

A jogger covers 9 km in 45 minutes. Find the average speed in km/h.

Given USD 1 = SGD 1.35, change SGD 405 into US dollars.

Tariff: first 100 units $0.28 each, next 200 units $0.34 each. A flat uses 250 units. Find the charge for the units used.

A meal costs $64 before GST. Find the price including 9% GST.

A bus leaves the interchange at 07:50. The ride takes 25 minutes and the walk to the office another 8 minutes. Find the arrival time.

A train leaves at 14:38 and arrives at 17:21. Find the duration of the journey.

An electricity tariff charges the first 50 units at $0.25 per unit and the next 100 units at $0.32 per unit. A home uses 120 units. (a) Find the energy charge. (b) Find the total bill after 9% GST, correct to the nearest cent.

A radio-controlled car accelerates uniformly from rest to 12 m/s in 6 s, holds 12 m/s for 10 s, then decelerates uniformly to rest in 3 s. (a) Find the acceleration. (b) Find the total distance travelled. (c) Find the average speed for the whole run, correct to 3 significant figures.

1. (a)Acceleration.[1]
2. (b)Total distance.[3]
3. (c)Average speed.[1]

A distance–time graph shows a delivery van: it travels 5 km in the first 15 minutes, rests for 10 minutes, then covers 7 km in the next 25 minutes. (a) Find its speed in the first stage, in km/h. (b) Describe the middle stage. (c) Find the average speed for the whole 50 minutes.

1. (a)First-stage speed.[2]
2. (b)Middle stage.[1]
3. (c)Average speed.[2]

A bicycle costs $960 cash. An instalment plan requires a 20% deposit plus 8 monthly payments of $105. (a) Find the deposit. (b) Find the total paid under the plan. (c) Express the extra cost as a percentage of the cash price.

1. (a)Deposit.[1]
2. (b)Total paid.[2]
3. (c)Extra as a percentage.[2]

A bank changes euros at 1 EUR = SGD 1.45 and charges a 1% commission on the SGD amount. Mdm Tan changes SGD 1,450. (a) Find the commission. (b) How many euros does she receive?

1. (a)Commission.[1]
2. (b)Euros received.[3]

A night bus leaves Singapore at 22:45 and reaches its city stop at 05:33. Find the duration of the trip.

A delivery rider travels 8 km at 24 km/h, rests 12 minutes, then rides 6 km at 18 km/h. (a) Find the total journey time. (b) Find the average speed for the whole outing, correct to 3 significant figures.

Two money changers quote for euros: changer A at 1 EUR = 1.48 SGD with no commission; changer B at 1 EUR = 1.52 SGD with a 2% commission on the SGD amount. You are changing SGD 740. (a) How many euros does A give? (b) How many euros does B give, correct to 3 significant figures? (c) Which changer gives more euros, and by how much (to the nearest euro)?

A train accelerates uniformly from rest to 30 m/s in 60 s, cruises at 30 m/s for 240 s, then decelerates uniformly to rest in 60 s. (a) Find the total distance. (b) Find the average speed in m/s and in km/h.

1. (a)Total distance.[3]
2. (b)Average speed both units.[2]

A family drives 294 km. The car travels 14 km per litre and petrol costs $2.55 per litre. Find the total cost of the petrol for the trip.

Plan A is a flat $28 per month. Plan B is $15 per month plus $0.05 for every minute beyond 100 minutes. A user makes 320 minutes of calls a month. (a) Find the monthly cost of plan B. (b) Which plan is cheaper and by how much?

1. (a)Plan B cost.[2]
2. (b)Comparison.[2]

A ferry arrives at 05:33. A coach to the city leaves at 06:15 and takes 55 minutes. A meeting is at 09:00 in the city. (a) How long is the wait for the coach? (b) At what time does the coach reach the city? (c) How much spare time is there before the meeting?

1. (a)Wait for the coach.[2]
2. (b)City arrival.[2]
3. (c)Spare time.[2]

A train accelerates uniformly from rest to 24 m/s in 48 seconds, travels at 24 m/s for 2 minutes, then decelerates uniformly to rest in 30 seconds. (a) Find the total distance travelled. (b) Find the average speed for the whole journey, correct to 3 significant figures. (c) Find the deceleration.

An electricity tariff charges the first 200 kWh at $0.2722, the next 300 kWh at $0.3253, and usage above 500 kWh at $0.3682, with 9% GST added to the energy charge. A household uses 640 kWh in a month. (a) Find the energy charge. (b) Find the GST-inclusive bill, correct to the nearest cent. (c) Find, correct to 1 decimal place, the percentage the bill would fall if the household used only 500 kWh.

1. (a)Energy charge for 640 kWh.[2]
2. (b)GST-inclusive bill.[1]
3. (c)Percentage fall at 500 kWh.[3]