Chapter 6 Practice Paper: Problems in Real-World Contexts — question paper (print)

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QQ/S4EM/CH6

Secondary 4 · Elementary Mathematics (G2 / G3)

Chapter 6 Practice Paper

Problems in Real-World Contexts

Duration: 40 minutes

Total: 30 marks

Name:

Class:

Date:

READ THESE INSTRUCTIONS FIRST

Write your name, class and register number in the spaces at the top of this page.
Answer all questions.
Show all necessary working. Omission of essential working will result in loss of marks.
Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.
Geometrical instruments and an approved calculator may be used.
The number of marks is given in brackets [ ] at the end of each question or part question.
The total number of marks for each paper is shown on its cover.

Original practice material written for the MOE Elementary Mathematics syllabus. It is not an official MOE or school examination paper. Chapter 6 (real-world contexts: distance-time and speed-time graphs, tariffs with GST, currency exchange, instalments, schedule planning).

For Examiner’s Use
Section A	/ 30
Total	/ 30

Section A: Structured questions[30 marks]

Answer all questions in the spaces provided. Show all necessary working — omission of essential working will result in loss of marks. Give non-exact numerical answers correct to 3 significant figures.

1
A taxi ride is shown on a speed–time graph: the taxi accelerates uniformly from rest to 15 m/s in 10 s, cruises at 15 m/s for 40 s, then decelerates uniformly to rest in 5 s.
1. (a)
  Find the acceleration during the first stage.
  [2]
2. (b)
  Find the total distance travelled.
  [3]
3. (c)
  Find the average speed for the whole ride, correct to 3 significant figures.
  [1]
2
A cyclist’s distance–time graph shows: 0 to 12 minutes — 4 km travelled; 12 to 20 minutes — distance constant; 20 to 48 minutes — a further 9.6 km travelled.
1. (a)
  Find the speed in the first stage, in km/h.
  [2]
2. (b)
  Describe the motion between the 12th and 20th minutes.
  [1]
3. (c)
  Find the average speed for the whole 48 minutes.
  [3]
3
An electricity plan charges the first 100 units at $0.28 per unit, the next 200 units at $0.34 per unit, and units above 300 at $0.40 per unit. A household uses 380 units in a month. GST of 9% is then added.
1. (a)
  Find the cost of the units used before GST.
  [3]
2. (b)
  Find the total bill including GST.
  [2]
3. (c)
  The next month the household cuts usage to 250 units. Find the new charge before GST.
  [1]
4
A money changer quotes 1 EUR = SGD 1.48 and charges no commission. A second changer quotes 1 EUR = SGD 1.45 but takes a 2% commission on the SGD amount. Mr Lim changes SGD 1,450.
1. (a)
  How many euros does the first changer give him?
  [2]
2. (b)
  How many euros does the second changer give him?
  [2]
3. (c)
  State which changer gives more euros, and by how much (to the nearest cent).
  [1]
5
A treadmill costs $1,800 cash. A store plan asks for a 15% deposit plus 10 monthly payments of $172.50.
1. (a)
  Find the deposit.
  deposit = $[1]
2. (b)
  Find the total paid under the plan and the extra cost compared with paying cash.
  [2]
3. (c)
  Express the extra cost as a percentage of the cash price.
  [1]
6
A coach leaves at 21:50 on Monday and arrives at 04:20 on Tuesday. (a) Find the journey duration. The first connecting shuttle after arrival leaves at 05:05 and takes 35 minutes. (b) Find the shuttle’s arrival time. A tour starts at 07:00. (c) How much spare time is there between the shuttle’s arrival and the tour?
1. (a)
  Journey duration.
  [1]
2. (b)
  Shuttle arrival time.
  [1]
3. (c)
  Spare time before the 07:00 tour.
  [1]

— End of paper —