The answer
(a) \(5.796 \approx 5.8\) L (correct)
(b) \(\approx 2.68\) L
(c) about $11.30 (half of the journey's fuel cost)
O-Level E-Math 2019 Paper 2 Question 10 · Verified worked solution by the Genius Plus Academy teaching team
What this question tests
This is Question 10 of the O-Level E-Math 2019 Paper 2. It tests reading a rate table, in the Rate, speed & problem solving area. It is worth 10 marks: 1 + 2 + 7. It is a worded / diagram-based question, so open your Ten-Year Series (TYS) or the official paper at this question, then follow our full worked solution below.
(a) City driving uses 6.3 L per 100 km. For 92 km: \(\dfrac{92}{100} \times 6.3 = 0.92 \times 6.3 = 5.796\) L, which rounds to 5.8 L. So Leila's estimate is correct.
(b) The expressway is out-of-city driving (4.2 L/100 km). Distance in 45 minutes (\(0.75\) h) at 85 km/h: \(85 \times 0.75 = 63.75\) km. Fuel \(= \dfrac{63.75}{100} \times 4.2 = 2.6775 \approx 2.68\) L.
(c) Let the first-stage distance be \(d\) km. The second stage is \((d - 25)\) km. Stage 1 is city driving (60 km/h is the city limit) and stage 2 is out-of-city (75 km/h is above the city limit). Time: \(\dfrac{d}{60} + \dfrac{d - 25}{75} = 3.25\) h. Multiply by 300: \(5d + 4(d - 25) = 975 \Rightarrow 9d - 100 = 975 \Rightarrow 9d = 1075 \Rightarrow d = 119.4\) km. So stage 1 \(\approx 119.4\) km (city) and stage 2 \(\approx 94.4\) km (out of city). Fuel used: - Stage 1 (city, 6.3 L/100 km): \(\dfrac{119.4}{100} \times 6.3 = 7.52\) L. - Stage 2 (out of city, 4.2 L/100 km): \(\dfrac{94.4}{100} \times 4.2 = 3.97\) L.
Total fuel \(\approx 7.52 + 3.97 = 11.49\) L. With regular fuel at $2.07/L and a 5% loyalty discount, the price per litre is \(2.07 \times 0.95 = \$1.9665\). Total cost \(\approx 11.49 \times 1.9665 = \$22.60\). Hamid offered to pay half, so a suitable amount for Leila to ask is \(\dfrac{22.60}{2} \approx \$11.30\). Justification: Hamid travels the whole journey too, so paying half the fuel cost is fair; $11.30 is half of the $22.60 spent on regular fuel after the loyalty discount Leila actually receives. (A student could reasonably round to about $11 or $11.50; the key is to compute the total fuel cost from the two stages and halve it.)
Answer: (a) \(5.796 \approx 5.8\) L (correct)
(b) \(\approx 2.68\) L
(c) about $11.30 (half of the journey's fuel cost)
Same structure, different numbers
Swap the constants, dress a quadratic as a length, hide a derivative inside an integral, and a student sees a brand new problem. The structure underneath is the same, and so is the method. Once a student can name the structure, a whole row of questions that look different start to open the same way.
That is where marks really leak: in choosing the method, not in the algebra that follows. We call it Lock and Key, name the lock, then the key follows.
Want more questions like this, with worked solutions?
Join our mailing list and we will send practice sets and worked solutions. One email, no spam.
Genius Plus Academy · O-Level & IP Mathematics
Our O-Level E-Math tuition trains the same recognise-the-structure method these worked solutions show, taught by a team that has marked these papers for years. It runs within our weekly Secondary Math programme, Sec 1 to 4 and IP.
It is a reading a rate table question from Rate, speed & problem solving, worth 10 marks: 1 + 2 + 7.
Yes. IP (Integrated Programme) schools teach the same O-Level Mathematics content; they just sequence it differently and set their own internal exams, so these worked solutions apply to IP students too.
Yes. Every worked solution here is free to read, with no sign-up wall.
Browse E-Math and A-Math by year in our worked-solutions library at /resources/solutions/o-level/.
Book a free trial and diagnostic. We will look at a real paper and show you exactly where the marks are going.