Problem in Real World Contexts

1 Liao wants to cycle around Singapore. He finds the following information below about the two types of shared e-bikes that he can choose from. Bike A Cost Rates Regular $1.00 per min Family $4.00 per min Special Pass* 7-Day Pass $6.90 30-Day Pass $9.90 90-Day Pass $26.90 *Free for first 30mins, $1.00 for every subsequent 30mins. (only for regular bikes) Bike B Cost Rates Regular $1.00 for first 30 mins $0.50 for every next 10 mins Family $4.00 per 30 mins Special Pass** 7-Day Pass $5.90 30-Day Pass $9.90 90-Day Pass $24.90 **Free for first 60 mins, $0.50 for every subsequent 10 mins. (only for regular bikes) (a) Liao cycles with his family in Sembawang Park for 40 mins. He chooses the Family Bike A. He estimates that the total cost is $240. Show that Liao is correct. [1] (b) Liao buys the 7-Day Pass for Bike A. He wants to travel around the perimeter of Singapore. The distance travelled is about 150 km. He travels about 30 km/h. How much does he need to pay including the special pass? [2] (c) Liao and Abid cycle together in East Coast Park. Liao chooses Regular Bike A. He buys the 7-Day Pass. Abid chooses Regular Bike B. The distance of East Coast Park is about 15 km. Liao travels 20 km/h while Abid travels 15 km/h more than Liao. The price for the bike will keep increasing even if they are not cycling. Abid waits for Liao at the end of their journey. Abid claims that he needs to pay more because he waits for Liao. Is his claim correct? Justify your decision. Show all your workings. [7]

2 A petrol oil tanker is a motor vehicle designed to transport gasoline to petrol filling stations. Its tank is shaped like a cylindrical container, with a diameter 3 m and a length 15 m as shown in Diagram I. Diagram II shows the cross-sectional view of the tank containing a certain amount of liquid gasoline. The line AB represents the width of the horizontal surface of the liquid in contact with the cylindrical tank. To satisfy the safety storage conditions for transportation, the liquid gasoline must not exceed 95% of the tank. (a) It is given that AB = 1.8 m and ∠BMO = 90°. Show that the volume in this liquid is safe for transportation. [3] (b) Calculate the height of the liquid gasoline from line AB. [1] (c) A petrol filling station requires an underground tank of 40 000 gallons of liquid gasoline. Petrol tankers are dispatched to the station to top up once its total petrol quantity is 20% of its maximum amount. Calculate the minimum number of petrol tankers required for each top up. Justify your decision. Show all your workings. [6]

3 Zhang wanted to have a shed house of his own in his backyard as shown below. The shed house, shaped like a prism, has a length of 7 m and has four sloping roofs. It also has a door of 2 m. CD = DE = EF = FG = 1.2 m AG = BC =