N2: RATIO AND PROPORTION COMMON QUESTIONS by @booksbfrboys on TikTok

N2: Ratio and Proportion (Common Questions w/ Real-World Applications) - Ratios involving Rational Numbers - Map scales - Direct and Inverse Proportion 1. The surface area of a sphere (S) is directly proportional to the square of its radius. If the radius increases by 15 , find the percentage increase in the % surface area. [2] 2. Arthur, Clement, John are to share a bag of sweets amongst themselves in the ratio . John obtained 6 sweets more than Arthur, find 2 : 3 : 4 (a) the total number of sweets received by Arthur [2] (b) the number of sweets received by Clement [1] 3. is inversely proportional to the square root of and the difference in the 𝑦 𝑥 values of when and when is 3. Find 𝑦 𝑥 = 9 𝑥 = 16 (a) an equation connecting and . 𝑥 𝑦 [3] (b) the exact value of when . 𝑥 𝑦 = 5 [1] 4. On a map, a straight road measuring 600 m is represented by a line segment of length 7.5 cm. (a) Express the scale of the map in the ratio . 1 : 𝑟 [1] (b) The length of a canal on the map is 25 cm. Find the actual length in km. [1] (c) The actual area of a school is . Find the area of the school 22 400 𝑚 2 on the map. [2] 5. A map of Singapore has a scale of 1 : 80 000. (a) The actual length of the Singapore River is 3.2 km. Calculate the length, in centimetres, of the river on the map. [2] (b) The actual area of the Bishan-Ang Mo Kio Park is . 620 000 𝑚 2 Calculate the area, in square centimetres, of the park on the map. [2]

6. A map is drawn to a scale of 1 : 40 000. (a) This scale can be expressed as 1 cm represents km. Find . 𝑛 𝑛 [1] (b) The distance between a seaport and an airport on the map is 60 cm. Find the actual distance, in kilometres, between the seaport and the airport. [1] (c) A bus depot has an actual area of 8 . 𝑘 𝑚 2 Find the area, in square centimetres, of the bus depot on the map. [2] 7. If and , write down the ratio of a : b : c. 𝑎 = 4 3 𝑏 𝑏 = 5 6 𝑐 [1] 8. It is given that is inversely proportional to the cube of . If is doubled, 𝑦 𝑥 𝑥 find the percentage decrease in . 𝑦 [3] 9. A packet of sweets is divided among Ahmad, Benny, Carl and Dexter. The number of sweets that Ahmad, Benny and Carl have are in the ratio 5 : 9 : 7. If Carl gets 12 sweets more than Ahmad and Benny gets twice as many sweets as Dexter, find (a) the total number of sweets [2] (b) the number of sweets that Dexter gets