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 [1] 10. (a) Express the ratio of 1 minute and 30 seconds to 1 hour in its simplest form. [1] 10. (b) If and , find a : b : c. 5 𝑎 = 4 𝑏 8 𝑏 = 3 𝑐 [1] 11. A map is drawn to a scale of 1 : 20 000. (a) The distance from one end of a grassland to the other end is represented by a line of length 8 cm on the map. Calculate the actual distance, giving your answer in kilometres. [1] (b) The actual area of the grassland is 2.5 hectares. Calculate the area on the map, giving your answer in square centimetres. . 1 ℎ𝑒𝑐𝑡𝑎𝑟𝑒 = 10 000 𝑚 2 [ ] [2]

12. The map of The Singapore Zoo has a scale of 1 : 3000. (a) If the length from the entrance to Reptile Garden is 4.5 cm on the map, calculate the actual distance, in kilometres. [1] (b) The actual area of the Baboon Enclosure is . Calculate the 0 . 0225 𝑘 𝑚 2 area on the map that represents the enclosure, giving your answer in square centimetres. [1] 13. A map is drawn to a scale of 1 : 50 000. (a) Two towns are 24 km apart. Calculate, in centimetres, their distance apart on the map. [1] (b) On the map, a farm has an area of . 20 𝑐 𝑚 2 Calculate, in square kilometres, the actual area of the farm. [1] 14. The map of a national park is drawn to a scale of 1 : . A lake, which has an 𝑛 actual area of , is represented by an area of on the map. 7 . 5 𝑘 𝑚 2 4 . 8 𝑐 𝑚 2 (a) Find the value of . 𝑛 [2] (b) Calculate the actual perimeter of the lake, in km, if its perimeter on the map is 9 cm. [1]

N2: Ratio and Proportion (Marking Scheme) 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. 𝑆 = 𝑘 𝑟 2 Let 𝑆 = 10 , 𝑟 = 2 10 = 𝑘 2 ( ) 2 𝑘 = 10 4 2 100 × 115% = 2 . 3 𝑆 = 10 4 2 . 3 ( ) 2 𝑆 = 13 . 225Percentage increase = 𝑛𝑒𝑤 𝑣𝑎𝑙𝑢𝑒 − 𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 × 100%Percentage increase = 13 . 225 − 10 10 × 100%Percentage increase = 32.25 ∴ 32 . 25% [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 𝐴 : 𝐶 : 𝐽 2 : 3 : 4 4 𝑢 − 2 𝑢 → 6 𝑠𝑤𝑒𝑒𝑡𝑠 6 sweets ∴ [2] (b) the number of sweets received by Clement 1 𝑢 → 3 𝑠𝑤𝑒𝑒𝑡𝑠 3 𝑢 → 9 𝑠𝑤𝑒𝑒𝑡𝑠 9 sweets ∴ [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 𝑦 = 𝑘 𝑥 𝑦 = 𝑘 3 𝑦 = 𝑘 4 𝑘 3 − 𝑘 4 = 3 𝑘 = 36 𝑦 = 36 𝑥 ∴ 𝑦 = 36 𝑥 [3] (b) the exact value of when . 𝑥 𝑦 = 5 5 = 36 𝑥 5 𝑥= 36 𝑥= 7 . 2 𝑥 = 1296 25 𝑥 = 51 21 25 ∴ 𝑥 = 51 21 25 [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 : 𝑟map : actual 7.5 cm : 600 m 7. 5 cm : 60 000 cm ★ [1 m = 100 cm] 1 cm : 8000 cm ∴ 1 : 8000 [1] (b) The length of a canal on the map is 25 cm. Find the actual length in km. 1 cm : 80 m 25 cm : 2000 m 25 cm : 2 km ★ [1 km = 1000 m] 2 km ∴ [1] (c) The actual area of a school is . Find the area of the school 22 400 𝑚 2 on the map. 1 cm : 80 m 1 𝑐 𝑚 2 : 6400 𝑚 2 22400 6400 = 3 . 5 3 . 5 𝑐 𝑚 2 : 22 400 𝑚 2 ∴ 3 . 5 𝑐 𝑚 2 [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. 1 cm : 80 000 cm 1 cm : km ★ [1 km = cm] 80 000 1 0 5 1 0 5 1 cm : 0.8 km 4 cm : 3.2 km 4 cm ∴ [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. 1 cm : m 80 000 100 1 cm : 800 m 1 𝑐 𝑚 2 : 640 000 𝑚 2 620 000 640 000 = 0 . 96875 0 . 96875 𝑐 𝑚 2 : 620 000 𝑚 2 ∴ 0 . 96875 𝑐 𝑚 2 [2]

6. A map is drawn to a scale of 1 : 40 000. (a) This scale can be expressed as 1 cm represents km.