Key Concepts: Simplify ratios by dividing by the HCF. Ratios can be written as fractions. In direct proportion, y = kx. Inverse proportion, xy = k. Use unitary method to scale quantities.
Section A: Ratio Basics
1. Simplify these ratios: [3]
(a) 24 : 60
(b) 45 : 30 : 75
(c) 6 m : 250 cm
2. Divide £360 in the ratio 2 : 3. [2]
Section B: Proportion
3. y is directly proportional to x. If y = 18 when x = 6, find y when x = 15. [2]
4. t is inversely proportional to p. If t = 12 when p = 4, find p when t = 8. [2]
Section C: Scaling
5. A recipe for 12 cookies uses 300 g flour. How much flour is needed for 18 cookies? [2]
6. A map scale is 1:50,000. What distance on the map represents 7.5 km in reality? [2]
Total marks: 13
Mark Scheme
1. (a) 2 : 5 [1]; (b) 3 : 2 : 5 [1]; (c) 600 cm : 250 cm → 24 : 10 = 12 : 5 [1]
2. 2 parts = £144; 3 parts = £216 [2]
3. k = 18/6 = 3; y = 3 × 15 = 45 [2]
4. tp = 48; p = 48/8 = 6 [2]
5. Scale factor 18/12 = 1.5; Flour = 300 × 1.5 = 450 g [2]
6. 7.5 km = 750,000 cm; on map = 750,000 / 50,000 = 15 cm [2]