1. Saturday, 05 March 2016 Objectives 1.Understand the idea 2.Calculate values Grade C - A Why am I doing this? It is an important idea that has many real life applications A favourite SAT and GCSE question Direct and Inverse Proportionality

2. Length (m)0123420 Cost (p)01030150 An example of direct proportionality Rope costs 10p per metre. Complete the missing values in this table.

3. Length (m)012341520 Cost (p)010203040150200 An example of direct proportionality Rope costs 10p per metre. Complete the missing values in this table.

4. p ~ m p = km 30 = k x 3 30 ÷ 3 = k 10 = k p = 10m Length (m)012341520 Cost (p)010203040150200

5. w ~ h w = kh 14.50 = k x 2 k = 14.5 ÷ 2 k = 7.25 w = 7.25h Hours (h)023540 Wages (w)014.5030 3 x 7.25 = 21.75 40 x 7.25 = 290

6. w ~ h w = kh 14.50 = k x 2 k = 14.5 ÷ 2 k = 7.25 w = 7.25h Hours (h)023540 Wages (w)014.5021.7530290

7. Length (m) 012345 Cost (p) 050 Length (m) 012345 Cost (p) 012.8 Length (m) 012345 Cost (p) 07.5 1. The values in the table below are directly proportion so p ~ m. Find the rule that connects p and m and use it to find the missing values.

8. Which of the relationships shown below are directly proportional? Length3410 Weight152150 Cost259 Length7.418.533.3 Base259 Height12.43155.8 15 ÷ 3 = 5 21 ÷ 3 = 7 50 ÷ 10 = 5 7.4 ÷ 2 = 3.7 18.5 ÷ 5 = 3.7 33.3 ÷ 9 = 3.7 12.4 ÷ 2 = 6.2 31 ÷ 5 = 6.2 55.8 ÷ 9 = 6.2 NO YES

9. Inverse Proportionality

10. Speed (s)102040100 Time (t)1

11. Speed (s)102040100 Time (t)21½ (0.5)0.2

12. t ~ s t = k/s 1 = k ÷ 20 1 x 20 = k k = 20 t = 20/s Speed (s)102040100 Time (t)1 t = 20 ÷ 10 t = 2 t = 20 ÷ 40 t = 0.5 t = 20 ÷ 100 t = 0.2

13. t ~ s t = k/s 1 = k ÷ 20 1 x 20 = k k = 20 t = 20/s Speed (s)102040100 Time (t)210.50.2 t = 20 ÷ 10 t = 2 t = 20 ÷ 40 t = 0.5 t = 20 ÷ 100 t = 0.2

14. Speed (s) 0.10.522.545 Time (t) 2 Speed (s) 0.10.522.545 Time (t) 4 Speed (s) 0.10.522.545 Time (t) 40 1. The values in the table below are inversely proportion so t ~ s. Find the rule that connects t and s and use it to find the missing values.