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.

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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

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

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

p ~ m p = km 30 = k x 3 30 ÷ 3 = k 10 = k p = 10m Length (m) Cost (p)

w ~ h w = kh = k x 2 k = 14.5 ÷ 2 k = 7.25 w = 7.25h Hours (h) Wages (w) x 7.25 = x 7.25 = 290

w ~ h w = kh = k x 2 k = 14.5 ÷ 2 k = 7.25 w = 7.25h Hours (h) Wages (w)

Length (m) Cost (p) 050 Length (m) Cost (p) Length (m) Cost (p) 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.

Which of the relationships shown below are directly proportional? Length3410 Weight Cost259 Length Base259 Height ÷ 3 = 5 21 ÷ 3 = 7 50 ÷ 10 = ÷ 2 = ÷ 5 = ÷ 9 = ÷ 2 = ÷ 5 = ÷ 9 = 6.2 NO YES

Inverse Proportionality

Speed (s) Time (t)1

Speed (s) Time (t)21½ (0.5)0.2

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

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

Speed (s) Time (t) 2 Speed (s) Time (t) 4 Speed (s) Time (t) 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.