GCSE Direct Inverse Proportion Dr J Frost jfrosttiffin

GCSE : : Direct & Inverse Proportion Dr J Frost (jfrost@tiffin. kingston. sch. uk) @Dr. Frost. Maths Objectives: (a) Determine and use equations involving a constant a proportionality, for directly and inversely proportional relationships. (b) Recognise graphs for directly and inversely proportional relationships. Last modified: 1 st February 2019

www. drfrostmaths. com Everything is completely free. Why not register? Register now to interactively practise questions on this topic, including past paper questions and extension questions (including UKMT). Teachers: you can create student accounts (or students can register themselves), to set work, monitor progress and even create worksheets. With questions by: Dashboard with points, trophies, notifications and student progress. Teaching videos with topic tests to check understanding. Questions organised by topic, difficulty and past paper.

Starter When Mo Farah runs at 8 m/s for some fixed period of time, he covers 240 m. Fill in the gaps. Speed 8 m/s 16 m/s 4 m/s 24 m/s Distance Covered 240 m 480 m ? 120 m ? 720 m ? ? If his speed doubled, the distance covered would similarly double.

Direct Proportion 8 m/s 16 m/s 4 m/s 240 m 480 m 120 m 24 m/s 720 m ? ? “constant of proportionality”

Worked Examples 1 ? 2 ?

Test Your Understanding A ? ? B ?

Exercise 1 1 6 ? ? 7 2 ? 3 ? ? 8 4 ? 5 ? 5 6 400 576 ?

Back in a Mo… Mo is running a 5000 m race. Here are his times when he runs at different speeds: Speed (s) Time (t) 5 m/s 1000 s 20 m/s 250 s 1 m/s 5000 s 6. 47 m/s 773 s (his PB) How are the speeds and times related? This time as his speed doubles, his time halves (i. e. the opposite). Note also ? that the speed and time also multiply to give the same value.

Inverse Proportion Speed (s) Time (t) 6. 47 m/s 773 s (his PB) 5 m/s 1000 s 10 m/s 500 s

Quickfire First Step Question… First thing you’d write… ? ? ? ? ?

Worked Examples ?

Test Your Understanding A ? ? B ?

Exercise 2 1 4 ? 2 3 5 0. 949 ? 4 1. 44 ? 40 6 8 5 5 8 ? N 1 2 5 10 100 ? 25? 4 1 1 25 3. 2 3. 84? 0. 768 3 1. 5 5 ? 0. 324 ? 0. 740 100 4 6. 5 6 4. 643 ? 0. 190 ? 27. 3 1. 142 ? 35 4 ? 1. 44 ?

Proportion and their Graphs Which of these graphs represent variables which are directly proportional to each other? hours on computer Temperature (F) electricity usage rabbit population years Temperature (C) Yay Yay Nay

Proportion and their Graphs Which of these graphs represent variables which are inversely proportional to each other? Smell intensity Distance from offender Yay Nay