YEAR 2 PARAMETRIC EQUATIONS Converting Parametric Equations to

YEAR 2 |PARAMETRIC EQUATIONS Converting Parametric Equations to Cartesian Equations: Examples Differentiation Parametric Equations: Examples | Exam Questions 13/12/2021 1

PARAMETRIC EQUATIONS | INTRODUCTION Example of a pair of parametric equations Another example of a pair of parametric equations 13/12/2021 2

PARAMETRIC EQUATIONS | EXAMPLE 1 13/12/2021 2 Substitute into (2) 3

PARAMETRIC EQUATIONS | EXERCISE (a) 13/12/2021 (b) Reveal Step Reveal Answer Reveal Step Reveal Answer 4

PARAMETRIC EQUATIONS | EXERCISE Multiply up by the denominator Expand Brackets Factorise Divide through Worked solution continues on next page…. 13/12/2021 5

PARAMETRIC EQUATIONS | EXERCISE 13/12/2021 Multiply up by the denominator Expand Brackets Factorise Divide through 6

PARAMETRIC EQUATIONS | EXERCISE 13/12/2021 You can skip this question if you found the last one easy. Reveal Steps 7

PARAMETRIC EQUATIONS | EXERCISE 13/12/2021 1 Expand brackets 2 Substitute (1) into (2) 8

PARAMETRIC EQUATIONS | EXERCISE 1 13/12/2021 2 9

PARAMETRIC EQUATIONS | EXERCISE 1 1 2 13/12/2021 2 10

PARAMETRIC EQUATIONS | EXERCISE 13/12/2021 By first finding the cartesian equation of the curves defined below, sketch the curve. 1 1 Reveal Steps 2 Reveal Steps Reveal Answer 2 11

PARAMETRIC EQUATIONS | EXERCISE Reveal Step Reveal Answer 13/12/2021 12

EXTRA PRACTICE QUESTIONS OCR June 2015 Q 10 Or textbook P 234 Q 4, Q 5 13/12/2021 13

DIFFERENTIATING PARAMETRIC EQUATIONS Earlier in the course we used the chain rule for differentiation where Chain Rule There is nothing ‘special’ about the letter ‘u’… Differentiating Parametric Equations or 13/12/2021 14

DIFFERENTIATING PARAMETRIC EQUATIONS | EXAMPLE-PROBLEM PAIRS 1 E. (b) Find the gradient at the points (a) 13/12/2021 15

DIFFERENTIATING PARAMETRIC EQUATIONS | EXAMPLE-PROBLEM PAIRS 1 E. (b) Find the gradient at the points (b) (i) 13/12/2021 16

DIFFERENTIATING PARAMETRIC EQUATIONS | EXAMPLE-PROBLEM PAIRS 1 E. (b) Find the gradient at the points (b) (ii) (using Pythagoras) 13/12/2021 17

DIFFERENTIATING PARAMETRIC EQUATIONS | EXAMPLE-PROBLEM PAIRS 1 P. (b) Find the gradient at the points (a) 13/12/2021 18

DIFFERENTIATING PARAMETRIC EQUATIONS | EXAMPLE-PROBLEM PAIRS 1 P. (b) Find the gradient at the points (b) (i) 13/12/2021 19

DIFFERENTIATING PARAMETRIC EQUATIONS | EXAMPLE-PROBLEM PAIRS 1 P. (b) Find the gradient at the points (b) (ii) 13/12/2021 20

DIFFERENTIATING PARAMETRIC EQUATIONS | EXAMPLE-PROBLEM PAIRS 2 E. 13/12/2021 21

DIFFERENTIATING PARAMETRIC EQUATIONS | EXAMPLE-PROBLEM PAIRS 2 P. 13/12/2021 22

DIFFERENTIATING PARAMETRIC EQUATIONS | EXAMPLE-PROBLEM PAIRS 3 E. At a stationary point, 13/12/2021 23

DIFFERENTIATING PARAMETRIC EQUATIONS | EXAMPLE-PROBLEM PAIRS 3 P. Find the coordinates of the turning points. At a stationary point, 13/12/2021 24

PARAMETRIC EQUATIONS | EXAM QUESTIONS AQA C 4 January 2007 Q 1 « AQA January 2011 Q 4 « « Click to reveal hint. AQA June 2007 Q 6 « « Click to reveal hint. AQA Jan 2008 Q 5 « « « AQA June 2015 Q 5 « « « 13/12/2021 25

INTEGRATING PARAMETRIC EQUATIONS 13/12/2021 26

INTEGRATING PARAMETRIC EQUATIONS | EXAMPLE 13/12/2021 4 E. (a) Find the values of the parameter at A and B. (b) Find the area bounded by the curve, the x-axis and the y-axis. A B 9 27

INTEGRATING PARAMETRIC EQUATIONS | EXAMPLE (a) (b) 13/12/2021 28

INTEGRATING PARAMETRIC EQUATIONS | EXERCISE 12 D | QUESTIONS: P 240 | ANSWERS: Q 1 -5 13/12/2021 29