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2.7 Calculus Methods AS 91262

 Achievement Standard 2.7 Calculus has two main components at Level 2 - differentiation and integration (antidifferentiation) Differentiation investigates the slope of graphs, especially curves. Tangent and normal lines to a curve can be found. The turning points on graphs (which have zero gradient) can be found and the maximum and minimum values. It also involves the rates of change of variables - such as finding the speed from a distance graph which is a curve. Calculus surfer - Thanks to Evelyn Knight for sourcing the link (homepages.gac.edu) Note: you need to remember to use * for anything multiplied, e.g. y = x*(x+1)*(x+2). Integration (antififferentiation) involves the reverse process (obviously) Given a gradient function, find the original function. It also involves rates of change. Link to 'the fundamentals of calculus' (thanks to Liz Curtis) Web links for calculus Manipulate maths with java great website

 Word doc 07/03 Theta Homework book (David Barton) Theta text book (David Barton) 2005 edn Web link Geogebra java animation Powerpoint Excel Spreadsheet (allow macros)

Approximate Lesson sequence

Achievement Criteria

1

2

3

Basic Differentiation

4

Harder Differentiation

5

Find the Gradient at a given point

6

Find a point on a curve from a Given Gradient

7

Find the Equation of a Tangent to a curve

8

The Second Derivitive

9

Finding Coodinates of Turning Points

10

Increasing and Decreasing functions

11

Differentiation Applications

12

Kinematics using differentiation

13

Antidifferentiation

14

Harder Antidifferentiation

15

Finding the value of 'C'

16

Practice finding the Originl Function

17

Harder Originl Function problems

18

19

Rates of change

20

Mixed problems

21

Mixed problems

22

Revision

23

Assessment