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2.7 Calculus Methods AS 91262

Calculus HOME | Achievement Objectives | Gradient | Gradient Functions | Differentiation | Gradient at a point | Find point with gradient | Equation of Tangent | Second Derivitive | Coordinates of Max & Min | Increasing, Decreasing Functions | Applications | Kinematics with differentiation | Antidifferentiation | Finding 'C' | Kinematics with anti-differentiation | Rates of Change | Mixed Problems | Revision

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

Gradient

2

Gradient Functions

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

Kinematics using anti-differentiation

   

19

Rates of change

20

Mixed problems

21

Mixed problems

22

Revision

23

Assessment

 

 

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