Pages: 1040

6 - Calculus## XLatest Additions

8193Differentiation : Trig functions : Visualise cos (x ± a) Addition Formulae

8192Differentiation : Trig functions : Visualise sin (x ± a) Addition Formulae

8057Differentiation : Slope : The graph of y = x³

8056Differentiation : Slope : Straight v curved

8050Differentiation : Slope : The graph of y = x²

8034Integration : Definite integration : Exam Question

8024Differentiation : Implicit differentiation : Exam Question

8018Integration : Substitution method : Exam Question

8013Differentiation : Implicit differentiation : Exam Question

8012Integration : Substitution method : Exam Question

8007Differentiation : Rules - the product rule : Exam Question

8003Integration : Definite integration : Exam Question

8001Integration : Volume of revolution : Exam Question

7999Integration : Substitution method : Exam Question

7996Differentiation : Related rates of change : Exam Question

Introduction

Tangents and Chords

Investigate Quadratics

Investigate Cubics

Investigate Higher Order Polynomials

Straight v curved

The graph of y = x²

The graph of y = x³

Constant multiplier

Sums and differences

Investigate with Negative Powers

Gradient curves

O-test 1

O-test 5

Finding tangents 2

The gradient curve

Tangents 1

Tangents 2

Tangents 3

Evaluating the gradient

Evaluating the gradient 3

Evaluating the gradient 2

Evaluating the gradient 4

Finding tangents 1

Finding tangents 3

Finding tangents 4

Finding tangents 5

Finding tangents 6

Check the method

Finding normals

Finding normals 2

Finding normals 3

Finding normals 4

Finding normals 5

Gradient on a GDC

Gradient on a GDC 2

O-test 4

Exam O-test 1

Timed O-test

Method O-test

O-test 1

O-test 2

Vocabulary O-test

O-test 3

Exam O-test 2

Exam O-test 3

Exam O-test 4

Exam O-test 5

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Investigate

Approximate gradient

Approximate gradient 2

Tangents and Chords of Polynomials

Function notation

Function notation 2

Function notation 3

Function notation 4

Function notation 5

Function notation 6

Delta notation

Randomised Exam Q 2008

Randomised Exam Q 2009

Investigate 1st & 2nd Derivatives

Investigate 1st & 2nd Derivatives 2

Second order derivatives

Exam O-test

Randomised Exam Q 2000

Randomised Exam Q 2007

Randomised Exam Q 2007

Investigate Increasing Functions

Decreasing f(x) = 3 - 3 to x

Increasing f(x) = 2 to x + 1

Increasing f(x) = log(x)

Prove an increasing function

Prove an increasing function 2

Decreasing f(x) = 1 - x - x to 3

A decreasing function 3

Increasing or Decreasing ?

Increasing and decreasing

Increasing and decreasing 2

Exam O-test

Randomised Exam Q 2000

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Introduction

The max-box problem 2

A minimising problem

A minimising problem 2

The max-box problem 3

View Maxima and Minima 2

Investigate Points of Inflection

Finding turnings points

View Maxima and Minima

Maxima and minima

Axis of symmetry

Finding turnings points 2

Finding turnings points 3

A maximising problem

A maximising problem 4

The max-box problem

A minimising problem 3

A minimising problem 4

A minimising problem 5

Finding turnings points on a GDC

Quiz

O-test 3

O-test 1

Method O-test

O-test 2

Exam O-test 1

Exam O-test 2

Exam O-test 3

Exam O-test 4

Exam timed O-test

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Investigate Trig Differentiation

Finding tangents 1

Finding tangents 2

Tangents and Chords of Trig Functions

Visualise cos (x ± a) Addition Formulae

Visualise sin (x ± a) Addition Formulae

Tangent and normal 2

More trig functions

sin x by first principles

cos x by first principles

sin kx

cos kx

Examples

Examples 2

Examples 3

Derivative puzzles

tan and cot

sec and cosec

Finding tangents 3

Differentiation on a GDC

True or false O-test

Exam O-test 1

Exam O-test 2

Randomised Exam Q 2004

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Assessment

Some 1st and 2nd Derivatives

Differentiate x

^{n}Differentiate simple functions

Differentiate products

Differentiate quotients

Check the steps

Memorise the rules

Logical order

2nd order derivatives

dy/dx = 1/dx/dy

2nd order derivatives 2

Verify dy/dx = 1/dx/dy

Spot the method

2nd order derivatives 3

2nd order derivatives 4

Derivative puzzles

Rational powers

Rational powers 2

Rational powers 3

True or false

True or false 2

True or false 3

Timed O-test

O-test 1

Matching O-test

True or false O-test

Sequence O-test 1

Sequence O-test 2

Matching O-test

Sequence O-test 3

Matching O-test

O-test

O-test 2

O-test 4

O-test 3

Exam O-test 1

Exam O-test 2

Exam O-test 1

Exam O-test 2

Exam O-test 3

Exam O-test 4

Exam timed O-test

Randomised Exam Q 2000

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Visualise the Product Rule

Investigate

The product rule

The product rule 2

The product rule 3

The product rule 4

The product rule 5

Finding gradients

Finding gradients 2

Finding gradients 3

Finding tangents

Finding normals

Sequence O-test

Exam O-test 1

Exam O-test 2

Exam O-test 3

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Finding gradients

Visualise the Quotient Rule

Investigate

The quotient rule

The quotient rule 2

The quotient rule 3

Finding turning points

Exam O-test 1

Exam O-test 2

Exam O-test 3

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Explanation

Explanation 2

The chain rule

Investigate the chain rule

(ax+b)ⁿ 2

(ax+b)ⁿ

The chain rule 2

The chain rule 3

The chain rule 4

The chain rule 5

The chain rule 6

Finding gradients

Finding gradients 2

Matching O-test

Sequence O-test 1

Sequence O-test 2

Exam O-test 1

Exam O-test 2

Exam timed O-test

Randomised Exam Q 2006

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How to solve...

A sand problem

Example 1

Example 2

Example 3

Example 4

Expanding cube

An expanding stain

Filling a water tank

Hot air balloon

Circle

Exam O-test 2

Exam O-test 1

Exam timed o-test

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By first principles

Gradients of a

^{x}Gradients of a

^{x}and e^{x}Differentiation of e

^{x}Examples

Finding tangents

Exam O-test 1

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Gradients of ln ax

Investigate Differentiation of ln ax

By first principles

Differentiation of ln ax

ln (ax+b)

Finding tangents

Differentiation of x

^{r}Exam O-test

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Investigate Log/Exp Differentiation Together

Examples

True or false

Matching O-test

Sequence O-test

Exam O-test

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Finding tangents

Assessment

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Example 7

Other variables

Finding a gradient

Finding normals

Finding normals 2

Finding tangents 2

O-test

Exam O-test 1

Exam O-test 2

Exam O-test 3

Exam timed O-test 1

Exam timed O-test 2

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Investigate Derivatives of Arcsin, Arccos, Arctan

Rugby kick

Derivative of arc sin

Derivative of arc cos

Derivative of arc tan

Compare function & inverse

Standard results

Exam O-test

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MIT video: differentation

MIT video: products,quotients

MIT video: limits

MIT video: chain rule

MIT video: implicit differentiation

MIT video: implicit differentiation 2

MIT video: limits

MIT video: exponentials & logs

Xtra 1

x

^{n}and n^{x}a

^{x}a

^{bx}Exam O-test 2

Exam timed O-test

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Simple d.e.s

Exponential growth

Gradient

Gradient 2

Gradient 3

Gradient 4

Gradient 5

Gradient 6

Leaking water tank

An expanding cube

Fish

Population

Newton's law of cooling

O-test

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Introduction

Reverse 1

Reverse 2

Rational powers

Matching O-test

O-test

Exam O-test

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Pattern A 1

Pattern A 2

Pattern A 3

Pattern B 1

Pattern B 2

Pattern B 3

Exam O-test

Exam timed O-test

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Key points

Simple functions 1

Integral of x

^{p}Simple functions 2

Simple functions 3

Find the constant

Find the constant 2

True or false O-test

O-test

Timed O-test

Sequence O-test

Exam O-test 1

Exam O-test 2

Exam O-test 3

Exam O-test 4

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Investigate Integration of

^{1}/_{ax}1/(ax)

1/(ax) with limits

1/(ax+b)

1/(ax+b) with limits

Definite integral

Exam O-test

Exam timed O-test

Randomised Exam Q 2007

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Introduction

Finding an area 1

Positive & negative area

Understanding areas

Finding areas

Multiplying by a constant

Using the notation

Check the steps

Finding an area 2

Finding an area 3

Finding an area 4

Reversing the steps

Positive & negative area 2

Vertical slices

Approximate area between curves

Approximate area 2

Approximate area 3

Area between curves

Area between curves 2

Area between curves 3

Using a GDC

Using a GDC 2

Exam timed O-test

O-test 1

O-test 2

O-test 3

Exam O-test 1

Exam O-test 2

Exam O-test 2

Exam O-test 3

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Trig substitution

Tan x substitution

Log substitution

Visualizing 2

Visualizing

Linear substitutions

Linear substitutions 2

Linear substitutions 3

Quadratic substitution

Power substitution

Trig substitution 2

Trig substitution 3

Trig substitution 4

Trig substitution 5

Square roots

Square roots 2

Square roots 3

Square roots 4

More examples

Exam O-test 1

Exam O-test 2

Exam O-test 3

Exam O-test 4

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Exam timed O-test 2

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Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

O-test

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Introduction

Integration Example 1

From the product rule

Example 2

Example 3

Example 4

Integrating logs

Integrating logs 2

With limits

With limits 2

With limits 3

Another special case

A special case

Exam O-test 1

Exam O-test 2

Exam O-test 3

Exam O-test 4

Exam timed O-test

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Investigate Trig Integration

sin x and cos x

tan x and cot x

sin ax and cos ax

sin ax and cos ax 2

Other trig functions

tan ax and cot ax

Other trig functions 2

Using identities

Other trig functions 3

Definite integrals

Definite integrals 2

Using a GDC

Matching O-test

Exam O-test

Exam timed O-test

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Area and volume

Example 1

Example 2

Example 3

Example 4

Volume about y-axis

Volume about y-axis 2

Volume about y-axis 3

Volume about y-axis 4

Volumes using a GDC

O-test

Exam O-test 1

Exam O-test 2

Exam O-test 3

Exam O-test 4

Exam timed O-test

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Investigate Integration of e

^{ax}Definite integral 1

e

^{ax+b}Definite integral 2

Definite integral 3

Matching O-test

Exam timed O-test

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Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Example 7

Radioactive half-life

Exam O-test 1

Exam O-test 2

Exam O-test 3

Exam timed O-test

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MIT video: calculus and trigonometry

Xtra 1

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Investigate Motion Calculus

Velocity & acceleration

Changing direction

Illustration

Illustration 2

Velocity & acceleration 2

A cyclist

A ball

Distance travelled

Test tube

Bouncing ball

Using integration

Using integration 2

A motorbike

A rocket

A racing car

An insect

A particle

A particle 2

A particle 3

Observation O-test 1

Observation O-test 2

O-test 1

Exam O-test 1

Exam O-test 2

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Chain Rule in Implicit Diff.

Product/Chain Rules in Implicit Diff.

Implicit Diff. of Ellipse

Implicit Diff. of Hyperbola

Definition

Definition 2

O-test

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Mindmap

Calculus glossary and quiz

The method

The method 2

The method 3

Population growth

Radioactive decay

Speed

Height of a tree

Cooling

Increasing radius

Inspector Holmes

Exam O-test

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