MathsNet IB: 6

Pages: 1031

6 - Calculus

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Latest 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

Differentiation

Slope

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

Curves

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

Randomised Exam Q 2002

Randomised Exam Q 2004

Randomised Exam Q 2005

Randomised Exam Q 2006

Randomised Exam Q 2007

Randomised Exam Q 2008

Randomised Exam Q 2009

Randomised Exam Q 2010

Randomised Exam Q 2011

Randomised Exam Q 2014

First principles

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

Higher derivatives

Investigate 1st & 2nd Derivatives

Investigate 1st & 2nd Derivatives 2

Second order derivatives

Exam O-test

Randomised Exam Q 2000

Randomised Exam Q 2007

Increasing and decreasing

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

Randomised Exam Q 2007

Randomised Exam Q 2008

Randomised Exam Q 2009

Randomised Exam Q 2010

Stationary points

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

Randomised Exam Q 2000

Randomised Exam Q 2001

Randomised Exam Q 2002

Randomised Exam Q 2003

Randomised Exam Q 2004

Randomised Exam Q 2005

Randomised Exam Q 2006

Randomised Exam Q 2007

Randomised Exam Q 2008

Randomised Exam Q 2009

Randomised Exam Q 2010

Randomised Exam Q 2011

Trig functions

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

Randomised Exam Q 2006

Randomised Exam Q 2007

Randomised Exam Q 2008

Randomised Exam Q 2009

Randomised Exam Q 2010

Randomised Exam Q 2011

Rules

Assessment

Some 1st and 2nd Derivatives

Differentiate xⁿ

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

Randomised Exam Q 2003

Randomised Exam Q 2004

Randomised Exam Q 2005

Randomised Exam Q 2006

Randomised Exam Q 2007

Randomised Exam Q 2008

Randomised Exam Q 2009

Randomised Exam Q 2010

Randomised Exam Q 2011

Randomised Exam Q 2014

Rules - the product rule

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

Randomised Exam Q 2007

Randomised Exam Q 2008

Randomised Exam Q 2009

Randomised Exam Q 2010

Rules - the quotient rule

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

Randomised Exam Q 2004

Randomised Exam Q 2005

Randomised Exam Q 2006

Randomised Exam Q 2007

Randomised Exam Q 2008

Randomised Exam Q 2009

Randomised Exam Q 2010

Randomised Exam Q 2011

Rules - the chain rule

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

Randomised Exam Q 2007

Randomised Exam Q 2008

Randomised Exam Q 2009

Randomised Exam Q 2010

Related rates of change

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

Randomised Exam Q 2006

Randomised Exam Q 2008

Randomised Exam Q 2009

Randomised Exam Q 2010

Randomised Exam Q 2011

Randomised Exam Q 2014

e^x

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

Randomised Exam Q 2000

Randomised Exam Q 2002

Randomised Exam Q 2004

Randomised Exam Q 2006

Randomised Exam Q 2007

Randomised Exam Q 2008

Randomised Exam Q 2009

Randomised Exam Q 2010

Randomised Exam Q 2011

Randomised Exam Q 2014

Ln x

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

Randomised Exam Q 2000

Randomised Exam Q 2003

Randomised Exam Q 2004

Randomised Exam Q 2006

Randomised Exam Q 2007

Randomised Exam Q 2008

Randomised Exam Q 2009

Randomised Exam Q 2010

Randomised Exam Q 2011

Ln x and e^x

Investigate Log/Exp Differentiation Together

Examples

True or false

Matching O-test

Sequence O-test

Exam O-test

Randomised Exam Q 2006

Randomised Exam Q 2007

Randomised Exam Q 2008

Implicit differentiation

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

Randomised Exam Q 2003

Randomised Exam Q 2004

Randomised Exam Q 2005

Randomised Exam Q 2006

Randomised Exam Q 2007

Randomised Exam Q 2008

Randomised Exam Q 2009

Randomised Exam Q 2010

Randomised Exam Q 2011

Randomised Exam Q 2014

Inverse trig functions

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

Randomised Exam Q 2002

Randomised Exam Q 2007

Randomised Exam Q 2008

XTRA

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

Exponential growth & decay

xⁿ and n^x

a^x

a^bx

Exam O-test 2

Exam timed O-test

Randomised Exam Q 2007

Randomised Exam Q 2009

Randomised Exam Q 2011

Forming differential equations

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

Randomised Exam Q 2008

Integration

Reverse of differentiation

Introduction

Reverse 1

Reverse 2

Rational powers

Matching O-test

O-test

Exam O-test

Randomised Exam Q 2008

Randomised Exam Q 2009

Randomised Exam Q 2010

Randomised Exam Q 2011

Observation

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

Randomised Exam Q 2007

Randomised Exam Q 2008

Rules

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

Randomised Exam Q 2000

Randomised Exam Q 2002

Randomised Exam Q 2003

Randomised Exam Q 2004

Randomised Exam Q 2005

Randomised Exam Q 2006

Randomised Exam Q 2007

Randomised Exam Q 2008

Randomised Exam Q 2009

Randomised Exam Q 2011

Randomised Exam Q 2014

1/x

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

Randomised Exam Q 2008

Randomised Exam Q 2009

Definite Integration

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 3

Randomised Exam Q 2000

Randomised Exam Q 2002

Randomised Exam Q 2003

Randomised Exam Q 2004

Randomised Exam Q 2005

Randomised Exam Q 2006

Randomised Exam Q 2007

Randomised Exam Q 2008

Randomised Exam Q 2009

Randomised Exam Q 2010

Randomised Exam Q 2011

Randomised Exam Q 2014

Substitution method

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

Exam timed O-test 1

Exam timed O-test 2

Randomised Exam Q 2000

Randomised Exam Q 2003

Randomised Exam Q 2004

Randomised Exam Q 2005

Randomised Exam Q 2006

Randomised Exam Q 2007

Randomised Exam Q 2008

Randomised Exam Q 2009

Randomised Exam Q 2010

Randomised Exam Q 2011

Randomised Exam Q 2014

Reverse of chain rule

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

O-test

Randomised Exam Q 2009

Parts

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

Randomised Exam Q 2000

Randomised Exam Q 2003

Randomised Exam Q 2006

Randomised Exam Q 2007

Randomised Exam Q 2008

Randomised Exam Q 2009

Randomised Exam Q 2010

Randomised Exam Q 2011

Trig functions

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

Randomised Exam Q 2007

Randomised Exam Q 2008

Randomised Exam Q 2009

Randomised Exam Q 2010

Volume of revolution

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

Randomised Exam Q 2000

Randomised Exam Q 2002

Randomised Exam Q 2003

Randomised Exam Q 2006

Randomised Exam Q 2007

Randomised Exam Q 2008

Randomised Exam Q 2009

Randomised Exam Q 2010

Randomised Exam Q 2011

Randomised Exam Q 2014

e^x

Investigate Integration of e^ax

Definite integral 1

e^ax+b

Definite integral 2

Definite integral 3

Matching O-test

Exam timed O-test

Randomised Exam Q 2004

Randomised Exam Q 2007

Randomised Exam Q 2009

Randomised Exam Q 2010

Separable differential equations

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

Randomised Exam Q 2000

Randomised Exam Q 2003

Randomised Exam Q 2004

Randomised Exam Q 2005

Randomised Exam Q 2006

Randomised Exam Q 2007

Randomised Exam Q 2008

Randomised Exam Q 2009

Randomised Exam Q 2010

Randomised Exam Q 2011

XTRA

MIT video: calculus and trigonometry

Xtra 1

Exponentials and logs

1st Order Differential Equations

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