4

Randomized Exam Q 2009

Investigate Integration of

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

1/(ax) with limits

1/(ax+b)

1/(ax+b) with limits

Definite integral

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Exam O-test

Exam timed O-test

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Trapezium rule 2

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Trapezium rule 1

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Investigate the Trapezium Rule

Trapezium rule 3

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Trapezium Rule for Difficult Integrals

Riemann sums

The trapezium rule

Approximate integration

More examples

Left-hand, Right-hand method

Left-hand rule

Right-hand rule

Left and Right-hand rules

The mid-point rule

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The mid-point rule 2

The mid-point rule 3

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The mid-point rule 4

The mid-point rule 5

The trapezium rule

Trapezium rule 4

Trapezium rule 5

Accuracy 1

Accuracy 2

Accuracy 3

Midpoint and trapezium 1

Midpoint and trapezium 2

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Quiz

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O-test 1

O-test 2

Exam O-test 1

Exam O-test 3

Exam O-test 2

Exam timed O-test 1

Exam timed O-test 2

Exam timed O-test

Finding an area 1

Understanding areas

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Positive & negative area

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Introduction

Finding areas

Multiplying by a constant

Using the notation

Check the steps

Finding an area 2

Finding an area 3

Finding an area 4

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Horizontal slices

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Horizontal slices 2

Horizontal slices 3

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Horizontal slices 4

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Reversing the steps

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Positive & negative area 2

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O-test 1

Vertical slices

Approximate area between curves

Approximate area 2

Approximate area 3

Using a GDC

Using a GDC 2

Area between curves

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Area between curves 2

Area between curves 3

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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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Investigate Integration of e

^{ax}e

^{ax+b}Definite integral 1

Definite integral 2

Definite integral 3

Matching O-test

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Exam timed O-test

First theorem

Investigate

Second theorem

Investigate

Second theorem 2

MIT video: Fundamental theorem 1

MIT video: Fundamental theorem 2

Pattern A 1

Pattern A 2

Pattern A 3

Pattern B 1

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Pattern B 2

Pattern B 3

Exam O-test

Exam timed O-test

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Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

O-test

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Reverse 1

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Introduction

Reverse 2

Rational powers

Matching O-test

O-test

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Exam O-test

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Simple functions 1

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Key points

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Integral of x

^{p}Simple functions 2

Simple functions 3

True or false O-test

Find the constant

Find the constant 2

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O-test

Sequence O-test

Timed O-test

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Exam O-test 1

Exam O-test 2

Exam O-test 3

Exam O-test 4

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Example 1

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Example 2

Example 3

Example 4

Example 5

Example 6

Example 7

Radioactive half-life

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Exam O-test 1

Exam O-test 2

Exam O-test 3

Exam timed O-test

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Visualizing 2

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Assessment

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Visualizing

Linear substitutions

Linear substitutions 2

Linear substitutions 3

Quadratic substitution

Power substitution

Trig substitution

Trig substitution 2

Trig substitution 3

Trig substitution 4

Trig substitution 5

Tan x substitution

Square roots

Square roots 2

Square roots 3

Square roots 4

More examples

Log substitution

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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

Investigate

Example 1

Example 2

Example 3

Average rainfall

MIT video: Mean value theorem

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Investigate Trig Integration

sin x and cos x

tan x and cot x

sin ax and cos ax

Other trig functions

tan ax and cot ax

sin ax and cos ax 2

Other trig functions 2

Using identities

Other trig functions 3

Definite integrals

Definite integrals 2

Matching O-test

Using a GDC

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Exam O-test

Exam timed O-test

Memorise the methods

True or false O-test

Matching O-test 2

Spot the method

Vocabulary O-test

O-test

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Worked example 2

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Worked example

Investigate

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Investigate 2

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Example 1

Area and volume

Example 2

Example 3

Example 4

Randomized Exam Q 2002

Investigate the washer method

The washer method 1

Randomized Exam Q 2003

The washer method 2

The washer method 3

Investigate cylindrical shells

Volumes with known cross-section

Known cross-section 2

Known cross-section 3

Known cross-section 4

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Volumes using a GDC

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O-test

Exam O-test 1

Exam O-test 2

Exam O-test 3

Exam O-test 4

Exam timed O-test

Xtra 1

MIT video: calculus and trigonometry

Definition

Definition 2

Finding h(x,t)

Finding h(x,t) 2

Finding h(x,t) 3

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Voltage

Population

Water tank

Newton's law of cooling

Hot air balloon

Can of drink

Pollution

A puddle

O-test

Randomized Exam Q 2009

The method

The method 2

Population growth

Radioactive decay

Speed

Height of a tree

Cooling

Increasing radius

Inspector Holmes

Using a substitution

Using a substitution 2

Using a substitution 3

Using a substitution 4

Using a substitution 5

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Exam O-test

Creating slope fields 4

Introduction

Slope fields

Slope fields 2

Slope fields 3

Slope fields 4

Slope fields 5

Creating slope fields

Creating slope fields 2

Creating slope fields 3

MIT video: slope fields

MIT video: seperable des

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Acceleration

Acceleration 2

Acceleration 3

A motorbike

A rocket

A racing car

An insect

A particle

A particle 2

A particle 3

Using a GDC

Exam O-test 1

Exam O-test 2

Exam O-test 3

Mindmap

Calculus glossary and quiz