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142Inequalities : Using algebra : Investigate Rational Inequalities 1

8168Integration : e

^{x}: Exam Question8161Integration : Applications : Exam Question

8152Integration : Volume of revolution : Exam Question

8150Integration : Rules : Exam Question

8142Integration : Separable differential equations : Exam Question

8133Inequalities : Using algebra : Exam Question

8130Integration : Definite integration : Exam Question

8124Integration : Definite integration : Exam Question

8119Integration : Volume of revolution : Exam Question

8110Integration : Approximate integration : Exam Question

8109Integration : Separable differential equations : Exam Question

5049Inverse Trigonometric Functions : Elementary properties of inverse trigonometric functions : Exam Question

5046Introduction to 3-Dimesional Geometry : Coordinate of a point : Identifying points 1

14Integration : Definite integration : Exam Question

Kicking a football

Batting a cricket ball

Randomised Exam Q 2008

Timed O-test 2

Timed O-test 1

How to...

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Example 7

Example 8

Example 9

Example 10

Example 11

Example 12

Powers wall O-test 1

Powers wall O-test 2

Powers wall O-test 3

Mistake 1

Mistake 2

Mistake 3

Mistake 4

Mistake 5

Example 1

Example 2

Exam O-test

Multiple choice O-test

How to solve...

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Example 7

Example 8

Example 9

Example 10

Example 11

Example 12

Example 13

Example 14

Example 15

Example 16

Timed O-test 1

Ordering O-test 1

Ordering O-test 2

How to solve...

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

O-test 1

O-test 2

Number line

Number line 2

Integer values

Integer values 2

Example 1

Example 2

Timed O-test

O-test 1

Multiple choice O-test 1

Graphing 1

Graphing 2

Graphing 3

Graphing 4

mx+c

Integer coordinates

Integer coordinates 2

Example 1

Example 2

Example 3

Polynomial inequalities

Rational Inequalities Problem

Investigate Rational Inequalities 1

Investigate Rational Inequalities 2

Quadratic inequalities

Cubic inequalities

Modulus inequalities

O-test

Exam O-test

Randomised Exam Q 2000

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Investigate Quadratic/Linear Inequalities

Investigate Rational Inequalities 3

Investigate Rational Inequalities 4

Investigate Modulus Inequalities 2

Investigate Modulus Inequalities 1

Investigate Further Inequalities

Randomised Exam Q 2005

Rule 1

Rule 2

Rule 3

Rule 4

Remainders

The division algorithm

O-test 1

Division algorithm extended

Division algorithm extended 2

Division algorithm extended 3

Fundamental theorem

GCD

Euclid's Algorithm for GCD

LCM

LCM using the GCD

O-test 2

Relatively prime numbers

Relatively prime numbers 2

GCD and LCM on a GDC

Exam O-test

Randomised Exam Q 2007

Randomised Exam Q 2009

Checking if solvable

General solutions

Addition

Multiplication

Linear congruences

Linear congruences 2

Other congruences

Fermat's little theorem

Convert to base ten

Convert to base ten 2

Binary to base ten 2

Convert from base ten

Addition

Subtraction

Multiplication

Perfect cube

Exam O-test

Randomised Exam Q 2006

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 2008

Randomised Exam Q 2009

Length of arc in parametric form

Investigate length of arc

Investigate length of arc 2

Investigate length of arc 3

Arc length with polar coordinates

Length of arc

Length of arc 2

O-test

Area of surface

Area of surface 2

MIT video: arc length, sector area

Exam O-test

Randomised Exam Q 2005

Randomised Exam Q 2015

Investigate the Trapezium Rule

Trapezium rule 3

Trapezium rule 1

Trapezium rule 2

Riemann sums

Trapezium Rule for Difficult Integrals

The trapezium rule

More examples

Approximate integration

Left-hand, Right-hand method

Left-hand rule

Right-hand rule

Left and Right-hand rules

The mid-point rule

The mid-point rule 2

The mid-point rule 3

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

Midpoint & Trapezium 3

Simpson's rule

Simpson's rule 2

Simpson's rule 3

Simpson's rule 4

Simpson's rule 5

Simpson's rule 6

Spreadsheet investigation

Spreadsheet investigation 2

Quiz

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

Randomised Exam Q 2000

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Positive & negative area

Finding an area 1

Understanding areas

Exam timed O-test

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

Horizontal slices

Horizontal slices 2

Horizontal slices 3

Horizontal slices 4

Reversing the steps

Positive & negative area 2

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

Area between curves 2

Area between curves 3

O-test 2

O-test 3

Exam O-test 1

Exam O-test 2

Exam O-test 2

Exam O-test 3

Randomised Exam Q 2000

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Investigate Integration of e

^{ax}e

^{ax+b}Definite integral 1

Definite integral 2

Definite integral 3

Matching O-test

Exam timed O-test

Randomised Exam Q 2004

Randomised Exam Q 2007

Randomised Exam Q 2007

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Randomised Exam Q 2010

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First theorem

Investigate

Second theorem

Investigate

Second theorem 2

MIT video: Fundamental theorem 1

MIT video: Fundamental theorem 2

Example 1

Example 2

Inverse hyperbolics

Inverse hyperbolics 2

Inverse hyperbolics 3

Exam O-test

Randomised Exam Q 2005

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Infinite integrals

Infinite integrals 2

Infinite integrals 3

Infinite integrals 4

Infinite integrals 5

Discontinuities

Discontinuities 2

Using Parts

Using Parts 2

MIT video: improper integrals

MIT video: improper integrals 2

Randomised Exam Q 2007

Randomised Exam Q 2008

Randomised Exam Q 2008

Inverse-function rule

Inverse-function rule 2

Introduction

Example 1

Example 2

Example 3

Standard integrals

A harder example

Exam O-test

Randomised Exam Q 2000

Randomised Exam Q 2007

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

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The method

The method 2

Finding area

Example 1

Example 2

O-test

Exam O-test

Randomised Exam Q 2004

Randomised Exam Q 2008

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Randomised Exam Q 2010

2 linear factors

3 linear factors

Quadratic factor

MIT video: partial fractions

MIT video: partial fractions 2

Exam O-test

Exam timed O-test

Randomised Exam Q 2000

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Integration Example 1

Introduction

From the product rule

Example 2

Example 3

Example 4

Integrating logs

Integrating logs 2

Integrating logs 2

With limits

Parts in circles!

With limits 2

With limits 3

A special case

Another 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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Modulus

Modulus 2

Heaviside functions

Heaviside functions 2

Heaviside functions 3

Example 1

Example 2

Example 3

Randomised Exam Q 2005

Basic functions

Matching O-test 1

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

O-test

Randomised Exam Q 2009

Reverse 1

Introduction

Reverse 2

Rational powers

Matching O-test

O-test

Exam O-test

Randomised Exam Q 2008

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Key points

Simple functions 1

Integral of x

^{p}Simple functions 2

Simple functions 3

True or false O-test

Find the constant

Find the constant 2

O-test

Sequence O-test

Timed O-test

Exam O-test 1

Exam O-test 2

Exam O-test 3

Exam O-test 4

Randomised Exam Q 2000

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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

Randomised Exam Q 2000

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Assessment

Visualizing 2

Visualizing

Sine

Sine 2

Linear substitutions

Tan

Linear substitutions 2

Tan 2

Linear substitutions 3

Tan 3

Quadratic substitution

Power substitution

Trig substitution 2

Trig substitution

Trig substitution 3

Trig substitution 4

Sinh

Cosh

Trig substitution 5

Tan x substitution

Square roots

Square roots 2

Square roots 3

Square roots 4

More examples

Log substitution

The t substitution

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

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Investigate

Example 1

Example 2

Example 3

Average rainfall

MIT video: Mean value theorem

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

Using identities

Other trig functions 2

Other trig functions 3

Definite integrals

Definite integrals 2

Matching O-test

Using a GDC

Exam O-test

Exam timed O-test

Randomised Exam Q 2007

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Memorise the methods

True or false O-test

Matching O-test 2

Spot the method

Vocabulary O-test

O-test

Worked example 2

Worked example

Investigate

Investigate 2

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

Investigate the washer method

The washer method 1

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

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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Xtra 1

MIT video: calculus and trigonometry

Identifying points 1

Using Laplace tables

Using Laplace tables 2

Using Laplace tables 3

Using partial fractions

Using partial fractions 2

Randomised Exam Question

y=sqrt(x+a)/x

Example 2

Example 3

Example 4

Example 5

Example 6

Example 7

Example 1

Example 2

Mindmap