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8181Matrix algebra : Eigenvalues : Exam Question
14026Mensuration : Units : What I'd do...
14021Measures : Summary : Mean, median and mode
14000Measures : Summary : What I'd do...
13997Mensuration : Time : What I'd do
13980Measures : The mode : How to...
13979Measures : The median : How to...
13962Measures : Compound measures : Example 11
13952Mensuration : Time : Example 6
13947Measures : Moving averages : Example 8
13924Measures : Compound measures : Example 10
13919Measures : The mean : Example 7
13882Mensuration : Units : Example 4
13769Matrices : Transformations : Game
13702Measures : The mean from a frequency table : Example 14
The error term
The error term 2
The Lagrange error bound
Lagrange error bound 2
Lagrange error bound 3
Lagrange error bound 3
Exponentials
Exponentials 2
Trig functions
Trig and exponential functions
Binomial series
Log functions
Log functions 2
ex
Higher derivatives
eax
sin ax
sin x
cos x
cos ax
tan x
O-test
ln(1+x)
ln(1+xn)
cosh x
sinh x
binomial
Using series
Using series 2
Using series 3
Using series 4
Finding approximations
Finding approximations 2
Finding approximations 3
Finding approximations 4
Compare approximations
Compare approximations 2
Finding definite integrals
Finding definite integrals 2
Finding definite integrals 3
Finding definite integrals 4
Exam O-test
Randomised Exam Q 2007
Randomised Exam Q 2007
Randomised Exam Q 2008
Randomised Exam Q 2008
Randomised Exam Q 2008
Randomised Exam Q 2008
Randomised Exam Q 2008
Randomised Exam Q 2008
Randomised Exam Q 2009
Introduction
Taylor polynomials
Taylor polynomials 2
Taylor polynomials 3
Visualizing
Visualizing 2
Visualizing 3
ln x
ex
1/x
MIT video: Taylor series
O-test
Randomised Exam Q 2006
Randomised Exam Q 2008
Example 1
Matchings
Maximal matchings
Alternating paths
Complete matchings
Alternating paths 2
Changing status
The matching algorithm
Vocabulary O-test
Determinant 1
Determinant 2
Determinant 3
Inverses 1
Inverses 2
Inverses 3
Simultaneous equations
Example 1
Example 2
Example 3
Example 4
Example 5
O-test 1
Adding matrices 1
Adding matrices 2
Subtracting matrices
Multiplying by a scalar 1
Multiplying by a scalar 2
Multiplying by a scalar 3
Multiplying matrices 1
Multiplying matrices 2
Multiplying matrices 3
Multiplying matrices 4
Multiplying matrices 5
Multiplying matrices 6
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
O-test 1
O-test 2
O-test 3
O-test 4
O-test 5
O-test 6
O-test 7
O-test 8
O-test 9
What is a matrix?
Sale prices
Price increases
Sales targets
Reflection 1
Reflection 2
Reflection 3
Reflection 4
Enlargement
Rotation 1
Rotation 2
Rotation 3
Game
Stretch 1
Stretch 2
Shear 1
Shear 2
Combinations 1
Combinations 2
Combinations 3
Find the matrix 1
Find the matrix 2
Find the matrix 3
Find the matrix 4
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Example 8
Example 9
Example 10
O-test 1
Adding matrices on a GDC
Minors
Minors 2
O-test 1
Determinant on a GDC
Determinants
Cofactors
O-test 2
Inverse on a GDC
Adjoint
Inverse
Adding and subtracting matrices
Multiplying matrices
Revenue
Football scores
Multiplying matrices on a GDC
Inverses and determinants
Exam O-test
Randomised Exam Q 2003
Randomised Exam Q 2006
Randomised Exam Q 2008
Randomised Exam Q 2008
Randomised Exam Q 2008
Randomised Exam Q 2009
Definition
Definition 2
Row operations
Row operations 3
Row operations 2
Row operations 4
Find a row operation
Find a row operation 2
Find a row operation 3
Convert to row echelon form
Reduced row echelon form
Using row echelon form
Inconsistent equations
Infinitely many solutions
Ill-conditioned equations
Ill-conditioned 2
Ill-conditioned 3
Ill-conditioned 4
Ill-conditioned 5
Augmented matrices on a GDC
O-test
Randomised Exam Q 2006
Diagonal form
Diagonal form 2
Powers of a matrix
The theorem
Using the theorem
Using the theorem 2
Using the theorem 3
O-test
Pauli matrices
Hermitian matrices
Skew-Hermitian matrices
Eigenvalues
Decomposition
Exam O-test
Illustration
2x2 matrices 2
2x2 matrices
3x3 matrices
3x3 matrices 2
O-test
Randomised Exam Q 2000
Randomised Exam Q 2002
Randomised Exam Q 2005
Randomised Exam Q 2006
Randomised Exam Q 2006
Randomised Exam Q 2007
Randomised Exam Q 2008
Randomised Exam Q 2008
Randomised Exam Q 2015
Inverses
Determinants
Determinants 2
Determinants 3
Determinants 4
Determinants 5
O-test 2
Inverses 2
Inverses 3
Inverses 4
Inverses 5
Inverses 6
Inverses 7
Property of Inverses
O-test 3
O-test 4
Exam O-test
Randomised Exam Q 2005
Randomised Exam Q 2006
Randomised Exam Q 2006
Randomised Exam Q 2007
Randomised Exam Q 2008
Randomised Exam Q 2008
Randomised Exam Q 2009
Randomised Exam Q 2009
Randomised Exam Q 2009
Randomised Exam Q 2009
Subtracting matrices
Adding matrices
Sums and products
Adding matrices 2
Adding matrices 3
O-test 1
O-test 2
Multiplying matrices
Multiplying matrices 2
Multiplying matrices 3
Multiplying matrices 4
Multiplying matrices 5
Multiplying matrices 6
Multiplying matrices 7
Multiplying matrices 8
The identity matrix
Multiplying by a scalar
Multiplying by a scalar 2
Multiplying by a scalar 3
Using scalars
Commutativity
Distributivity
Associativity
O-test 3
O-test 4
O-test 5
O-test 6
O-test 7
Exam O-test
Randomised Exam Q 2007
Randomised Exam Q 2007
Randomised Exam Q 2007
Randomised Exam Q 2008
Randomised Exam Q 2008
Randomised Exam Q 2008
Randomised Exam Q 2009
Simultaneous equations
Solving with a GDC
No solutions
Simultaneous equations 2
Infinitely many solutions
Unique solutions
Infinitely many solutions 2
Infinitely many solutions 3
Cramer's Rule
Exam O-test
Randomised Exam Q 2006
Randomised Exam Q 2007
Randomised Exam Q 2007
Randomised Exam Q 2008
Randomised Exam Q 2008
What is a matrix?
Sale prices
Price increases
Sales targets
Matrix equations
Transpose
Matrix equations 2
Matrix equations 3
Matrix equations 4
Matrix equations 5
Matrix equations 6
Matrix equations 7
O-test
Exam O-test
Randomised Exam Q 2006
Randomised Exam Q 2007
Randomised Exam Q 2007
Randomised Exam Q 2008
Randomised Exam Q 2009
Quick O-test
Various transformations
Various 2
Various 3
Find the matrix
Find the matrix 5
Find the matrix 6
Find the matrix 7
Find the matrix 8
Find the matrix 9
Shear
Find the matrix 10
Rotations
Reflections
O-test 2
Stretch
O-test 3
O-test 4
Matching O-test
Exam O-test
Randomised Exam Q 2008
Randomised Exam Q 2008
Randomised Exam Q 2008
Randomised Exam Q 2008
Randomised Exam Q 2009
Randomised Exam Q 2009
Randomised Exam Q 2009
Randomised Exam Q 2014
Visual
Find the matrices
Find the matrices 2
Find the matrices 3
Example
Rotations
Enlargements
O-test
Example 4
Transformations Example 1
Example 2
Example 3
O-test 5
Transforming Coordinates Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Example 8
Example 9
Find the matrix
Invariant points
Invariant points 2
Invariant points 3
Invariant points 4
Invariant lines 2
Transforming the plane
O-test 1
O-test 2
O-test 3
Randomised Exam Q 2006
Randomised Exam Q 2006
Randomised Exam Q 2008
Randomised Exam Q 2008
Exam O-test
How to...
Example 2
Example 1
Example 3
Example 4
Example 5
Bicycle journey
Runner
A horse
Mileage chart 1
Mileage chart 2
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Example 8
Example 9
Example 10
Example 11
O-test 1
How to...
Example 2
Example 1
Example 3
Example 4
Example 5
Example 6
O-test 1
Multiple choice O-test
Definition
Example 1
Example 2
O-test 1
4-point moving average
2- and 3-point moving average
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Example 8
O-test 1
O-test 2
O-test 3
Spot the Mistake 1
Mistake 1
Spot the Mistake 2
Mistake 2
Mistake 3
Timed O-test
Multiple choice O-test
Example 1
Example 2*
O-test 1
O-test 2
O-test 6
Exam O-test 1
Multiple choice O-test
How to calculate the mean
Example 1
Example 2
Example 1
Example 3
Example 2
Example 3
Example 4
Example 4
Example 5
Example 5
Example 6*
Example 7
Exam O-test 2
O-test 5
O-test 3
How to...
Example 2
Example 1
Example 3
Example 4
Example 5
Example 6
Example 7
Example 8
Example 9
Example 10
Example 11
Example 12
Example 13
Example 14
O-test
Exam O-test
How to calculate it
Test marks
Earnings
Exam O-test
How to...
Example 1
Example 2
Example 3
O-test
How to...
Example 1
Example 2
Test marks
Weights
Exam O-test
Distances 1
Distances 2
O-test 2
O-test 3
Ruler 1
Ruler 2
Ruler 4
Ruler 3
Milometer
Speedometer
Kitchen scales
Protractor
Meter reading
Ammeter
Voltmeter
Thermometer
O-test 1
O-test 4
O-test 5
Timed O-test 2
Timed O-test 1
12 and 24 hour clocks
Clock
Hours, minutes, seconds
Days, hours, minutes
Weeks, days, hours
Time intervals 2
Time intervals 3
Time intervals 4
Time intervals 5
Time calculations 1
Time calculations 2
Bus timetable
Example 1
Example 2
Example 3
Example 4
Example 5*
Example 6
O-test 4
O-test 3
O-test 2
O-test 1
The imperial system
Metric and imperial
Example 1
Example 2
Example 3
Example 4
Moments 5
Moments 3
Moments 2
Moments
The lever principle
Moments 4
Moments 6
O-test
Pole vaulter
Example 2
Example 1
A uniform beam
Two spheres
Exam O-test 1
Exam O-test 2
Exam O-test 3
Exam O-test 4
Randomised Exam Q 2001
Randomised Exam Q 2002
Randomised Exam Q 2003
Randomised Exam Q 2003
Randomised Exam Q 2005
Randomised Exam Q 2007
Randomised Exam Q 2007
Randomised Exam Q 2007
Randomised Exam Q 2008
Randomised Exam Q 2008
Randomised Exam Q 2009
Randomised Exam Q 2009
Randomised Exam Q 2010
Randomised Exam Q 2014
Labelling Diagrams - Plank
Moments
Moments 2
Moments 3
Moments 4
A hanging sign
A ladder
A deck crane
A roundabout
Exam O-test
Randomised Exam Q 2006
Randomised Exam Q 2008
Example 1
Example 2
Exam O-test
Randomised Exam Q 2000
Randomised Exam Q 2006
Example 1
Exam O-test
Randomised Exam Q 2000
Randomised Exam Q 2007
Randomised Exam Q 2008
Randomised Exam Q 2008
Old records
Roundabout
Illustration
Units
Space satellite
Clock hands
Cricket ball
Wall of death
Car wheel
Car wheel 2
Water wheel
Circular saw
Diver
O-test
A particle
Minimum radius
Bend in the road
Fruitbowl
Skittles
Planetary orbits
O-test
Horizontal disc
Horizontal disc 2
Conical pendulum
Conical pendulum 2
Banked surface
Banked surface 2
Banked surface 3
Exam O-test
Randomised Exam Q 2007
Randomised Exam Q 2007
Randomised Exam Q 2007
Randomised Exam Q 2008
Randomised Exam Q 2014
A particle
Particle on sphere
Girl on a swing
Exam O-test
Randomised Exam Q 2006
Randomised Exam Q 2007
Randomised Exam Q 2007
Randomised Exam Q 2008
f(x,y)=x²+y²
f(x,y)=1/(x²+y²)
f(x,y)=root(x²+y²)
f(x,y)=sin(x+y)
f(x,y)=cos(x-y)
f(x,y)=2cos(x)-y²
Total differentials
Small errors
Small errors 2
Small errors 3
Exact differentials
Stationary points
Stationary points 2
Stationary points 3
Stationary points 4
O-test
Directional derivatives
Directional derivatives 2
grad f
Examples
Example 2
Example 3
Example 4
Product rule
Product rule 2
Quotient rule
Quotient rule 2
Chain rule
Chain rule 2
Chain rule 3
Chain rule 4
Combinations
Stationary points
Stationary points 2
O-test 1
O-test 2
O-test 3
Definitions
More definitions
Example
Example 2
Find the equation
Find the equation 2
O-test
MIT video: min-max problems
MIT video: partial derivatives
MIT video: y'=f(x,y)
Mindmap