HM1

Symbols are the basic building blocks of mathematics. After you have studied mathematics at advanced level for a while you will come to appreciate that certain symbols tend to mean certain things. For example x and y are used to represent variables, whereas a and b are used to stand for constants. Greek symbols are commonly used too.

Set notation

Timed Symbols O-test

Greek Symbols O-test

Set notation O-test

Functions O-test

Numbers O-test

Changing the subject 3

Equation buster

Simplifying 2

Simplifying expressions

Brackets

Brackets 2

Identities

Identities 2

Identities 3

Powers

Evaluating

Evaluating functions

Evaluating functions 2

Know your factors

Solving an equation

Solving an equation 2

Solving an equation 3

Solving an equation 4

Solving an equation 5

Solving an equation 6

Changing the subject

Changing the subject 2

Find the function

Basic algebra quiz

True or false O-test

Timed O-test 1

Timed O-test 4

Timed O-test 5

Vocabulary O-test

Timed O-test 2

Equation or identity O-test

Timed O-test 3

Matching O-test

O-test 1

Timed O-test 6

O-test 2

O-test 3

Randomised Exam Q 2006

Randomised Exam Q 2007

Randomised Exam Q 2008

Randomised Exam Q 2009

Introduction

Example 1

Example 2

Example 3

Practice

Sort out the method

Application 1

Application 2

Application 3

True or false O-test

Timed O-test

Method O-test 1

O-test 1

Method O-test 2

Exam O-test 1

Exam O-test 2

Exam O-test 2

Exam O-test 4

Randomised Exam Q 2000

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y=(x-a)(x-b)(x-c)

Solving ax³+bx²+cx+d=0

y=ax³+bx²+cx+d

Identify the coefficients

Cubics using a GDC

True or false

True or false 2

Plotting O-test 1

Observation O-test

Plotting O-test 2

Randomised Exam Q 2006

Domain and Range Introduction

Investigate Domain and Range

Domain and range

Domain and range 2

O-test 1

O-test 2

Randomised Exam Q 2006

Randomised Exam Q 2008

Randomised Exam Q 2009

Timed O-test

Introduction

Match Composite Functions 2

Explore Composite Functions 2

Investigate Odd and Even Functions

Function notation

Evaluating

Values of functions

Values of functions 2

Values of functions 3

Values of functions 4

Composition 3

Composition 4

Composition 5

Composition 6

Composition 7

Composition 8

Composition 9

Composition 10

Even functions

Even functions 2

Even functions 3

Odd functions

Odd functions 2

Odd functions 3

O-test 3

O-test 4

O-test 5

True or false O-test 1

True or false O-test 2

Matching O-test 1

O-test 6

Matching O-test 2

Exam O-test

Exam timed O-test

Randomised Exam Q 2000

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Quartics

Curve recognition

Other powers

Match Polynomial Curves

Curve recognition 2

Matching O-test

Plot Quadratics (y=ax²+bx+c)

Investigate Quadratic Roots

Min and max

Plot Quadratics (y=(x-a)²+b)

More on y=(x-a)²+b

y=c(x-a)(x-b)

Plot Quadratics (y=(x-a)(x-b))

Basic shape

More on y=(x-a)(x-b)

Curve recognition

Axis of symmetry

Match Factors of Quadratic Curves

Curve recognition 3

Using a GDC

Quadratic curve quiz

True or false O-test 2

Plotting O-test 2

O-test 1

O-test 2

Observation O-test 1

Plotting O-test 1

Observation O-test 2

Timed O-test

True or false O-test 1

Randomised Exam Q 2008

Randomised Exam Q 2007

Randomised Exam Q 2008

Timed O-test

Exam O-test 1

Exam O-test 3

Randomised Exam Q 2001

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y=a/x

y=1/(x+a) +b

Symmetries

Plotting O-test

Exam O-test

Randomised Exam Q 2007

Introduction

More y=f(x+c) Examples

Spot the transformation

The cubic graph

More y=af(x) Examples

More y=f(x-c) Examples

More y=f(x)+d Examples

More y=f(bx) Examples

y=f(x)+d Practice

Some More y=af(x) Examples

y=af(x) Practice

y=f(x-c) Practice

y=f(bx) Practice

Symmetries

Symmetries 2

Matching O-test

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

O-test 10

O-test 11

O-test 12

Exam O-test 1

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Coordinates and points

Midpoint

Distance between 2 points

Midpoint 3

Midpoint 2

Midpoint 4

Distance between 2 points 2

Distance between 2 points 3

Sides of a triangle

Isosceles triangle

Isosceles triangle 2

Parallelogram

Observation O-test

Vocabulary O-test

Timed O-test

True or false O-test

O-test 1

O-test 2

O-test 3

O-test 4

Randomised Exam Q 2005

Randomised Exam Q 2006

Victorian sewer

Midpoint, length, gradient

Between two points

Find the gradient

Find the gradient 2

The gradient using tan t

Collinear points

Line between 2 points

True or false O-test

O-test 1

O-test 2

Timed O-test

Randomised Exam Q 2000

Randomised Exam Q 2008

Introduction

Plot y=mx+c

y-y

_{1}=m(x-x_{1})Match Lines (y=mx+c) to Points

Practise

ax+by+c=0

Straight line recognition 2

Finding equations

Finding perpendicular lines

The vertical wedge

Equations in intercept form

Straight line recognition 3

Axis intercepts

Perpendicular distance

Match Lines (y=mx+c)

Straight line recognition

Finding equations 2

Finding equations 3

Finding parallel lines

Finding parallel lines 2

Finding parallel lines 3

Parallel and perpendicular lines

Perpendicular gradients

Perpendicular gradients 2

Right angles

Finding perpendicular lines 2

Finding perpendicular lines 3

Finding perpendicular lines 4

Finding lines - the method

Analysis

Linear graph quiz

True or false

True or false 2

Quiz

Quiz 2

O-test 2

Observation O-test

O-test 1

O-test 3

O-test 4

Vocabulary O-test

True or false O-test 1

True or false O-test 2

Timed O-test

O-test 5

O-test 6

Exam O-test 1

Exam O-test 2

Exam O-test 3

Exam O-test 4

Exam O-test 5

Exam O-test 6

Exam O-test 7

Randomised Exam Q 2000

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The formulae

Memorise the formulae

Altitudes

Perpendicular & altitude

Orthocentre 2

Centroid 2

Circumcentre 2

Circumcircle

Orthocentre

Centroid

Circumcentre

Perpendiculars

Medians

Investigate

Forming recurrence relations 3

Forming recurrence relations 2

Forming recurrence relations

Forming recurrence relations 4

u

_{n+1}= f(u_{n})Example

Example 2

Example 3

Bird feeder

The Isle of Blight

The Reservoir

Quiz

Using a GDC

Graphing on a GDC

Timed O-test

O-test

Exam O-test 1

Exam O-test 2

Exam O-test 3

Randomised Exam Q 2002

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Degrees to radians

Radians to degrees

Quiz

Timed O-test

O-test

The Sine/Cosine Curves

a sin (bx+c) + d Transformations

a cos (bx+c) + d Transformations

a tan (bx+c) + d Transformations

Exact values (with degrees)

Exact values (with radians)

Exact values (with radians) 2

Transforming the sine graph

Recognising trig graphs

Recognising trig graphs 2

Symmetries

From circle to graph on a GDC

y=asin(bx+c)+d on GDC

Trig graph quiz

Timed O-test

True or false O-test

Plotting O-test 1

Plotting O-test 2

Plotting O-test 3

Plotting O-test 4

Plotting O-test 5

Plotting O-test 6

O-test 1

O-test 2

O-test 3

O-test 4

Randomised Exam Q 2007

Randomised Exam Q 2008

Randomised Exam Q 2008

Randomised Exam Q 2008

Exact values

Exact values 2

Exact values 3

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

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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

Randomised Exam Q 2007

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Differentiate x

^{n}Differentiate simple functions

Differentiate products

Differentiate quotients

Check the steps

2nd order derivatives

2nd order derivatives 2

2nd order derivatives 3

2nd order derivatives 4

Derivative puzzles

Rational powers

Rational powers 2

Rational powers 3

Timed O-test

O-test 1

True or false O-test

Sequence O-test 1

Matching O-test

Sequence O-test 2

Sequence O-test 3

O-test 2

O-test 4

O-test 3

Exam O-test 1

Exam O-test 2

Exam O-test 3

Exam O-test 4

Randomised Exam Q 2005

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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

Introduction

The max-box problem 3

The max-box problem 2

A minimising problem

A minimising problem 2

View Maxima and Minima

View Maxima and Minima 2

Investigate Points of Inflection

Finding turnings points

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

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MIT video: differentation

MIT video: limits

MIT video: limits

The solution of a

^{x}=bThe graph of a

^{x}The graph of a

^{x}2Solving with a GDC

Solving with a GDC 2

Investigate Log Transformations

Inverses

Graph of Log

_{10}and its TransformationsGraph of log ax 2

Mindmap