Friday, 18 December 2009

Trigonometry: Cosine Rule

A good animated example

You need to be familiar with how to find a side and how to find an angle using the cosine rule

1. When all three sides of a triangle are known or can be calculated. In this situation, the Cosine Rule can be used to find any and all of the three angles

2. When two sides are known, and the included angle is either known or can be calculated (e.g. using the other two angles). In such a situation, the length of the third side can be calculated, and so can the other angles.

3. If two sides and an angle besides the included angle is known, the Cosine Rule can still be used, but the Sine Rule is easier to use.

Bitesize Revision

Thursday, 17 December 2009

Trigonometry: Sine Rule

Can be used in triangles without right angles when given

Two sides and an angle opposite to one of the sides
One side and any two angles


This video lasts 10 minutes but goes through examples

Statistics: Histograms

Histograms are a favourite GCSE topic, you need to know

  • what grouped data is
  • how to calculate the frequency density

The frequency on a Histogram is shown by the area in the box (frequency density x class width)
The class width is often unequal

Histograms are most often used with grouped data

In the diagram below

  • there are 20 people aged between 60 and 100
  • there are 42 people aged between 40 and 60

Statistics: Moving Averages

A pdf file with worked examples of GCSE questions - useful when you revise
Bitesize gives a simple example and a graph to show why we do them

Wednesday, 16 December 2009

Algebra: Surds

Surds are numbers left in 'square root form' (or 'cube root form' etc). They are therefore irrational numbers. The reason we leave them as surds is because in decimal form they would go on forever and so this is a very clumsy way of writing them. (See here for notes and examples )

Skills needed to answer GCSE questions
  • Using Surds in calculations
  • Simplifing Surds
  • Rationalise Surds (which needs you to remember the difference of 2 squares)

    Helpful resources, examples and links


    BBC Bitesize is always good

    GCSE Maths tutor - technical but some worksheets and videos

    Some people fing watching a YouTube video can help, but be aware that they use real Maths teachers

    MyMaths Surds1 goes through the topics in a gentle way.
    Surds2 - a little harder

  • Monday, 14 December 2009

    Revision Guides - Higher Edexcel

    I think the following at around £3.50 each are well worth the money.

    GCSE Success Edexcel Maths Higher Revision Guide
    This book puts all the notes you need in one place with limited examples. All of the Specification is set out.
    GCSE Success Edexcel Maths Higher Workbook (GCSE Success Revision Guides and Workbooks)
    This gives lots of examples with answers to reinforce your ideas.
    There are lots of sites that give you help (videos, worked examples, etc). This one is the BBC Bitesize – Statistics Site

    Sunday, 6 September 2009

    Statistics: Probability 1

    Read and work out missing information from a two-way table
    Design-two way tables and complete using data from a graph
    Review the term Probability
    Understand the term relative probability
    Number of trials and reliability
    Calculating the probability of an event using relative frequency

    Sample size must be large enough to be reliable (or representative)
    Using Relative frequency to estimate the results of an experiment and judge if fair or biased
    Consolidate by looking at Chapter Review (Q 7, 8, 9 if time permits)



    Saturday, 5 September 2009

    Statistics – Handling Data

    This is the AQA Website for this Maths GCSE
    Module 1 (worth 18% of the GCSE) looks at data and includes topics such as averages (should I use the same average for shoe sizes as for the average price of beer), probability (how likely are you to contract ‘swine flu?) and correlation (is it true that ‘the less alcohol and fatty foods, the longer the life’?).
    This is the text book used across the college – you will need to have this to follow the course (about £18)
    AQA GCSE Maths: Modular Higher Student Book and ActiveBook

    With private tuition students I find the following successful (£3.50 each)
    This one puts everything in place
    GCSE Success AQA Maths Higher Revision Guide (GCSE Success Revision Guides and Workbooks)
    Maths Higher Workbook (GCSE Success Workbooks)
    This one gives examples of each to help you understand.
    There are lots of sites that give you help (videos, worked examples, etc). This one is the BBC Bitesize – Statistics Site

    Tuesday, 19 May 2009

    Revision: Foundation

    1 Go through 2 past Papers

    2. Graphs
    Quadratic Graphs - be able to write down co-ordinates
    Identify maximum, minimum points and lines of symmetry
    Identify graphs p.238-237 q2, q4, q8
    Use a graph to find solutions p.241 q2, 4

    3. Using a formula p337 q1, 4, 5
    Changing the subject of a formula p347 q4,5

    4 Angles in shapes
    acute, obtuse, reflex
    equilateral, isosceles, scalene
    constructing triangles
    p550 q2

    5 Algebra
    Simplifying Terms (Expanding brackets) p197 q7, p199 q3
    FOIL p.262 Q1 and 2
    Factorise p259 q1

    6 Sequences
    term to term rule p.433 1 and 2
    patterns of shapes p440 q5,6

    7 Constructions
    Perpendicular Bisector of a line p.460
    Angle Bisector p.462
    Locus of points p.464
    p.466 q1, p.467 q3

    Revision: Higher

    1. Go through 2 past Papers

    2. Prove that triangles are Congruent P520, P521 Q1
    ASA or AAS

    3. Calculate equations of a line through a point and perpendicular to a given line
    P514 questions 4 to 8
    P515 questions 2 to 8

    4. Use Sine and Cosine Rule P661, 662 q2
    Area 1/2absinC P664 Q2
    Cosine Rule P665 Q2 (see P667)

    5. Graphs - I don't have time to teach!

    Recognise non-linear graphs

    quadratics, reciprocal, cubic, sine, cosine
    p576 3,5,7
    p580 8,9,11

    Transforming functions
    recognise functional notation

    y = f(x) + a
    y = f(x+a)

    y = f(ax)
    ExB p594 questions 1 to 5, ExB p599 questions 1 to 3

    Tuesday, 12 May 2009

    Revision - Higher Tier

    1.Vector Geometry
    P679 1 and 3 , P681 Do yourself Chapter Review 1 to 10
    2.Simultaneous Equations P540 Q2
    3.Algebraic Fractions P.305 (Covers factorising as well!) ***
    4.Graphs/Gradients p500 Q5, perpendicular gradient p506, Q1, 6, 7
    5.Equalities/Inequalities p387, p392 q7, p395 Q9,10
    6.Sequences Chapter 28 p.433 q2, p439 q4
    7.Graphs of cubic etc. Chapter 37, 40 (Probably paper 2)
    8.Transforming Graphs Chapters 40/41
    9. Chapter 23 //lines, rhombus, //gram p.316 exb, polygons p.324 q6 &7, Pythagoras p.329 q9
    10. Indices p.333, writing formulas p.343
    11 Changing subject of a formula p.345, 352 q.5
    12. Chapter 25 perimeter and area //gram, triangle, circle, composite
    13 Volume of Prism p.429 q6 to 10
    14 Chapter 30 Constructions
    15 congruent, similar p527
    16 chapter 35 paper 2 SOHCAHTOA, 3D
    17 Arc length, Are sector, dimensions p568
    18 circle theorems ch39 p.635 ALTERNATE SEGMENT THEOREM
    19 Quadratic equations p.640 q1 to 4, p643 q3 to 8, COMPLETE THE SQUARE p.646 all
    20 sine rule, cosine rule ch41
    21 Chapter 42 Vectors
    22. Past Papers (see November 2008)

    Monday, 11 May 2009

    Revision: Foundation Tier

    Do you need any help from the following? I have given references to the Trevor Senior (Blue Book you have)

  • Finish the three Previous Papers 2006, 2007 and 2008
  • Solving Equations p434-435

  • Using formulas p464-465, P468

  • Sequences p499-501

  • Distance Time Graphs p.562-566

  • Factorising p.613, 615

  • Parallel lines p.621, quadrilaterals, p623, p625

  • regular polygons

  • writing as equations p.649

  • Area //gram , triangles p.660-661

  • circumference p.665, 669

  • area p.671

  • equalities p.686

  • inequalities p.692, 693, 694

  • nets, volumes p.718

  • finding the nth term p.734, 737

  • graphs/gradients p.745-747

  • quadratic graphs p.750-751

  • constructions
  • Friday, 8 May 2009

    Algebra (Higher)

    A collection of links, videos etc that will give you last minute revision

    Bitesize has a comprehensive list
    Bitesize does Simultaneous Equations
    A really, really good Mind Map - I like these

    Common Factors

    If you can stay awake this is video 35 of 51

    Factorising Quadratics
    A worksheet explaining quadratics such as 2x2 + 5x − 7.

    a^2-b^2 = \left(a+b\right)\left(a-b\right)

    Oh dear he tries to be funny - a difference of 2 Squares

    Thursday, 7 May 2009

    Trigonometry: Graphs

    Chapter 37 Graphs

    I'll add things later - but do subscribe/follow it'll help - this topic will be on the second paper.

    Cubic Functions
    • Have a look at Bitesize Cubic Function )
    • Have a look at the links - there is a good summary of the graphs you should know.

    A video that is American but watch once!

    Reciprocal Function look at how this is plotted

    Trigonometric functions sine, cosine - be aware of what they look like

    Solving Quadratic equations graphically

    37.3 Transformations and Functions

    A very good start is to look at Bitesize
    Translations, Stretch, Reflection
    There is a pdf here - 9 pages that will need printing out.

    Monday, 23 February 2009

    Algebra: Index Numbers

    Reminder of Rules

    Recap p.247

    Standard Index Form p 249 (Straightforward)
    Exercise B p250/251