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

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

Bitesize

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

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

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

Number: Recurring Decimals to Decimals

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)

Plenary

• Skillswise

USEFUL LINKS

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

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
SAS
SSS
ASA or AAS
RHS


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


TRANSLATIONS P 589
y = f(x) + a
y = f(x+a)

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

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)

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

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



Factorising
Common Factors


If you can stay awake this is video 35 of 51

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

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

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.

Algebra: Index Numbers

Reminder of Rules


Recap p.247

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