A-Level: Exponentials and Logarithms

Chapter 18

• This sets out the theory you need to know.
• Wikibooks has a dry presentation
  
• Log functions and exponential functions are inverses of each other. One undoes the other.
• This Utube video is lengthy but very comprehensive. If you watch this a couple of times it should click.
• The graph of y=a^x
  

A-Level: Differentiation (including negative and fractional indices)

Chapter 20 Try this. Notes from MathsRevision.net so worth printing out

• Differentiation
  
• Tangents & Normals
  
• Turning Points
• Second Derivative

You Tube

• AS & A Level Maths No.15 Calculus 1 10 minute introduction (Gradients)
  
• AS & A Level Maths No.16 Calculus 2 rate of change, ds/dt
  
• AS & A Level Maths No.17 Calculus 3 finding the equations of tangents and normals to a curve
• Exercise 20E p.367 (Review) Q all. See the Key points p.369
• Test yourself and Extension Exercise
• Complete sections in Past Examination Questions
  

A-Level: Integration and Trapezium Rule

Chapter 21 Try this.

• Integration can be used to find area though be aware that area beneath the x-axis is counted as negative area.
• WikiBooks is a good reference - but be selective i.e. scan read and just follow what you need to.
  

Trapezium Rule

• Also known as a Riemann Sum
• You need to know and be able to write down the formula for the Trapezium Rule P.379
• When this rule gives an overestimate and an underestimate
• The fact that splitting into more and more trapezia improves the approximation.
  
• I strongly recommend you to look at this Utube video for an explanation. 8 minutes.
  

Think in English first

Area = 1/2 (width of step)[1st height + 2(sum of all middle height) + last height]

Terms

• Trapezium
• Integral
• Area
• Ordinate

Resources

• Notes and worked examples
• Key Points Handout see pp385/386
  
• Past examination questions with answers. Make sure you can answer every part of every question. Use the following coding *Yes can do, ** Been taught but unsure, *** Missed this/never understood it/not a chance.
• Remember to follow how marks are allocated - write down in English the stages you are doing, write down the calculations you are doing on calculator.
• For a Question with 3 marks - if you correctly use a Calculator full marks, if you make a mistake 0 marks. Method marks can be picked up by writing your method down - but that makes sense?
  
• Exercise 21D p382 Q6, 7, 8 (Note in rare cases tables have been given)
• Exercise 21E Review p384 Q5, 6, 7

Note

• The trapezium rule has invariably been on each C2 exam paper either as a stand-alone or part of a Question. This topic should now be secure - i.e. *Yes
• Work to be completed from previous lessons Exercise 20A, Ex 20C (turning points)
  

Qualifications to Teach Mathematics

• I did A-level Mathematics and Further Mathematics when I was your age.
• Then went straight to University where I did a Joint Mathematics and Economics degree.
• I then studied to become an accountant for 3 years until I got bored and then decided to take up teaching.
• Teaching is not boring for sure.
• I then taught Mathematics for 7 years at Kaskenmoor School - 11 to 16, up to O-Level as it was then.
• I took a parallel move to North Chadderton (with slightly less money) in order to teach A-Level Mathematics.
• I taught the A-Level Applied and Mechanics modules for 4 years as well as 16+ maths and youngsters. Lots of A's and B's during that time.
• There were very few computers in school - I'd come from a school with hundreds of computers.
• So over the next 22 years I gradually dropped Mathematics and went into ICT.
• I even gave away my mathematics notes.

But

• Can do the theory but rusty - certainly with Pure Mathematics.
• Will be prepared.
• Will be able to see the pitfalls that new entrants to A-Level Maths have.
• Have to regain ways of explaining maths - picking up tricks.

I like all kinds of music - a friend gave me this a link to the Rock Hall of Fame