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April 28th, 2015

4/28/2015

Today we continued with applications of Differentiation.
With Ms McGuinness for the next few days.

p.1_2012_q.8_a-c.pdf
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p.1_sample_a_q.9.pdf
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2012 Sample Paper 1 Q.9 a

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April 27th, 2015

4/27/2015

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Today we considered:

Max, min and points of inflection
Slope of tangent to circle
Applications of differentiation

HW: Paper 1:

p.96 Sample A Q.9
p.34 2014 Sample Q.9 c
p.64 2012 Q.8

Related rates of change

Applications of differentiation

Tangent to a circle using implicit differentiation

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Requested solution

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Today we looked over yesterdays notes on functions and differentiation. We then looked at the Differentiation questions on the revision page of the website. We spent time exploring the ideas of: a limit, asymptotes, continuity.

HW: Try the differentiation questions below. (Solutions on Differentiation page)

Functions (Including continuity)

Differentiation

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April 22nd, 2015

4/22/2015

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Today we looked at:

Functions
Graphing functions
Using the calculator to get the equation of a quadratic function given 3 points (note this could be also used to get the expression for a quadratic sequence)
Injective, surjective and bijective functions
The inverse of a function
Graphs of derivatives
Slope function
Positive & negative slopes
Differentiation from 1st principles

Functions

functions_revision_22-4-2015.pdf
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April 21st, 2015

4/21/2015

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Today we completed our look at proofs and constructions that must be known:

1. Derive formula for sum of geometric series

2. Prove root 2 is not rational

3. Construct root 2 and root 3

4. Derive the Amortisation Formula

Deriving the Amortisation Formula

5. Proof by Induction

Linked here are the solutions to last nights HW on Proof by Induction

Proof by Induction

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April 20th, 2015

4/20/2015

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Today we referred to things that must be learned off for the LC maths exam.

Paper 1

Proof of by Induction (i) Sums (ii) Factors (iii) Inequalities and (iv) deMoivre's Theorem
Derive Amortisation formula
Derive sum of infinite geometric series formula
Prove root 2 is not rational
Construct root 2 and root 3
Differentiate Linear and Quadratic Functions from 1st Principles
Define Injective, surjective and bijective functions

Paper 2

Define geometry terms: Theorem, proof, axiom, corollary, implies, converse, is equivalent to, if and only if, proof by contradiction
Prove theorems 11, 12 and 13
Derive trigonometric formulae 1-7 and 9
Constructions 16-22
Define sample types: Simple random, stratified, cluster and quota