Uses of Partial Fractions

Some links on the uses of partial fractions.

1. http://www.s-cool.co.uk/a-level/maths/advanced-algebra/revise-it/uses-of-partial-fractions

2. http://www.karlscalculus.org/calc11_5.html

3. http://www.sosmath.com/algebra/pfrac/pfrac.html

Answers for pg 51 - 53 (Long and synthetic division)

The answers are:

Practice 5

quotient = 2x^2-x-12
remainder = 2

Practice 6

quotient = 6x^2 - 4x - 2
remainder = 0

Practice 7

quotient = 2x^4 + 3x^2 + 9
remainder = 0

Practice 8
(a) quotient = 2x^2 - x - 12
     remainder = 0

(b) quotient = 3x^2 -12x + 6
      remainder = 3

Long Division Practice 2

Yes it's very messy and blur sorry ._.

Math Notes Part 1 Answers

Punishment for not knowing which Practice 02 in the math notes as homework :(

Practice 04 - Page 50 of Math Notes Sec 3 Part 1
by Ryan Yeo

Long Division involving polynomials

Polynomials Revision

BY MR JOHARI
source: http://www.regentsprep.org/Regents/math/ALGEBRA 

Attempt the following Quiz and post your score as a comment.
Not to worry about the score - it is non evaluative for CA but would enable me to gauge your understanding and assist you.

Homework for 15 Jan 2013 (Polynomials Worksheet A01B)

Here are the modifications for the homework.

Q3) (b) 3x^2-4x+20 = A(x-2)^2 + B(x+2) + C

  

       (c) 2x^3-x^2 - 7x+C = (2x-3) (x^2 + x - 2) +1

Please complete them by tomorrow.

3 Things Learnt from Today

1. The image of a function is the output
2. f -> x = f(x)
3. Differentiate a function from non-functions.

Yeah!
Try and find what 1/9801 is equal to, the answer is amazing.

Answers for practice 2,3,4,5

Edited for better viewing!! :)

Gotfried Wilheim Leibniz: Contribution as Mathematician

Leibniz was the first to employ function to denote any of several geometric concepts derived from a curve, such as abscissa, ordinate, tangent, chord, and the perpendicular. In the 18th century, "function" lost these geometrical associations. Leibniz was the first to see that the coefficients of a system of linear equations could be arranged into an array, now called a matrix, which can be manipulated to find the solution of the system, if any. This method was later called Gaussian elimination.

Daniel Bernouli: Bernouli's principle

In fluid dynamics, Bernoulli's principle states that for an inviscid flow, an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy. Bernoulli's principle is named after the Swiss scientist Daniel Bernoulli who published his principle in his book Hydrodynamica in 1738.

Leonhard Euler

He is a Swiss mathmetician and physicist.

He is the one responsible for the "e" you see in your calculators. It is a constant that is approximately equal to 2.71828.
Basically it means this:

The base of the natural logarithm.

From "e" he derived "Exponential Function" from f(x) = e^x. It is used to model a relationship in which a constant change in the independent variable gives the same proportional change (i.e. percentage increase or decrease) in the dependent variable. 

http://www.mathsisfun.com/numbers/e-eulers-number.html

WANNA SHARE:

I've found this nice math video that is got to do with youtube:

FUNCTION (GRAPHICAL PERSPECTIVES)

by Mr Johari

The previous activities explicated the definitions of Relation and Function.

In the following task you have to use a suitable graphing tool to identify the graph and equation of

(1)  a FUNCTION 

(2)  a Non FUNCTION 

The graph below is an example.

graph from GEOGEBRA
The above shows a FUNCTION (property one to one)
equation y = x

GCP - ITALY

Please complete this by 13 January 2013

What can you tell about these machines?

Coffee Making Machine

Chocolate wrapping Machine

Popcorn making machine

Tidbits vending machine

In groups of 2's or 3's, discuss and post your observation in this thread.

Math Olympiad and Math Italy Trip

Here are two programmes for your consideration. 

 1. Math Olympiad 

     - Saturday Morning for 15 weeks 

      

     Please send me an email before this Friday, 11 Jan 2013, if you are interested.

2. Math Italy Trip

    - Mr Ingham has briefed you on the trip last year.

    - June or Oct (not confirmed yet)

    Please send me an email before this Friday, 11 Jan 2013, if you are interested. More information may be obtained from Mr Ingham.

Thank you.

Mutual Swap between Math and SS & Chem

Dear students

 As I will be away on course this Friday, 11 Jan 2013, your SS and Chemistry teachers have kindly agreed to swap their lesson with me.

11 Jan (Fri) Math 08 55 - 09 45 --> SS
11 Jan (Fri) Math 0945 - 1035 --> Chemistry
14 Jan (Mon) 10 45 - 11 35 Chemistry --> Math
15 Jan (Tues) 1155 - 1245 SS --> Math Thank you.

Sec 3 Scheme of Work

BEGIN WITH THE END IN MIND

by Mr Johari

Welcome to an exciting year 2013
Success comes with adequate preparation and as a start do take note of the following.

1. Know your Syllabus for 2013.
    Elementary Mathematics 4016 (SEAB site)
    Additional Mathematics 4038 (SEAB site)

2. Right Resources.
    SST Maths Note (Sec 3 term 1)
    Optional Reference Book
    Calculator (with approved SST seal)
    SST Foolscap paper and graph papers (for assignments)
    ICT Resources (Class Maths Blog, ACE Learning, graphing tools etc)

3. Assessment for 2013
    Term 1   Level Test 1 + Authentic Assessment         10% + 10%
    Term 2   Common Test 1                                         20%
    Term 3   Level Test 2 + Authentic Assessment         10% + 10%
    Term 4   End of Year Summative Assessment          40%
  
4. Diagnostic Test will be conducted as Follows:
    Beginning of new topic
       - to assess prerequisite knowledge and linkages to new knowledge
    End of topic
       - to assess level of understanding and competency
    duration - 20 -30 minutes

5. Daily learning and monitoring platforms
    Class work -  in the form of activities and practice questions
    Assignment - to be done on SST foolscap papers
                         (or SST exercise books - pending style of teacher)
    all classwork to be completed within designated time

6. Character is Destiny
    Your destiny should begin with your daily routines
    A.   Be Present
    B.   Listen without Prejudice
    C.   Be Socially Aware (we are after all living in a gregarious community)
    D.   Manage your impulses
    E.   Know that the choice that you have chosen has its own consequences