April 22nd Math Summary

INTEGRATION

- If you differentiate the bottom and it is the same as the top, just ln the denominator to integrate it. Or else, you will have to use partial fractions.

BINOMIAL THEORM

General Form:
(a+b) ^n = nCr (a)^(n-r) (b)^r

Answers to worksheet:
Q1

Q2

Q3

Q4

Q5

Toughest kind of question that will come out for O levels is Question 3. 

Click to Run

Lesson Summary for 11th February (Tuesday)

Today we started of with a G+ discussion (LINK HERE) of the differences between a
1. CIRCLE
2. ELLIPSE
3. PARABOLA
4. HYPERBOLA 

Where Xintong's explanation was accurate and recommended by Mr Johari.

Conic Sections

A parabola has a line of symmetry, while a Hyperbola has 2 lines of symmetry, the transverse and longitudinal (Vertical and Horizontal)

Equations of Circles

Discriminant

D<0 
Imaginery Roots

D>0
Real and Distinct Roots

D=0
Real and Equal Roots










Methods to finding the centre of the circle and the Radius

Method 1 (Completing the Square)

Method 2 (Comparing Coefficients)

General Form of the equation of a circle

Assignment Questions in (Further Coordinate Geometry: Equations of Circles)

Question 5 (Tier B)

Apparently it can intersect with each other 

Question 8 (Tier C)

Closing Note

Homework: Use GeoGebra or any graphing application to test out assumptions

Quote:
"Your level test is going to hit you like a Meteor" - Mr Johari 2014

Done By Ryan Tan S4-09

Lesson summary for Wednesday, 5th February

We did a quiz and went revised what standard deviation is.

—

Standard deviation (σ is the symbol, is a measure of the variance from the mean for a set of data. It is calculated as follows:

x̄ (pronounced as x bar) is the mean of the data set.
n is the number of data in the set.
Σ, or summation, is the addition of all the following datum. In this case, it is (x-x̄)^2.

—

Showing the proper working during the examples is essential to getting the method mark(s).

For example,

Calculate the mean, median and standard deviation for the following set of data.

1,2,3

mean = (1+2+3)/3
     = 3

Tmedian = (3+1)/2
        = 2
median = 2
                                    _________________________________
standard deviation = √(  (  (1-2)^2  +  (2-2)^2  +  (3-2)^2  ) / 2  )
                   = 1

—

The standard deviation’s and mean’s working can be in the form of a table containing all the data, and you can just use the values of Σ(x-x̄), n and Σx to calculate your answers.

If there are UNITS in the question, be sure to write them down in your answers as well.

Other reminders:

- Write scale when drawing graphs
- Show ALL the working when calculating the standard deviation, mean and median.

Check out these G+ posts to learn how to use STAT functions in your calculator
https://plus.google.com/101616184095512416932/posts/19rLzDFWtzz
https://plus.google.com/101616184095512416932/posts/bucASRsM3jJ

p.s. Sorry for the late post!

29th Jan Recap

Homework = Statistics (b) Due next friday

Probability summary

(Sorry I just realized I posted this on the old 309 math blog)

Probability: 
_________________________________________________________________________________

Probability: How likely an event can occur

Probability =   The number of ways of achieving desired outcome
                                    Total number of possible outcomes

Event will definitely occur = 1

Event will never occur = 0

Event will not occur = 1 - probability of event occurring
_________________________________________________________________________________

Sample space: All the possible outcomes of an experiment

S = {a, b, c ...}

Sample point = 1 of the possible outcomes
_________________________________________________________________________________

Mutually exclusive: Both events cannot occur at the same time

Probability (A or B) = P(A) + P(B)

Independent events: Both events can occur at the same time; Outcome does not affect probability of outcome of other event

Probability (A and B) = P(A) x P(B)
_________________________________________________________________________________

Diagrams:

Probability diagrams:

Used for two independent events

Tree diagram: 

Used for two or more events

28th Jan Recap

Math File
Use an orange/red ring file .
1.  Notes                                Earliest at the bottom .
2. Assignments
3. Quizzes    
> Repeat for each topic
----------------------------------------------------------------------------------------------------------------------------------
Mean , Median and Mode
.They are important for their own purposes depending on the analysis you want to carry out .
. Mean is very subjective as there is an outlier that can severely affect the data .
. Median is the 50% mark , letting you see how the performance of a group is .
. Mode lets you see the most popular set of data and the trends .

Box Plot 

Lower percentile - Underperforming
Upper percentile - Excelling                                > Able to plot data using the 2 points

. Box Plots let you see performances better for evaluation ( Better than Ogive)
- It is easier to see if the data is skewed ( Biased or shifted towards) based on where Q1 , Q2 and Q3 is
- Look at interquartile range and range to determine spread and performance as a whole .

To transfer the box plot into a cumulative frequency against value graph ,
a) Plot it vertically using Q1 , Q2 and Q3 as points
b) Plot it horizontally to see how everyone is performing .