## Wednesday, January 15, 2014

### SUMMARY || 13.1.14

Main topic: Statistics

Bar graphs
Discrete: only definite values
Continuous: all values within range

Histograms
Frequency Polygon: to compare the trend of 2 histograms
How to draw? Split the top of each bar of the graph in half, connect the middle points of the top of the bars together.

Figure 1.1 - Frequency Polygon (source: Wikibooks)

Dot diagrams
Rearranging of data in ascending order which makes it easier to find median term.

Things important in graphs
- scale
- accuracy

## Thursday, January 9, 2014

### 9 Jan Thursday Lesson Summary

Points to remember from previous lessons:

- Don't state the obvious
~> eg. 5 years = 60 months X

- Rate and Duration MUST be in the same time frame.
~> keep them exact

- Foreign exchanges are Ratios :D
eg. 1 euro = S\$1.7306
US\$ 1 = S\$1.3021
* to compare ratios, there must be a same BASE. *
therefore,
S\$ 1 = US\$ (1/1.3021)
1 euro = US\$ (1.7306 x 1/1.3021)
1 euro = US\$ (1.7306/1.3021)
So, we get: US\$ 1 = (1.3021/1.7036) euro
= 0.7524 euros (to 4dp)

For interests, always write the formula first! (presentation is important~)

Simple Interest = (principal x rate x duration) / 100

Compound interest = Principal (1 + r/100)^duration

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Tax: GST

A restaurant bill came to \$300. Find the total bill if there is a 10% service charge and a 7% GST added to the bill.

Bill = \$(300x1.1x1.07)
= \$353.10

What if there is a 5% discount given on the bill. What is the amount payable then?

Bill = \$(300x1.1x1.07x0.95)
= \$335.45
# discount doesn't make a difference no matter when it is added since it is multiplied.
-> although the order can determine which party benefits from it.

Income tax~
Tax salary = balanced leftover pay per annum after deduction of tax relief.
Eg. Tax salary = \$34 750
Tax bill = \$200 + (\$4750 + 3.5/100)
(Tax bill = payment for 1st \$30 000 + payment for next \$10 000)

Question to think about:

When two variables, A and B, increase or decrease at the same time, it is directly proportional (y=kx) but when one increases and one decreases, it is supposedly indirectly proportional (y=k/x). But is there a way to make it directly proportional when one variable increases and the other decreases?

Discussion's on the next lesson :)

## Tuesday, January 7, 2014

### Jan 7 Tuesday Lesson Summary

Percentage: Parts per 100 of a whole

Similar across both types of interest
Principal amount (eg. \$10000)
Rate (eg. 5% p.a.)
Duration/time (eg. 4 years)

Rate and duration must have the 'same time frame', like pa (per annum) and 4 months is not acceptable.

Money must always be expressed in 2dp!

Calculating Interest
Simple:
Interest = (Principal x rate x duration) / 100

In the event if the duration is in 'months' and rate is in 'year'
divide the duration by 12 (since 1 year has 12 months, obviously)

In the event the rate is in 'months' and duration is in 'year'
Multiply the rate by 12.

Compound:
Year(final year) = principal amount x (1 + rate in decimals)^(final year)

Same rules apply for 'same time frame'.

Hire Purchase
Principal amount/capital + interest paid off in installments

Disclaimer: If I got something wrong please comment or something and this is the first ever post so I don't know what Mr Ingham is going to think about it :(

## Sunday, January 5, 2014

### 21st CENTURY CHALLENGES - REVERSING POVERTY

REVERSING POVERTY –

Singapore is well know for its model of FINANCIAL PRUDENCE.

Can you think about examples that shows (or negates) this point?

So, as an initial look at how Math is relevant to the REAL WORLD, we will be taking a look at Singapore’s model in helping its citizens to manage debt through the policies associate with UNSECURED LOANS, VEHICLE LOANS, MORTGAGE AMOUNTS, BUY-TO-LEASE MORTGAGE.

Each TABLE group will be responsible for ONE of the following policies of the MAS to help its citizens to better manage their finances.  You might like to think about the RAMIFICATIONS of the Government NOT putting these policies in place.

You may refer the Monetary Authority of Singapore website for more information

In terms of the WORLD AT LARGE -
Consider the effect of DEBT in the developing world.  How many people are kept in servitude in order to maintain their debt repayment and how some people’s debt are inter-generational.

Taking the effect of MORTGAGE RATES and how property prices can be soaring around the world, how it might be possible for debt to roll-over to the “next generation” so as to keep mortgage repayment amounts low, especially for the properties that have > 90% debt.

We can check out the Singapore government’s policy of checking the debt-to-income ratio in the purchase of property … the deposit requirement to purchase cars (why is this necessary?) … the total amount of debt that each person can have at any time.

### LEVEL TEST 1 (WEEKS 8 & 9)

Hi everyone,
Sorry to start the year with such a DEPRESSING topic but I will need to let you know that the topics for LEVEL TEST 1 has been confirmed and I have listed them below

EMath -

1. Practical Situation – utilities + hire purchase + SI and CI + forex + profit and loss + taxation
2. Statistics
3. Probability
4. Mensuration
AMath

1. Circles and Ellipses
2. Trigonometry

This means that the REMEDIALS from now till LT1 will be focusing on these topics.

REMEDIALS will take place EVERY MONDAY from 3pm - 4pm.  I'll be booking a venue should there be an overwhelming number who are keen to participate.