Arithmetic

If you work through all the part a,b and c type questions you got in class today and practice from previous exam papers, you'll be well prepared for Paper 1 Question 1.

We went over 2 types of percentages problems in class:

a) An item is reduced by 10% and the new price is 1125. What was the original price?

and

b) An amount is invested for 1 year at 6% interest rate and amounts to 5618 at the end of the year. What was the original principle invested?

To answer both questions you need to look at the number you are given and work out what percentage this represents.

In a) the amount 1125 represents 90%, so you can write down
90% = 1125 <- This is the most important step. Now I know 90%, I can work out what 10% is by dividing both sides by 9 10% = 125 100% = 1250 <- 100% is the original amount before the reduction. In b) the amount at the end of the year is the original principle (100%) plus 6% so you can write 106% = 5618 1% = 53 [dividing both sides by 106 to find what 1% is] 100% = 5300 <- 100% is the original principle that was invested.

In both cases the first step is key .. look at the number you are given and work out what percentage it represents. Then use the equation technique of multiplying or dividing on both sides of the equals by the same amount to find the percentage you are asked for.

Here is the 1-page overview of arithmetic.


Note that the formula for compound interest can be expressed in two ways.
You can say

1 + (Rate/100)

or

(100 + Rate)/100

The key point is that if the rate is, say, 19%, then you will end up with
Amount = Principle(1.19)^Years

(Sorry about formatting , ^ means raised to a power)