Compound interest

Compound interest is quite similar to simple interest just that it is the amount of money earned. For example,if you leave a sum of $1000000(1 million)in your bank ,the interest rate is 50% and you leave it there for 10 years.The amount of money you will get after 10 years is
1 million x (50% x 10 years) = 1st year 1.5 million 2nd year = 2.25 million 3rd year .........
The final answer would be $57665039.06 whereby your money has grown almost up to 58 times the original amount! Note that a 50% interest rate is definitely impossible.
The formula for compound interest is
Amount= Original Amount(1 + interest/number of times compiled each year)to the power of
the number of years lapsed x the number of times compiled in a year.

Simple Interest

Simple interest is whereby when an amount of money is borrowed,the person who borrows the money must pay back the original amount + interest.The amount paid back is dependent on the amount borrowed,the interest rate,how long the money is borrowed.Therefor, the formula for finding Interest is Interest=Borrowed Money x Interest Rate x Time.
For example, if a person borrows $1000 with an interest rate of 20% for 5 years,the amount of money would be $1000+($200x 5 years)=$2000. Of course nobody does charge an interest of 20% nowadays.

Introduction to Rate

Rate is the measurement of how long a certain process is taken to be completed or how much can be completed in a certain time. For example,the rate of the number of papers that can be printed from Printer A is 70 papers per minute. It can also be phrased in another way like, the rate of child birth in Singapore is 1.24 babies for each mother. Rate questions are usually quite simple to deal with but they may also be phrased like this:

Q1. It takes Mary 5 hours to fix a jigsaw puzzle. If Mabelle helps her, they would take 3 hours to fix the jigsaw puzzle together. How long does Mabelle take to fix the jigsaw puzzle herself?
Ans + formula:
Mary--->1 hour 1/5 done
3 hours 3/5 done
With Mabelle = Mabelle does 2/5 in 3 hours
2/5 = 6/15
Mabelle = 3 hours 6/15 1 hour 2/15
15/2=7.5

Q2. If 3 girls can fold 3 paper origami in 3 minutes,how many pieces of paper origami can be folded by 30 girls in half an hour?
Ans + formula:
3 girls 1 origami 1 minute
30 girls 10 origami 1 minute
30 girls ? origami 30 minutes
10 origami x 30 minutes = 300 origami
Common Mistakes: Students may be confused and infer that 1 girl 1 origami 1 minute and their answers would go completely off.

Complex Speed 1 (Q)

Ali, Betty and Peter were on their way to a shopping centre. Ali drove 1/3 of the journey at a speed of 64km/h. Then Betty took over and drove for 20 minutes at a speed of 60km/h. Then Peter took over and drove the remaining 1/4 of the journey. For how many minutes did Peter drive?

This question made use of fractions with speed.

Introduction to Speed

Speed is the rate of motion, or equivalently the rate of change of distance. Uniform speed is a speed which is constant throughout the whole process of something. To find average speed, first find the distance travelled and the time taken to travel this distance. Following, divide the distance travelled by the time taken and you will get the average speed. For example,
John is driving a car at 50km/h for 1 hour and 80km/h for 30 minutes, what is his average speed?
Distance travelled = 50km + 80/2 km
= 50km + 40km
= 90km
Time Taken = 1 hour and 30 minutes
Average speed = 90km/90minutes x 60 minutes
= 60km/h
Remember the unit is km/h, not over 10 or 30 minutes. Time may be used together with speed. Average speed is very practical if you are planning to travel to somewhere in a period of time.

More complex Ratio

Note: In the following questions, / will be substituted for the division sign.Answers in BOLD
Ratio, as i have said before,can be manipulated to suit many questions.Now, i shall introduce to you some methods you might consider using when doing problem sums.
Some basic questions.
1. 16/23 of a class of pupils are girls.What is the ratio of the number of girls to the number of boys?
Ans:16:7


2. The ratio of A's stamps to B's stamps is 8:11.If A gives 9 stamps to B, both of them will have an equal amount of stamps. How many stamps does B have?
Ans + formula:
8 units + 11 units = 19 units (total stamps of A and B)
19 units / 2 = 9.5 units (in the end when they have the same amount of stamps.)
9.5 units - 8 units = 1.5 units (difference between at first and in the end)
1.5 units --> 9
0.5 units --> 3
1 unit --> 6
B has 6 x 11 = 66 stamps.


3. A is 1:3 the total of the number of sweets.The ratio of sweets for B is to C is 5:2.Find the ratio of A:B:C.
Ans + formula:
A:A+B+C B:C
1:3 5:2
B+C=7 units= 2/3 of total sweets.
Let us make this easier to do. B:C=5:2=10:4 B+C=14 units=2/3 of sweets
Total number of sweets=21 sweets. A=7 sweets B= 10 sweets C= 4 sweets
Thus,the answer is 7:10:4

Common mistakes:
Do take note that if you use the initial ratio of B:C=5:2, your answer would be incorrect.

4.Shanti will be 13 years old next year.The ratio of Shanti's age to Michael's age is 2:3 now.Find the ratio of Shanti"s age to Michael"s age 5 years ago.
Ans + formula:
Shanti = 12 years old (present)
2 units = 12 years old
3 units = 18 years old = Michael"s present age
Michael"s age 5 years ago= 18-5=13
Shanti"s age 5 years ago= 12-5=7
Ans:7:13
Common mistakes:
A few people may have read the first sentence wrongly and intepreted that Shanti was 13 this year.If they have,they would find a wrong answer.Always remember to read your question carefully.

5.The ratio of apples to pineapples in a basket was 4:5. After 290 apples and pineapples were added into the basket,there were twice as many apples and thrice as many pineapples as before.What was the total number of fruits in the basket at first?
Ans + formula:
4:5 -------------->8:15
+ 280 each
Difference made by the addition of 280=8u-4u 15u-5u=10u 10u+4u=14u
280/14=20
1 unit =20
9 units =180

6.James and Ming had the same amount of money.After James spent $120 and Ming spent 1:4 of his money,the ratio of James"s money to Ming"s money was 1:2.How much money was James left with?
Ans + formula:
J:M(shortform for James and Ming)=1:2=3:6
6 units=3:4 of Ming"s original amount of money.
Ming spent=2 units
8:8 at first ------>3:6
$120= 8 units - 3 units = 5 units
1 unit = $24
3 units= $72

7.Last year,the ratio of the number of boys to the number of girls in the Chess club was 5:3.This year,20 members joined the club.The new ratio was then 3:2.There are 36 boys in the club now.How many of the 20 new members that joined this year are girls?
Ans + formula:
3 units =36 1 unit =12 2 units = 24
36 boys and 24 girls this year.
Total members=24+36=60
Original members=60-20=40
8 units = 40 members
Boys = 5 units=25 Girls=3 units =15
15+?=24
Increase in girl members=15+9=24
Common mistakes:Students are confused between the two ratios.Students should label the first ratio as "last year" and the second ratio as "this year".

8.The ratio of the number of chairs to the number of tables in a shop was 3:1.After selling 53 chairs and 7 tables,the ratio of the number of chairs to tables left became 1:3.How many tables were there in the shop at first?
Ans + formula:
C:T(shortform for chairs to tables)= 3 u:1 u------->x:3 x
sell 53 C and 7 T
1 u-7=3x___________________________________
3 u-53=x
3(3 u -53=x)=9 u-159=3x which also means that 9 u-159 = 1 u-7
Therefor,I can cancel out the u and it will become
8u-159 =-7 which also means that 159-7 = 8 u
8 u=152
1 u=19
Note: Some may feel uncomfortable using algebra and ratio together.You should try coming up with your own solutions.

Introduction to Ratio

Ratio is the comparison of two amounts. Ratio is always expressed as (Numeral):(When said in normal conversations,it is defined as "is to")(Numeral). An example of how ratio is used.
I have 10 apples. John has 50 apples. Express this statement as a ratio.
I : John=
10 : 50 which can be further simplified into
1 : 5(1 is to 5)
Remember, always leave your answer in the simplest form, just like fractions. Ratio,when used to do problem sums, is a very effective method as it can be manipulated to suit different questions. I will share with you more on these methods in later posts.

Maths tip of the day 8

Perfect your mental calculation ability so as to save time for solving other questions.Time is precious.

Maths tip of the day 7

When doing problem solving questions,use a variety of methods and only use Guess and Check as a last resort.

Math tip of the day 6

When working with fractions, always remember to convert all fractions to simplest form as this will help in the calculation of your answer.

Maths tip of the day 5

Do not lose faith if you have received low marks on your first practice paper.It is okay if you learn from your mistakes and do not commit them in the next test.

Maths tip of the day 4

Do not do last minute revision and stay up very late just to revise for your test tomorrow.Frequently revise your work and have a good night's rest the day before the test.

Maths tip of the day 3

When you are working with long sums involving positive and negative numerals,remember to transfer the correct symbol in front!
Example:-5+7+1+(-3)=5+7+1-3=10 X WRONG!

Math tip of the day 2

Don't let your careless mistakes hinder your path to A1.Check your work carefully!

Math tip of the day 1

(changed daily around 8pm to 9pm)
Do not skip challenging questions that you are unable to do. Try approaching them with a different method after the rest of the paper has been finished.

Purpose of blog

To all 1P1, this blog is for the use of maths self-study module. Please do not spam the tagboard or the comments thanks.