singaporeolevelmaths

Simple Tips for Better Maths Results!

Ai Ling Ong

How to gain most?

first of all, we would love to thanks all those who have posted your comments, shared your thoughts, asked your questions :)

Keep them coming! we welcome all! Since O Level is coming by in 25 days time, we would love to continue to see this blog active. btw, did i mention that there are on average 100 of you viewing this blog daily? not a huge number but both me and sean are happy that there are people who visit this blog. and we will continue to provide you with tips to do well.

well, to ensure that you gain the most of out this, you yourself must participate! yeah participate is the key! ask all sorts of qns, answer qns the way u think is correct, just do it anyway! it is through participation that we can truly experience and learn at the maximum potential.

so when there are qns, have a pen and paper and work things out! see if your concepts and understanding are firm and clear.

keep the fire burning!

Cheers!

A-Math More P & C Qn! On forming numbers

Another question from O Level Additional Mathematics (A-Math).

How many even 5-digit numbers more than 50000 can be formed using the digits, 1,2,3,4,5,6,7 if no digit is to be repeated?

Conditions
#1: Even
#2: 5-digit number
#3: no digit is to be repeated

Case 1:When the first digit is odd (must be more than or equal to 5)

2C1 * 5P3 * 3C1

Logic & Reasoning:

first digit: either 5 or 7 so 2C1
last digit: either 2,4 or 6 so 3C1
the remaining 3 digits can be choosen from the leftover 5 numbers so 5C1*4C1*3C1 also = 5P3

Case 2:When the first digit is even

5P3 * 2C1

Logic & Reasoning:

first digit: 6 so no need to choose just put!
last digit: either 2 or 4 so 2C1
the remaining 3 digits can be choosen from the leftover 5 numbers so 5C1*4C1*3C1 also = 5P3

Total even 5-digit numbers more than 50000 can be formed using the digits, 1,2,3,4,5,6,7 if no digit is to be repeated = Case 1 + Case 2 = 480

:)

Application of Differentiation - Maximum/Minimum & Rate of Change

Qn2
A closed box with a square base of length x and height h, is to have a volume, F, of 150m^3. The material for the top and bottom of the box costs $2 per square metre, and the material for the sides of the box costs $1.50 per square metre. Fnd the value of x and h, correct to 3 decimal places, if the total cost of the materials, C is to be a minimum.
Qn3
A viscous liquid is poured onto a flat surface. It forms a circular patch which grows at a steady rate of 6cm^2/s. Find,
a) the radius r, in pie, of the patch 24 seconds after pouring has commenced.
b) the rate of increase of the radius at this instant, correct to 2 decimal places.

Done reading the qns? Do and see if your answers are correct!

:)

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Trouble with Integration of Ln & Expo

I seem to have trouble now with integrating ln and e.

Haha, you are having trouble because you are learning sth you don't have to know at O'Level. You don't have to know how to Integrate Ln directly.

Having said this, you note that you must know how to Differentiate Ln, e and Integrate e

For more info on how to differentiate Ln and e, refer to this post >>
http://askalwayslovely.blogspot.com/2007/09/math-differentiation-with-ln.html

Okie how to Int e
Example
Int e^(2x+3) = e^(2x+3)/2 + c (since there are no limits given)

In short to Int e^(wadever) = e^(wadever) OVER (Differentiate wadever)

A-Math P & C Qn!

The no. of applicants for a job is 15. (i)Calculate the no. of ways in which 6 applicants can be selceted for the interview.

The six selected applicants on a particular day. (ii)Caluculate the no. of ways in which the order of the six interviews can be arranged.

Of the 6 applicants, 3 have backgrounds in business, 2 have backgrounds in education and 1 has a background in recreation. Calculate the number of ways in which the order of the 6 interviews can be arranged, when applicants having the same background are interviewed in succesion.

Who's up for this challenge?

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Of the 6 applicants, 3 have backgrounds in business, 2 have backgrounds in education and 1 has a background in recreation. Calculate the number of ways in which the order of the 6 interviews can be arranged, when applicants having the same background are interviewed in succesion.

BBB EE RSo there are 3 groups of people and there are 3! ways of arranging these 3 groups
Within BBB group, there are 3! ways of arrange these 3 B people, similar within EE group, there are 2! ways of arrange these 2E people
so Total = Arrange Big Groups * Arrange within each group = 3! * 3! * 2!