Khmer Math Page: January 2017

This is the collection of Secondary Teacher exam from 2002 to 2011. For those who want to take teacher exam have to review all these exercises because it may appear again in the exam.

math of the day

Find the letters 9 x HATBOX = 4 x BOXHAT

Khmer Math Page 5:34 PM

Each letter must represent a digit from 1 to 9 with no two letters representing the same digit.

Solution

We have: 9 x HATBOX = 4 x BOXHAT

set "HAT" =x and "BOX"=y(x,y has 3-digit)

the equation becomes

9(1000x+y) = 4(1000y+x) or

8996x = 3991y

which on division by 13 becomes

692x = 307y

where the coefficients are relatively prime.

This has the obvious solution we can set as:

x = 307n, y = 692n for any integer n

The only solution in which x and y are both 3-digit numbers is for

n = 1. Then

HAT = 307

BOX = 692

9(HATBOX) = 9(307692) = 2769228

4(BOXHAT) = 4(692307) = 2769228

Thus: H=3,A=0,T=7,B=6,O=9,X=2

math of the day

Bell Problem

Khmer Math Page 5:29 PM

A first bell ring at every 6 minutes, a second bell rings every 7 minutes and a third bell rings every 1 hour, if all the bells start ringing at 12 noon today when the next day will all ring at the same time?

Solution

-The 1st two bells will ring at the same time every 6*7 = 42 mn

-The 3rd bell ring once every hour, or once every 60mn

-What is the smallest multiple of 42 that is evenly divided by 60?

(10*42)/60 = 420/60 =7

-So, every 420 min, all 3 bells ring together

420/60 = 7h

-12 noon : 12pm + 7h = 7pm is when they all ring together

math of the day

Find the value of M

Khmer Math Page 5:27 PM

M is a positive number that follow these conditions:

M is a number that 80<M<100
if M divided by 4 the remainder is 3
and if M divided by 5 the remainder is 1.

Find the value of M?

Solution:

M divided by 4 gives remainder 3. So M can be written as 4r + 3 for some integer r
M divided by 5 gives remainder 1. So M can be written as 5*t + 1 for some integer t

So M=4*r + 3 or M=5*t + 1

But 80<M<100

Thus 80<4*r + 3<100 , 77<4r<97 , 19.25<r<24.25 so r={20,21,22,23,24}

r=20 => M=4*20+3=83
r=21 => M=4*21+3=87
r=22 => M=4*22+3=91
r=23 => M=4*23+3=95
r=24 => M=4*24+3=99

Only r=22 that M=91 can be written as 91=5*18+1 so the only one value of M=91 that apply to these two forms.

math of the day

Math Problem of the Day

Khmer Math Page 5:26 PM

Spend about 10 seconds, what is the value of A. It is not too hard to think. Let say the value of A!

Math

Find the value of x^2 + y^2

Khmer Math Page 5:18 PM

Let x+y=1 and x^3+y^3=19

Find the value of x^2 + y^2?

Answer

We have x^3 + y^3=(x+y)(x^2 - xy + y^2) = 19

and x+y = 1 Thus x^2 - xy + y^2 = 19

and also we can write as 2x^2 + 2y^2 - 2xy = 38(1)

Then also (x+y)^2 = x^2 + y^2 + 2xy = 1(2)

Adding (1) and (2):

We get 3x^2 + 3y^2 = 39

so that  x^2 + y^2 = 13

Math

How to improve your Mathematics

Khmer Math Page 8:01 AM

Learning Mathematics is not easy to all student in the world. Many student say that Maths is the most difficult subject to them. But to me I do not agree with that at all.

The more you do, The more you know

When I was in high school I am the best student of Maths. I have spent lot of times for this subject because I love Maths so much. I have my own strategy to learn Maths.

To improve your Maths you have to:

1. Make a schedule/plan
- set your own timeline for learning this subject
- you must follow this timeline
- review weekly for your schedule
- set your goal for short time/ long time plan for your lessons

2. Self study
- study at school is not enough
- learn more at home, at your free time

3. Do more, know more
- do more exercises as much as you can
- do all exercises in text book
- do more exercises in other related book

4. Research
- many books are selling in the market, you can find many good books
- online: research more with online e-books, references
- many web site are sharing about Maths
- research for old exam paper in the previous years

5. Ask for help
- no one perfect, if you can not solved the problems ask for help
- ask teacher, friends

6. Keep in touch with outstanding student
- make friends with outstanding student
- you will learn/ improve your self from them

7. Study hard
- nothing easy, keep going
- the more you study hard, the more you know

Math

Math Formulas Grade 12

Khmer Math Page 7:55 AM

This paper will help you to figure out to all Math Formulas for grade 12 high school. Let's review these formulas for doing your math problems.

Outstanding

How To Become an Outstanding Student of Math

Khmer Math Page 7:43 AM

An outstanding student of Math must do these follow points:

1. Set Schedule for Daily Studying
You have to set a daily studying schedule for your own. Set an appropriate time for doing Math problems and other Subjects in order to control your time efficiency. Time to do Math problems is very important because the more you do the problem the more you understand about it.

2. Do Math Problem Everyday

The more you do the more you know. Let's do Math problem everyday follow your own schedule. Many math book are currently selling on the market so it is very easy to buy those book to improve your knowledge of Math.

3. Do Research for More Knowledge of Math

Now internet is very useful for all student so they can do research or find supporting document easily. You can go to the book store to find the new book of Math too.

4. Good Relationship with Outstanding Student or Others

Relationship is very important for all student. If you know some outstanding student you can learn from their experiences or activities. You can contact with your former high school outstanding student to find the book that they used to learn from in order to achieve your goal.