O-Level Additional Math
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Ps help me to solve .
Binomial theorem ~
Expand (1-x+x^2)^5 up to term x^3
Please show your working thank you
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can someone help to solve this.
Q1> What is the unit digit in (243^10)(163^9)(633^8)? -
Hey there! My DD wans to clarify a statement in Math and the topic is real Nos.
The statement is: A rational nos. is not a whole nos.
I tried explaining to my DD, but she couldn’t understand…Could anyone help to explain and simplify in an easier way?
Thx so much:) -
A rational number is any number that can be expressed as a fraction x/y of two integers, with the denominator y not equal to 0. (If the denominator is 0, the expression will evaluate to infinite).
Examples of rational numbers: 2/3 = 0.6666666..., 2/5 = 0.4 etc.
Examples of irrational numbers: pi (22/7 is just a good approximation and is not exactly pi), e (base of the natural logarithm) etc.
It might be difficult for you to illustrate irrational numbers to your child because he/she has not learnt of irrational numbers such as pi and e yet. However, you can just try to get him/her to understand the definition of rational numbers and contrast that of whole numbers.
Whole numbers are numbers that are not 'broken' like 0, 1, 2, 3, 4, 5 and so on so forth. Note that whole numbers include 0, unlike natural numbers.
The important thing to know is that whole numbers are rational numbers since they can be expressed as fractions (3 = 3/1) but not all rational numbers are whole numbers. In fact, most rational numbers are NOT whole numbers. Therefore, a rational number may be a whole number but is NOT necessarily a whole number.
(Actually, this is somewhat controversial; it really depends on the teacher; some would say that whole numbers are not rational numbers because whole numbers are WHOLE and not meant to be expressed as fractions. however, I think most would agree that whole numbers ARE indeed rational numbers.)
Subsequently, when you child learns of integers, you may take note to teach him/her that integers are pretty much like whole numbers except that they can negative i.e. -2, -1, 0, 1, 2, 3 and so on so forth.
Hope this helps to clarify. -
archie2:
answer: 7 :imcool:can someone help to solve this.
Q1> What is the unit digit in (243^10)(163^9)(633^8)?
http://www.facebook.com/photo.php?fbid=500572910002062&set=a.500572863335400.1073741830.466376010088419&type=1&relevant_count=1 -
My DD says: So does that mean that rational nos. are whole nos.?
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Rational numbers can be whole numbers but are not necessarily whole numbers.
For example, 2/3 = 0.66666666 is a rational number but it is not a whole number.
In fact, most of the time, rational numbers are NOT whole numbers. But they can be whole numbers. -
Can someone help in this question:
There are some $2 notes, $10 notes and $50 notes in Mr Singh’s wallet . The number of $50 notes is 1 more than twice the number of $2 notes. The number of $10 notes is 1 less than the number of $2 notes. Let x, y and z be the numbers of $2, $10 and $50 notes respectively.
(a) Express y and z in terms of x.
(b) Express the total amount of money in terms of x.
If there are 4 $2 notes, find the total amount of money. -
Okay…Thx so much.
If this qn comes out, will the teacher accept both ans.?
Sry for being too inquisitive:(
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