O-Level Additional Math

[archie2]

pinkapple:

archie2:

can someone help to solve this.

Q1> What is the unit digit in (243^10)(163^9)(633^8)?

answer: 7 :imcool:

http://www.facebook.com/photo.php?fbid=500572910002062&set=a.500572863335400.1073741830.466376010088419&type=1&relevant_count=1

thanks for the explaination
however when the power is high, the value has lots of zero at the back, say, does your method works for 3^50?

[pinkapple]

archie2:

pinkapple:

[quote=\"archie2\"]can someone help to solve this.

Q1> What is the unit digit in (243^10)(163^9)(633^8)?

answer: 7 :imcool:

http://www.facebook.com/photo.php?fbid=500572910002062&set=a.500572863335400.1073741830.466376010088419&type=1&relevant_count=1

thanks for the explaination
however when the power is high, the value has lots of zero at the back, say, does your method works for 3^50?[/quote]yes. look at Method 2. it's using number pattern 3, 9, 7, 1, 3, 9, 7, 1, 3, 9, 7, 1,...
so for powers which are multiples of 3, the digit unit will be 7, while powers of multiples of 4 will be 1. anything else, u just work forward of backwards.

for 3^50, the nearest power to multiple of 3 or 4 is 48 (a multiple of 4)
so 3^48 = ...1
3^49 = ...3
3^50 = ...9

[pinkapple]

archie2:

can someone help me again with this similar questions

Q1a>> what is the last digit of 7^128?
Q1b>> what is the last two digit of 7^128?
Q1c>> what is the last four digit of 7^128?
thank you

last digit of 7^128 is 1
last two digit of 7^128 is 01
last four digit of 7^128 is 6401

[archie2]

can someone help with the below questions


How many zeroes does 50! end with?
How many zeroes does 2013! end with?

[archie2]

Can someone explain this question on Geometric series

Sn = a*(1-r^n)/(1-r)

Question: For what values of the common ratio r will the sum to infinity of a geometric series exists?

Answer given: the sum of infinity of a geometric exists if and only if -1<r<1 and is equals to a/(1-r)

Doubt : why does the sum of infinity of a geometric does not exist if -1<r>1?
i thought the sum of infinity of the geometric series will be very large and exists in either -ve or +ve sum. OR could I have misinterprete the question?

[pinkapple]

AP, GP was previously introduced in AMath at O levels but taken out since 2008 or earlier.


nonethless, it can be in IP so still secondary.

[lost boy]

Urgent! Please answer as quickly as possible. I have no idea whether this is related to mathematics because its an arithmetic progressions question. This is a Secondary one question


Q1. Find the sum of the first N odd numbers.
Q2. Find the sum of the first n natural numbers
Q3. Write down three integers in A.P whose produce is a prime number

[pinkapple]

lost boy:

Urgent! Please answer as quickly as possible. I have no idea whether this is related to mathematics because its an arithmetic progressions question. This is a Secondary one question


Q1. Find the sum of the first N odd numbers.
Q2. Find the sum of the first n odd numbers
Q3. Write down three integers in A.P whose produce is a prime number

eh.. 1st 2 questions same mah

[lost boy]

I had changed q 2 . Ps show me the working . Thanks.

[pinkapple]

answer to Q2: http://www.9math.com/book/sum-first-n-natural-numbers

look at the picture. it'll help.

from here, try to answer Q1 yourself.

As for Q3, think what is the definition of prime numbers.
then what are integers.
work from here. tell u the answer tmrw.