O-Level Additional Math

PSLE marks the graduation of Primary school students and their entry into Secondary schools as teenagers. Discuss all issues about Secondary schooling here.
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questionable_i
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Re: O-Level Additional Math

Post by questionable_i » Sat Mar 19, 2016 5:46 pm

Can anyone help me with these questions?

Q1 Image

Q2 Image

Q3. Show that if n is a positive integer, 4^n+5(4^n+1)-2^2n+1 is divisible by 19.

Thank you

EconsPhDTutor
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Re: O-Level Additional Math

Post by EconsPhDTutor » Sat Mar 19, 2016 6:22 pm

questionable_i wrote:Can anyone help me with these questions?

Q1 Image

Q2 Image

Q3. Show that if n is a positive integer, 4^n+5(4^n+1)-2^2n+1 is divisible by 19.

Thank you
Hello.

Q1. 5^(-x).
Q2. 15/(√2).

Please see this PDF for the full solutions.

For Q3, I think there might be a typo. Because if you try for example n = 1, we have 4^1 + 5 × (4^1 + 1) - 2^(2 × 1) + 1 = 4 + 5 × 5 - 4 + 1 = 26, which is not divisible by 19.

Hope this helps and feel free to ask for any clarifications.

- Dr. Choo Yan Min

questionable_i
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Re: O-Level Additional Math

Post by questionable_i » Sat Mar 19, 2016 6:59 pm

EconsPhDTutor wrote:
questionable_i wrote:Can anyone help me with these questions?

Q1 Image

Q2 Image

Q3. Show that if n is a positive integer, 4^n+5(4^n+1)-2^2n+1 is divisible by 19.

Thank you
Hello.

Q1. 5^(-x).
Q2. 15/(√2).


Please see this PDF for the full solutions.

For Q3, I think there might be a typo. Because if you try for example n = 1, we have 4^1 + 5 × (4^1 + 1) - 2^(2 × 1) + 1 = 4 + 5 × 5 - 4 + 1 = 26, which is not divisible by 19.

Hope this helps and feel free to ask for any clarifications.

- Dr. Choo Yan Min

www.EconsPhDTutor.com

If you found this answer helpful, then please help me out by spreading word of my services. I’m a new tutor in Singapore so I need some help getting word out! Thank you!
Maybe this might help as the question goes:
Show that if n is a positive integer, Image is divisible by 19.

questionable_i
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Re: O-Level Additional Math

Post by questionable_i » Sat Mar 19, 2016 7:15 pm

kennethTutor wrote:
questionable_i wrote:Can anyone help me with these questions?

1. The straight line 3y=6-2x meets the curve (2x+1)^2+6(y-2)^2-49=0 at the points P and Q. Find the point P and Q and leave your answer in surd form.

2. α and β are roots of the equation x^2+2x=h. The quadratic equation 8x^2-6x+k=0 har roots of (1-α)/α and (1-β)/β. Find the values of h and k.

3.Find the range of values of k for which the expression 2(k-3)x-25-x^2 is always negative for all real values of x.

I need it ASAP. :thankyou:
For Q1, basically we solve simultaneous equations by using Substitution method. I did not get any surds for my answer, so you might want to check the question again.

Solution: http://imgur.com/OIhjQ0W

For Q2, we find the Sum of Roots (SOR) and Product of Roots (POR) for both equations. We use the SOR and POR to find the values of the unknowns h and k.

Solution P1: http://imgur.com/zkog0A5
Solution P2: http://imgur.com/L552BGx

For Q3, we use discriminant b^2 - 4ac < 0, as the curve is always negative. This means that the curve does not cut the x-axis, therefore there are no real roots.

Solution: http://imgur.com/sbKZD3A
:thankyou: for your help :lol:

kennethTutor
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Re: O-Level Additional Math

Post by kennethTutor » Sun Mar 20, 2016 2:23 am

questionable_i wrote: Maybe this might help as the question goes:
Show that if n is a positive integer, Image is divisible by 19.
We simplify to get 4^n for every term. Two indices law are required here (stated in my solution).

Solution: http://imgur.com/Gxpte6T

Once we get 19.4^n, it is divisible by 19 as 19 is a factor of the expression.


KSP2013777
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Re: O-Level Additional Math

Post by KSP2013777 » Tue Mar 22, 2016 9:53 am

Can somebody please help me prove this?
I tried many times but my answer has an extra 1/2. Pls help.

Image

Thank you.

kennethTutor
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Re: O-Level Additional Math

Post by kennethTutor » Tue Mar 22, 2016 2:16 pm

KSP2013777 wrote:Can somebody please help me prove this?
I tried many times but my answer has an extra 1/2. Pls help.

Image

Thank you.
Since c is an constant, we can absorb the 1/2 into the constant. Remember when we differentiate a constant, we get 0.

Solution: http://imgur.com/a/pBRcn

Look for the second solution.

KSP2013777
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Re: O-Level Additional Math

Post by KSP2013777 » Wed Mar 23, 2016 9:30 pm

Thank you very much for your help, kennethTutor.

KSP2013777
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Re: O-Level Additional Math

Post by KSP2013777 » Sun Apr 03, 2016 5:07 pm

Can somebody pls help me with this question?
Image
Thank you.

KSP2013777
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Re: O-Level Additional Math

Post by KSP2013777 » Sun Apr 03, 2016 5:11 pm

My problem is I cannot factorise after I differentiate. Pls help.

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