## O-Level Additional Math

- questionable_i
- BrownBelt
**Posts:**535**Joined:**Sat Oct 10,**Total Likes:**1

### Re: O-Level Additional Math

Can anyone help me with these questions?

Q1

Q2

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

Thank you

Q1

Q2

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
- OrangeBelt
**Posts:**39**Joined:**Sat Jan 23,**Total Likes:**1

### Re: O-Level Additional Math

Hello.questionable_i wrote:Can anyone help me with these questions?

Q1

Q2

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

Thank you

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
- BrownBelt
**Posts:**535**Joined:**Sat Oct 10,**Total Likes:**1

### Re: O-Level Additional Math

Maybe this might help as the question goes:EconsPhDTutor wrote:Hello.questionable_i wrote:Can anyone help me with these questions?

Q1

Q2

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

Thank you

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!

Show that if n is a positive integer, is divisible by 19.

- questionable_i
- BrownBelt
**Posts:**535**Joined:**Sat Oct 10,**Total Likes:**1

### Re: O-Level Additional Math

for your helpkennethTutor wrote: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.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.

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

- kennethTutor
- OrangeBelt
**Posts:**39**Joined:**Mon Jul 13,**Total Likes:**2

### Re: O-Level Additional Math

We simplify to get 4^n for every term. Two indices law are required here (stated in my solution).questionable_i wrote: Maybe this might help as the question goes:

Show that if n is a positive integer, is divisible by 19.

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
- OrangeBelt
**Posts:**92**Joined:**Fri Dec 28,

### Re: O-Level Additional Math

Can somebody please help me prove this?

I tried many times but my answer has an extra 1/2. Pls help.

Thank you.

I tried many times but my answer has an extra 1/2. Pls help.

Thank you.

- kennethTutor
- OrangeBelt
**Posts:**39**Joined:**Mon Jul 13,**Total Likes:**2

### Re: O-Level Additional Math

Since c is an constant, we can absorb the 1/2 into the constant. Remember when we differentiate a constant, we get 0.KSP2013777 wrote:Can somebody please help me prove this?

I tried many times but my answer has an extra 1/2. Pls help.

Thank you.

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

Look for the second solution.

- KSP2013777
- OrangeBelt
**Posts:**92**Joined:**Fri Dec 28,

- KSP2013777
- OrangeBelt
**Posts:**92**Joined:**Fri Dec 28,

- KSP2013777
- OrangeBelt
**Posts:**92**Joined:**Fri Dec 28,