Maths, Addmaths and Statistics: Post your doubts here!

[SalmanPakRocks]

Re: O'level Maths, Addmaths and Statistics help available he

its functions !! very easy but lengthy question !!

 

[leosco1995]

Re: O'level Maths, Addmaths and Statistics help available he

I am just confused with part (a) in Q8.. otherwise the rest of the question isn't that difficult (but if part a = wrong, then the entire question goes wrong). Also, many questions are of like 2 or 3 marks but involve a lot of working.

 

[intelnehalem]

Re: O'level Maths, Addmaths and Statistics help available he

I am just confused with part (a) in Q8.. otherwise the rest of the question isn't that difficult (but if part a = wrong, then the entire question goes wrong). Also, many questions are of like 2 or 3 marks but involve a lot of working.

Don't worry mate ! e.c.f will aid you in such an event provided that you follow through the rest of the questions in an appropriate manner even though you used incorrect results from a previous part of the question in your calculations.

 

[OakMoon!]

Re: O'level Maths, Addmaths and Statistics help available he

The first part of question 8 can be solved by identity method. F(x) is a degree1(maximum power of x=1) expression while gf(x) is a degree 2 exuation. By recognition we can see that g(x) will be a quadratic expression of the form ax^2+bx+c. Substitute the f(x) in.
a(2x-1)²+b(2x-1)+c=12x²-12x+5
Solve it by identity method. Find the values of a and b.
a(4x²-4x+1)+2bx-b+c=12x²-12x+5
4ax²-4ax+a+2bx-b+c=12x²-12x+5
Since the coefficient of x² is 4a and 12 respectively. 4a=12, a=3. Find b and c like this.
-4a+2b=-12
-4*3+2b=-12
b=0
a-b+c=5
3+c=5
c=2
Hence, g(x)=3(x)²+2

If you need help in the following parts, tell me. I'll be glad to help.

 

[OakMoon!]

Re: O'level Maths, Addmaths and Statistics help available he

Q9 is not as difficult as it seems to be. The given equation is sin²x+3sinxcosx=4cos²x, you just need to use one identity that is tanx=sinx/cosx to convert the whole equation as a quadratic equation of tanx.
Divide the whole equation by cos²x. Which goes on like this; (sin²x/cos²x)+(3sinxcosx/cos²x)=(4cos²x/cos²x)
Simplify: (sin²x/cos²x)+3(sinx/cosx)=4
Use the identity to form the quadratic equation: tan²x+3tanx=4

 

[SalmanPakRocks]

Re: O'level Maths, Addmaths and Statistics help available he

Yeah as simple as that !!

 

[OakMoon!]

Re: O'level Maths, Addmaths and Statistics help available he

@salmanpakrocks. It wasn't that simple. I haven't seen a function question like that. Not even in A'level maths. I just made up that identity method.

 

[HarisShahzad]

Re: O'level Maths, Addmaths and Statistics help available he

actually it wasnt really that hard :/

 

[SalmanPakRocks]

Re: O'level Maths, Addmaths and Statistics help available he

Yeah I couldn't solve it with the function !!
btw if we use function method then g(2x-1)=12x^2 - 12x + 5
is this correct can we subtitute the value of x now ?

 

[OakMoon!]

Re: O'level Maths, Addmaths and Statistics help available he

Where will you substitute the value of x? You have to substitute the function F(x) in place of the x of g(x). And so you need an expression such as ax²+bx+c to solve this question. g(2x-1)=a(2x-1)²-b(2x-1)+5=12x²-12x+5
I don't see another method to solve this question.

 

[OakMoon!]

Re: O'level Maths, Addmaths and Statistics help available he

@Harisshahzad: You can easily find an answer by trial and error method too. But this is a new type of question. Otherwise, there was nothing special about it. It was just a reverse process.

 

[SalmanPakRocks]

Re: O'level Maths, Addmaths and Statistics help available he

Where will you substitute the value of x? You have to substitute the function F(x) in place of the x of g(x). And so you need an expression such as ax²+bx+c to solve this question. g(2x-1)=a(2x-1)²-b(2x-1)+5=12x²-12x+5
I don't see another method to solve this question.

yeah I did the same !! but answer is coming wrong !!

 

[leosco1995]

Re: O'level Maths, Addmaths and Statistics help available he

It's not the typical function question they normally give and I was really confused when I first saw it. Thanks for the solutions hamidali, it's much appreciated.

btw if we use function method then g(2x-1)=12x^2 - 12x + 5

Actually, this method does work. It just never occurred to me when I was giving the paper. :s

 

[SalmanPakRocks]

Re: O'level Maths, Addmaths and Statistics help available he

yeah answer from this method is coming wrong !!

 

[leosco1995]

Re: O'level Maths, Addmaths and Statistics help available he

I'm getting 3x^2+2 with both methods..

 

[OakMoon!]

Re: O'level Maths, Addmaths and Statistics help available he

@salmanpakrocks: Try looking at my solution and then solve the question.
This method is supposed to end up like what I did. You just can't do it by using the inverse. Leosco can you elaborate the second method. How do you go ahead after g(2x-1).

 

[leosco1995]

Re: O'level Maths, Addmaths and Statistics help available he

I found the inverse of 2x-1 ((x+1)/2) and placed it on the other side of the equation, like this:

Isn't it possible to solve it like this? :?

 

[OakMoon!]

Re: O'level Maths, Addmaths and Statistics help available he

That did work perfectly. Great job. You solved it yourself in the end. This was a better way than mine. A straightforward process.

 

[leosco1995]

Re: O'level Maths, Addmaths and Statistics help available he

Yeah, but I still owe a lot of thanks to you and Salman for helping me out with this question and the other one.

 

[abcde]

Re: O'level Maths, Addmaths and Statistics help available he

AOA people!
This is a one mark question from maths paper 1: 1/p + 1/q = 7/12. Find the integers p and q.
Well, instinctively I knew the answers would be 3 and 4 but can there be a method for these type of questions? I just need a proper method.