Higher Maths CfE 2015-2016

What's everyone doing just now? I'm doing recurrence relations but I still can't get my head around composite functions the layout is so hard..


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I find composite functions "fun" in a way. The layout does look daunting so try not to worry about that, whatever you are substituting as x in the given function just replace all the "x" with the value so if the functions was f(x) =3x^2
Then just remember whatever "stuff" whether it's a number or an expression you are putting into the bracket , replace the x in the function with the exact same thing
For example f(3a+2) = 3(3a+2)^2
Remember - Everything else remains unchanged.
If there are more than one x in the function then substitute the "stuff" for ALL the x's. I know the stuff isn't the most mathematical word but it helps to understand when you put it into street language.

When you have to substitute a function into a function then do exactly the same. If f(x)=3x^2 and g(x)=4x-3x^3 then if asked for g(f(x))=?
Here you already know what f(x) is then go ahead and sub it into the bracket ; g(3x^2) and simply sub the f(x) into all x value of the g(x) function.

So, g(3x^2) =4(3x^2)-3(3x^2)^3

The main thing is whatever "stuff" you put into bracket , replace the x in the function with the "stuff"


Hope that helps.

Find the equation of both medians, and solve them either simultaneously/ set them = to one another, either ways fine.

Then find x or y, and plug the one you find back into one of the original equations to get the other coordinate

It's a show that question, so you need a statement in the end to summarise your working.


Posted from TSR Mobile

Find the equation of both medians, and solve them either simultaneously/ set them = to one another, either ways fine.

Then find x or y, and plug the one you find back into one of the original equations to get the other coordinate

It's a show that question, so you need a statement in the end to summarise your working.


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Thanks, don't know what I'm doing wrong but my equations don't solve, got like y = -23/9 which can't be right

Do you want to see how I'd do it? I'll post a photo of the solution I got ?


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Can someone help me with 12b and 13a?

12b) Remember a quadratic has either a minimum or a maximum at it's vertex (so the tip). For a quadratic with real and distinct roots (so it crosses the x-axis twice at different points) this point will have an x-coordinate at the midpoint of the line connecting its two roots. (So if a quadratic has roots at x= 2 and 6, the vertex will have x-coordinate 4.

Alternatively, if you've done differentiation then the minimum value of the composition is just the zero of it's derivative, as the square term is positive.

13a) A domain is the range of values that the input of a function has. So if we have a function f, then f maps a value x to a corresponding value f(x). So here you're given the values that x can take for the function, which is x >= 0, So all you have to do is sketch the graph of f(x) = x^2+1 as you normally would, but just cut off all the negative values for x.

I'm finding maths really good so far I got 80% (so an A1) at nat5 last year and was one of the top in my year for it so I'm looking forward to this year. After so many people failing both higher and nat5 in the 2015 exams I'm hoping ours may be slightly easier this year. We are doing differentiation just now and I'm finding it pretty simple. What books do you guys recommend this year?

Getting A1 at Nat 5 only guarantees you a borderline A at higher. Evidently, a guy last year who got 100% in his Nat 5 exam failed his prelim.

Didn't say it guaranteed me anything. Just saying that it went well last year so I'm looking forward to it this year

Same I don't think it will be too difficult but it is higher so I don't think anyone will find it a breeze. I just don't like questions which give a story or scenario I just don't want that to come up too much in this years paper. What are you doing in class just now?


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We are doing differentiation which is going well so far. What about you?

Has anyone bought any books yet? If so, what books and what do do you think of them? Any recommendations?


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Is it just me or does anyone else really struggle this year for maths since there are so many types of example questions on each topic! Nat 5 was a piss take compared to higher. The exam was sooo easy but higher sucks