1)Understand what you are doing.
Methods is application based maths, if you do not understand what you are doing and simply try to remember formulas – it will not get you too far. Question all material you learn and be very critical of it. Don’t just accept the knowledge question, question, QUESTION.
2) Use the calculator LESS.
Yes the calculator is a wonderful tool, but if you over rely on it you will not be able to confidently do maths. You should train your brain to think in a logical way – this can be achieved when you lower reliance on the calculator. Fractions, multiplication, division are more fun that way – and you improve the speed taken to complete questions.
3) Be neat and set out your work in a logical flow
Poor Student Excellent Student
Graph the following (i) Find intercepts
f(x) = x2 + 6x +9 Let f(x) = 0 to find x.
Solution of student; 0 = x2 + 6x +9
0 = (x + 3)(x + 3)
0 = x2 + 6x +9 x = 3
x = 3 Therefore ~ (3, 0)
y = 9 Let x = 0 to find f(x)
f(0) = (0)2 + 6(0) +9
f(0) = 9
Therefore (0, 9)
Lets analyse the poor student vs excellent student;
1) Lack of description of what they are doing.
Your work is a piece of communication, it should be understood by other people too – not just yourself! If you go wrong somewhere – then the examiner will know that you understood the process but did a silly mistake somewhere and so they will not give you 0/3 …. you might get 1 or 2/3.
2) Hardly any workings;
This makes the examiner suspicious… was it a fluke? Or is this student really good? Examiners do not have time to guess – they have 100’s of other papers to mark …. there goes your chance to impress them.
3) Not knowing the difference between y and f(x).
If your equation is in terms of f(x) …. use it! Do not put y = _____ if it isn’t y! The poor student did y = 0 to find intercepts, yes this is what you do , but it is NOT Y it is f(x)!!!!
Then when you are making x = 0 do not use y!!! Use f(x) …. however remember that it is f(0)= not f(x)=.
4) Defined and consistent intercepts.
After the intercepts were found the student converted it back into coordinate form. I.E. from x = 3 (point) to (3,0) (coordinate). That was good.
Also when sketching the graph, the excellent student chose to write all the intercepts in coordinate form. The poor student decided to write one in coordinate and one as point – this is not consistant.
5) Label your axis.
Axis should be labelled ie. f(x) and x … you lose credit if you forget.
4) Find graphs and sketch them in the correct domain, DO NOT forget to find the endpoints of the domain of interest.
You must always sketch graphs in the correct domain. Also do not forget to include the endpoints. Here is an example to do that.
y = 4x – 7 x ? (-1, 9]
Min x value is x = -1 Max value is x = 9
Put into formula Put into formula
y = 4(-1) -7 = -11 y = 4(9) -7 = 29
(-1,-11) is the endpoint (9, 29) is the endpoint
5) Label all the asymptotes
When you draw out the asymptotes be sure to label all the asymptotes and their equations.