Hey Jake!
I'm currently doing 3 sciences, 4u maths and 2u english and was planning on dropping to 10 units (I would drop biology) however, I'm slightly hesitant as this would mean every single one of my units would count. Right now, I'm behind on biology which is giving me the incentive to drop it so I wont have to invest time catching up. What are your thoughts? Since you did 12 units? Did you feel it was more beneficial? And also, what would you say is the best way to approach 4U maths and do you think it's doable for everyone? I get stumped on quite a few questions and I feel like I'm more a rote learner than an innovative thinker if that makes sense.. Also, what are your thoughts on dot point summaries for Physics and Chemistry? Necessary or nah? My school puts a lot of emphasis on it but I find that it's extremely time consuming and I don't exactly trust my own notes anyway, but I'm scared I'm disadvantaging myself by not writing them! Thanks Jake!
Hey Neutron:
Im Jake (For sure!) Im also doing physics, chem, ext 1 and ext 2 mathematics, same as you. And to be honest, I stuffed up three assessments already in the first term so Im in the same shoe as you. But what I tell myself is that the assessment is only gonna to contribute to 5% of your RAW atar for THIS ONE SUBJECT. Perhaps you and the person that came first were 20% apart from one another, if you multiply that difference by 0.05, then really you are only losing to him by 1 atar in this subject and if you consider again this 1% might go into 0.5% after scaling and then if you consider how you have 6 subjects all together you pretty much is only 0.08% apart from that guy.... So this is what l tell myself (and it is actually true!) and this is what motivates me to try even harder for my half yearlies which would weigh 5% more.
But thats all not-so-important. I would just like to share some of my extension 2 experience with you so that I can perhaps help you out in some ways. I would list them in dot points form so that it would be easier for you to understand.
1.
Do LOTS AND LOTS AND LOTS of exercises on each topic, especially for complex numbers. The outrageously strange questions they can give you in complex numbers is just frustrating, so I would have done as much past HSC questions on complex numbers as possible, you can easily find ext 2 trial papers online and do questions from there. If you just can just manage to do 10 questions everyday, imagine how prepared you will be after 239 days (THATS 2390 QUESTIONS DONE!) when HSC comes.
2. Everyone pretty much knows this first tip. But what Im going to tell you now is something people might not do:
FOR ALL THE QUESTIONS THAT YOU DO NOT KNOW HOW TO SOLVE, WRITE THE ENTIRE SOLUTION DOWN AND MEMORIZE HOW TO SOLVE IT. Extension 2 is a weird sort of maths, to my perpsective. Back in the 2unit days, I would be able to solve some questions on the spot without having previously encountered it before. But when I see an unfamiliar extension 2 question, it takes me almost double or even triple the time to solve it. So through memorising questions of diverse styles, there is a higher chance you will be familiarised with the questions in your exam
3.
MADE A MISTAKE? JOT IT DOWN! Collect all the mistakes you have made during both your practises and your exams, write a specific question that you have made a mistake on if you want to. Look through it at least once a week. For example, in my notes I have "cos(x) - isin(x) doesnt equal to cis(x)!" and " Simplify cis(x) answers wherever necessary"
4. The first three points are just generally how you would study for extension 2. Now let's talk about some skills for complex numbers. One of the most important thing to remember is SIN (X) is an ODD FUNCTION and COS(X) is an EVEN FUNCTION. This means that
sin(-x) = -sinx and cos(-x) = cos (x). This will be very useful in complex number proofs involving de'moivre's theorem
5. Another key thing to do is to
MEMORISE ALL THE COMPLEX NUMBER PROPERTIES.These are your best friends in proofs, For example, |z| = |conjugate of z| = sqrt (x^2 + y^2), arg(conjugate of z) = -arg(z), z(conjugate of z) = |z|^2 = |conjugate of z|^2 = x^2 + y^2, z + conjugate of z = 2x, z - conjugate of z = 2iy. These are only a few of the complex properties, you can find the rest either online or in your textbooks.
6.
REMEMBER THE SHAPE OF YOUR LOCUS. This is so important. Of course, you can always work out your locus through algebraic means, but by remembering the general shape of your complex locus, you would not be required to spend as much time. Just to list a few:
- |z| = r is a circle
- |z-w| = r is the equation of a circle with the centre at w=a+ib and radius r.
- |z - z1| = |z - z2| is the equation of the perpendicular bisector of the line AB
- arg (z-z1) = x, where x is a constant, is the equation of a half-ray, starting at the fixed point z1
- arg(z-z1) - arg(z-z2) = x, 0<x<pi, is the equation of an arc of a circle on the chord AB, where A and B represent z1 and z2 respectively7.
MULTIPLYING A COMPLEX NUMBER THROUGH BY CIS(X) TURNS THE GRAPH ANTI-CLOCKWISE BY X DEGREES, and of course, multiplying a complex number through by i turns the graph by 90 degrees anti-clockwise
8. These are just some of the core tips of complex numbers, I can go into the specifics if you are willing to supply some questions? Now let's have a look at some essential tips for the topics of Graphs.
- -f(x) = reflection of graph over the x-axis
- f(-x) = reflection of graph over the y-axis
- f(x) + t = moving the graph up by t units in the y-direction
- f(x) - t = moving the graph down by t units in the y-direction
- f(x+t) = moving the graph t units to the left along x-direction
- f(x-t) = moving the graph t units to the right along x-direction
- |f(x)| = reflect everything below the y-axis over to above the y-axis
- f(|x|) = delete left hand side, reflect everything on the right over y-axis
-|y| = f(x) = delete everything on the bottom, reflect everything above x-axis over to the bottom of x-axis
And of course, if you want to sketch 1/f(x), sqrt (f(x)), [f(x)]^2 and [f(x)]^3, always draw the lines y = 1 and y = -1 and locate where f(x) = 0
In regards to the dot point summaries I would definitely recommend to do them and begin revising them 1 month before your exam and constantly revise them over time. This is something l do and I would strongly recommend you to make revision notes that would suit your own style.
Anyways I hope my tips would help you in extension 2 and best of luck!
Best Regards
Happy Physics Land
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