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Q7 (sec\theta + tan\theta)^2 + (sec\theta - tan\theta)^2 \\ \\ = sec^2\theta + 2sec\theta tan\theta + tan^2\theta + sec^2\theta - 2 sec\theta tan\theta + tan^2\theta \\ \\ = 2 sec^2 \theta + 2 tan^2\theta \\ \\= 2(tan^2 \theta + 1) + 2tan^2\theta \\ \\=4tan^2\theta + 2

If we can ignore substitution: \int \frac {xdx}{(25+x^2)^{\frac{3}{2}}} = \frac{1}{2}\int (25+x^2)^{-\frac {3}{2}}d(25+x^2) \\ \\ = \frac{\frac{1}{2}(25+x^2)^{-\frac{1}{2}}}{-\frac{1}{2}} + C = \frac{-1}{\sqrt{25+x^2}} + C

\frac {sin2\theta - cos2\theta + 1}{sin2\theta+cos2\theta - 1} = \frac {2sin\theta cos\theta + 2sin^2\theta}{2sin\theta cos\theta - 2sin^2\theta}= \frac {2sin \theta(cos\theta + sin \theta)}{2sin\theta (cos\theta - sin\theta)} =\frac {\frac{cos\theta}{cos \theta} + \frac {sin\theta}{cos...

If you can handle it, do Advanced. Greatly widens your future options.

dx/dt = c dy/dt = -c/t^2 .: dy/dx = dy/dt / dx/dt = -c/t^2 / c = - 1/t^2 As you can see, you've got so many things wrong.

The 2 curves intersect at x = 2, -2, and at y = 4 The solid of rotation is made up of 2 parts: i) the rotation of y = x^2 about the Y-axis for y=0 to y=4 and ii)the rotation of y = 12 - 2x^2 about the y-axis for y = 4 to y = 12. V = V_1 + V_2\\ \\ = \pi \int _0 ^4 x^2dy + \pi \int _4 ^{12}...

It is possible you may never need any maths after your HSC. But what if you decide to embark on a course that requires some maths background. Then what would you do? Bridging course etc; can you rely on that? ATAR considerations should not determine whether or not to drop maths.

With maths tutoring twice a week, you'll have to ask yourself what's your innate maths aptitude? If you believe you do not have a head for maths, then you may wish to drop your Ext 1 Maths. But don't rush into doing this: think carefully if this is the right thing to do: if you have the innate...

The fact you want to improve yourself is an important first step. You want to get out of 5.2 into 5.3 as soon as you can. When you are in 5.2, they assume you cannot handle the more advanced material and continue to feed you with unchallenging material. How can you get out of this trap? For...

Why don't you just spend your time here on improving on your Maths instead. When you improve your Maths, your ATAR will take care of itself.

T_1 = 1 + 3^1 = 3 Therefore true for n=1. Now Assume formula true for n <= k (stronger version), i.e. T_k = k + 2^k \\ \\ \therefore T_{k+1} = 3T_k - 2T_{k-1} -1 =3(k+2^k) - 2((k-1) + 2^{k-1}) - 1\\ \\ = (3k - 2k + 2 - 1) + 3\times2^k - 2^k\\ \\ = (k+1) +(3-1)2^k\\ \\ = (k+1) + 2^{k+1}...

Agree

What concepts couldn't your teacher explain?

Sure.

jojo You can message me and arrange to speak to me. Maybe we can arrange a Skype session so I can demonstrate how. Also take a shot of your handwriting and forward it to me on my mobile phone so I can have a look at it.

If you want to learn how to write, maybe, I can help you, if you can travel to Epping. Don't expect to change your writing in 3 weeks. You have to be shown how to write. Good thing is you are in Yr 11; so have time to improve, before you sit the HSC.

I'll just do part (i) \frac {1 + cos\theta+isin\theta}{1-cos\theta-isin\theta} = \frac {2cos^2\frac{\theta}{2}+2isin\frac{\theta}{2}cos\frac {\theta}{2}}{2sin^2\frac{\theta}{2}-2isin\frac{\theta}{2}cos\frac{\theta}{2}}= \frac...

That's life. Some people are born into well-off families. So they have a good start in life. Is that fair or unfair? If unfair, you can only blame yourself for not having chosen your parents more wisely.

What do you mean?

Thanks CM-Tutor. So that's how you get the column vectors in LaTeX.