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which steps? Every one?

For Maths, why don't you try Drongoski. I heard he is quite good.

Q9. So a vector eqn of the line is: [x, y, z] = [2,2,1] + k[5-2, 1-2, -2-1] = [2,2,1] + k[3,-1, -3]\\ \\ x = 2 + 3k = 4 \implies k = \frac {2}{3} \implies z = 1-3k = -1 Here, a direction vector is found by subtracting the position vector of one point, viz: [2, 2, 1] from that of the other...

Q8. You are here given the Cartesian equation of a line. \frac {-x+2}{7} = \frac {3y-1}{5} = \frac {2z+1}{3} $ is equivalent to $ \\ \\ \frac{x-2}{-7} = \frac {y-\frac {1}{3}} {\frac {5}{3}} = \frac {z - (-\frac{1}{2})}{\frac {3}{2}} $ a line passing thru the point $ (2, \frac{1}{3}, -\frac...

Q6. Can use as direction vector: [2, 5, 3] = [2, 7, 4] - [ 0, 2, 1] So a vector eqn of the line is: [x, y, z] = [0, 2, 1] + k[2, 5, 3] Parametric eqns: x = 2k, y = 2 + 5k, z = 1 + 3k When y = 1, 2 + 5k = 1 ==> k = -1/5 Therefore a1 = 2k = -2/5 and a3 = 1-3/5 = 2/5 Here I've found a vector...

I don't know how to do the column vector in LaTeX; so I'll use the horizontal equivalent. Q7. [x, y, z] = [2, 1, 3] + \lambda [1, 1, 2] \\ \\ = [2, 1, 3] + [1, 1, 2] + \frac {\lambda - 1}{2} [2, 2, 4] = [3, 2, 5] + \mu [2, 2, 4] Therefore the same line. For vector eqn of a line: you have one...

Testing LaTeX: \left[ \matrix 3 \\ 2\\ 5 \endmatrix \right]

Sydney Grammar may be an exception. Its scholarships are partial(not full fee relief) scholarships. It is also a selective independent school. It can afford to not dish out scholarships, because it is already a sought-after private school. Many of the richer private schools that can afford it...

If this is Jonathan Le's centre, it must be very good.

There are no "rice farms in Shanghai". It is a city of over 20 million; land too expensive for rice farming.

Looks very legible to me. A lot better than many I've seen. Your writing a little too squashed and skinny; and an angle of about 60 degrees to the horizontal would be better( a little too slant). But I don't think you can change much now. But still I think your writing is pretty good.

Why are you looking for a godsend? No such thing. Better don't waste your time and start putting in some serious work on your extension maths. Get some other textbooks and start reading up yourself. Doesn't matter if at first you understand only 21.7%; still better than 0%.

Yes: Cambridge questions are structured - basic, intermediate and then challenging. In my view, always do the basics first. Make sure you get the main concepts. Then do harder ones to test your understanding on how to apply them. Then, when you are OK with that, do the more challenging ones...

No need to be confused. Maths in Focus is more palatable to those who are weaker in maths. Does not delve deeper into the subject matter. Maybe that's why it is still adopted by many lower performing schools; for such schools textbooks like Cambridge would be beyond their students. Don't want...

I've been working on the questions of Cambridge 4U (Sadler & Ward) and have completed about half of them. I'm working in a leisurely pace. Unfortunately, they're handwritten.

illai.

Nearly 20 years. But not cheap. And may or may not be any good.

Are you looking for a personal maths tutor?

With the 1000 years of good luck on offer, I thought this would be an insanely difficult one. Turns out to be quite straightforward.