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At uni, an average sort of mark is a credit. A pass is below average, but still OK (in that you don't have to take that course again). May still have an impact on your ability to get into honours, and stuff like that later, though. For most courses, probably 5-10% of students will get a HD...

You need to know how fast the parabola is increasing (and whether it is concave up or concave down) in order to uniquely specify the equation. For example, the parabola y-4=-(x-2)^2 fullfils two of those conditions but not the last one.

One of the reasons that it costs so much (apart from all the facilities that they maintain) is that the class sizes are smaller than public schools and the teacher wages are higher, so they have a much larger salary bill to pay.

Solve x^2 - 4=0.

Graphics calculators are a gimmicky toy invented by calculator companies to rip of high school kiddies. No mathematician, scientist or engineer ever uses one. Consequently, unless you need this thing for your high school course, I wouldn't bother buying it, and I wouldn't bother wasting time...

Apparently this is a modern English translation http://www.research.ibm.com/people/h/hirzel/papers/canon00-goedel.pdf Can't say I've read it.

Try the substitution u = sqrt(x).

a^2(b+c)+b^2(a+c)+c^2(a+b) = ab(a+b+c) + ac(a+b+c) + bc(a+b+c) - 3abc

No. I'm a maths teacher.

for the limit q, multiply both numerator and denominator by sqrt(20-x) +5, then simplify.

Well, this is my solution. It isn't exactly what I would call brief.

The Wikipedia entry on symmetric matrices might be useful. http://en.wikipedia.org/wiki/Symmetric_matrix In particular note, part way down the page: "Every real non-singular matrix can be uniquely factored as the product of an orthogonal matrix and a symmetric positive definite matrix, which...

Well, the problem is not the constant term - you know that the original function passes through (0,0), so the inverse must pass through the origin also. The problem is that you end up with gradient in terms of the wrong variable, and it is not clear how to substitute back into the correct one...

Call that sicko number w. We need to use the converse of Pythagoras' theorem, that is, we want to show that |z1 - z2|^2 = |z1-w|^2 + |z2-w|^2 Now to do this, you need to remember that is |z|^2 = z times the conjugate of z. If you do that, the algebra is not actually all that bad - you'll...

The General Maths course includes z-scores, but they don't use statistical tables to convert percentiles into z-scores (apart from the Empirical rule, that is). So I guess you could say it is outside the syllabus.

I agree. I have tried enumerating all the possibilities for the case n=3, and that [1^n + 2^n + 3^n + ...... + (n-1) ^n ] / n^n formula just doesn't work.

You have to convert to z-scores. According to the table that I looked up, the 90th percentile corresponds to a z score of approx. 1.28, and the 25th percentile corresponds to a z-score of -0.67. So, if X is the mean and s the standard deviation, (1.8-X)/ s = 1.28 (1.35-X)/s = -0.67 So...

Well, basically you make sure that you enrol and complete the correct courses, which you will find listed somewhere in the uni handbook. It's your responsibility to make sure that you have taken the correct courses for your major. At some stage, you lodge a form with the science students'...

That function is only defined over a set of discrete values (i.e., the natural numbers), so if you represent it as an integral, where you are assuming that the function is defined over a set of continuous numbers, you will only get an approximation. I mean, you can do what 3unitz just did...

I think 4 unit maths was a two year course back then, so naturally it had more content in it. Most of the unrecognizable stuff in that exam paper (eigen values, MVT, convergence results) are now covered in first year maths at uni.