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Both right angled triangles, with one other angle the same (see my reasoning above - properties of transversals falling on parallel lines) hence they are similar. If you draw the little triangle on the left hand side of the picture, you might see what I mean more easily

O.K, you made a little triangle that is right angled. it has hypotenuse 5 metres and one leg 4 metres, so we can figure out that the other leg is 3 metres. I assumed that the road is a constant 4 metre width (which seems reasonable to me). ...This question would be much easier to explain if...

because the question said that the road was 4 metres wide and the paddock is a rectangle.

You use similar triangles and some of the theorems about transversals on parallel lines to work out that the width is 32m. 32:24 = 4:3

Q1) Use similar triangles. Don't forget the friendliest pythagorean triple of them all, (3,4,5). Q2) You know the theorem about the sum of the exterior angles of a polygon? You can use it for non-convex polygons as well, you just have to count oriented turns (eg, count rotations in an anti...

I think the trick with Q3 is that since the polynomial, which appears to be a cubic, has four roots, this means that it must actually be the zero polynomial. So you have to find values for a and b which make both the coefficients zero.

The problem with stats at high school is that they haven't done any multivariable calculus, which limits what you can do to some extent. I agree about the conic, though - it is pretty well totally useless.

They do vector algebra (dot and cross products, stuff like that) in Victoria and I think its in the advanced maths course in the IB, so it is not that unusual to do it at high school level. I think it brings together alot of the coordinate geometry nicely, (hence making it considerably easier.)...

Up to 30% of the exam can be on the prelim course (although you won't know which parts of the prelim course they will ask about). The distinction between the prelim and hsc courses is largely artificial - mathematical knowledge always builds on top of what you know previously, so the two...

Best background for uni level stats is a good grasp of calculus. Combinatorial probability has almost nothing to do with what professional statisticians do. On balance, I think I'd vote for conics, but I'm not really enthralled with either option. Personally, I think they should put vector...

For the first one, you could use partial fractions. For the second, try multiplying the numerator and denominator by (1 + cosx).

Elite private schools will always be the employer of choice for most teachers. Why? Mainly, the pay starts at 5-8% higher than the public system. At the top of the pay scale (eg, principals) the difference is huge. In addition, class sizes are generally smaller and disruptive students are...

I really liked series solutions to ODEs. You construct the right answer rather than finding one. What else is good? Biomathematics, number theory of any kind, abstract algebra. Don't like analysis. Stats, per se, I don't like but could probably tolerate if it was being used to study an...

The two units have different dimensions and hence can't be converted. mls measure length cubed, grams measure mass. It is like asking how many seconds are there in a kilometer.

You can, but you have to count the joints on your fingers, not the fingers themselves.

^ Typically, SBSH has the largest candidature with about 120 people in MX2. Ruse caps the numbers in the low 90s. SGSH has about 75. Grammar has about 50.

Put all the junk in the absolute value sign over a common denominator and you get something like 7/9(3x+2). Then we can do some "sloppy maths" (which we can get away with in this case cause we're dealing with inequalities) to get what we want. So we are trying to make 7/9(3x+2)...

I don't think statistics can be studied profitably at the high school level. To do anything interesting you need more calculus than is covered in the syllabus. Descriptive statistics merely bores people to death. I also think an over emphasis on *practical applications* without mastery of...

Yeah, unfortunately, it also looks like they are also going to add lots of statistics, which will be mindbogglingly boring.

I think that document you are referring to discusses proposed changes to the syllabus, not the current one.