Maths Ext 1 Preliminary Exam 2014 (2 Viewers)

[jkerr138]

Hi,

I did the Ext 1 paper today for Prelim, and wow I found it very difficult along with the four other people in my class. We had been given a couple of past papers in previous years from Western Mathematics for 2013 and 2011 and this one was no where close to this one.

Three quarters of the questions we had never done in that type of difficulty. I also come from the regional area of Singleton. We only have 4 lessons a fort night which really doesn't help.

I wanted to see how others went with it?
The text book my school uses, had half the stuff in it, and nothing to do with focal chord's which was one of the parts of the last question that wasn't in the textbook, only the Excel Prelim book, which I only had in the class. Most of the exam, the questions were too difficult to complete and hadn't even got near that type of difficulty, which was surprising, which means that the teacher mustn't be teaching correctly, if all five of us failed.
Felt like the teacher taught us the bare minimum and just threw us in to the exam, with the basic knowledge, unable to complete difficult questions. Possibly the panel was of high socio-economic background teachers who wanted to test their students. I would have thought this would be testing the very academic students in Sydney, who have a stronger knowledge and understanding with greater educational resources, maybe I'm right or wrong.

This was by far the most difficult out of the 4 year cycle. So please provide feedback on how you all went and what you weren't happy with.
Thanks

 

[iStudent]

Do you have a copy of the exam that maybe you could share? (so we can see if your exam really is difficult)

 

[jkerr138]

I can give you an example of a couple of the questions.
One was p(x) = mx^4 + nx^3 + 12x^2-22x-12. and had a double root at x=1
Find the values of m and n and then factor it as its products.
Another one was:
2x+3/x^2-5x+6 , find the value of a/x-2 and b/x-3

There was also a very good induction question. It started off with the pattern 2x1, 3x2, 4x3, ... (2n-1)x n = 1/3 n (n-1) (n-2)
Prove it.

It may not have been difficult for others, but we didn't have exposure to these type of questions, so it was difficult for myself.

 

[jkerr138]

Exam was kept within the examination room, otherwise I would have posted it. It was an independent paper though.
Another question in the multiple choice was;
given the cartesian equation of: x= a cos theta, y=b sin theta
Find the parametric equation.
I thought of x=2at, and y= at^2, but I wasn't sure how, as we weren't taught how.

 

[faisalabdul16]

Exam was kept within the examination room, otherwise I would have posted it. It was an independent paper though.
Another question in the multiple choice was;
given the cartesian equation of: x= a cos theta, y=b sin theta
Find the parametric equation.
I thought of x=2at, and y= at^2, but I wasn't sure how, as we weren't taught how.

you make the trig stuff the subject. Square them both, and add which = 1. trig identity, sin^2theta + cos^2theta = 1

 

[Kurosaki]

Exam was kept within the examination room, otherwise I would have posted it. It was an independent paper though.
Another question in the multiple choice was;
given the cartesian equation of: x= a cos theta, y=b sin theta
Find the parametric equation.
I thought of x=2at, and y= at^2, but I wasn't sure how, as we weren't taught how.

That's 4U stuff. And I think you mixed around Cartesian and parametric equations.
The equation is that of an ellipse:

 

[faisalabdul16]

That's 4U stuff. And I think you mixed around Cartesian and parametric equations.
The equation is that of an ellipse:

I think some schools teach the root of multiplicity stuff in 3u.

 

[mreditor16]

I think some schools teach the root of multiplicity stuff in 3u.

not allowed to I think....

 

[jkerr138]

That is exactly what I thought it was, an ellipse. I'm sure it said it wanted to find the parametric equation. I did Conics last year in Maths C in QLD, but I thought it can't be in a 3U subject.
I might have read it wrong, maybe it was asking for the cartesian, given the parametric.

 

[jkerr138]

what would have been the solution by the way if it was asking for the cartesian?

 

[Kurosaki]

what would have been the solution by the way if it was asking for the cartesian?

 

[Kurosaki]

I think some schools teach the root of multiplicity stuff in 3u.

not allowed to I think....

They might cover it in an exam Q and have you prove the theorem but don't think it's formally taught as a part of MX1.

 

[jkerr138]

I know how to derive the ellipse equation, but what I don't understand is, that you can unexplicitly be taught of an ellipse in a 3U subject. I knew it was an ellipse straight away, but I thought I would be wrong, as it is a 3U course not 4U, so I thought my teacher would go what an idiot.

 

[Joshmosh2]

I can give you an example of a couple of the questions.
One was p(x) = mx^4 + nx^3 + 12x^2-22x-12. and had a double root at x=1
Find the values of m and n and then factor it as its products.
Another one was:
2x+3/x^2-5x+6 , find the value of a/x-2 and b/x-3

There was also a very good induction question. It started off with the pattern 2x1, 3x2, 4x3, ... (2n-1)x n = 1/3 n (n-1) (n-2)
Prove it.

It may not have been difficult for others, but we didn't have exposure to these type of questions, so it was difficult for myself.

Hey, that polynomial question is quite interesting. Not 100% sure, but does the solution include P(1) = 0 and also P'(1) = 0 (since double root)
so my final answer is P(x) = 2(x-1)(-32x^3+11x^2+17x+6)

Also for the next question, do you mean (a/x+2) + (b/x-3) ?
If so, looks like an identical expression, so (a+b)x -3a-2b / ....
so a = -7 and b = 9

 

[jkerr138]

Hey, that polynomial question is quite interesting. Not 100% sure, but does the solution include P(1) = 0 and also P'(1) = 0 (since double root)
so my final answer is P(x) = 2(x-1)(-32x^3+11x^2+17x+6)

Also for the next question, do you mean (a/x+2) + (b/x-3) ?
If so, looks like an identical expression, so (a+b)x -3a-2b / ....
so a = -7 and b = 9

The question said a/x-2 + b/x-3 , so you had to find the values of a and b.
With the polynomial, did you look for another root, to get it to simultaneous equations, solve for m and n, used one of the roots using factor theorem to find the remaining roots?

 

[photastic]

I can give you an example of a couple of the questions.
One was p(x) = mx^4 + nx^3 + 12x^2-22x-12. and had a double root at x=1
Find the values of m and n and then factor it as its products.
Another one was:
2x+3/x^2-5x+6 , find the value of a/x-2 and b/x-3

There was also a very good induction question. It started off with the pattern 2x1, 3x2, 4x3, ... (2n-1)x n = 1/3 n (n-1) (n-2)
Prove it.

It may not have been difficult for others, but we didn't have exposure to these type of questions, so it was difficult for myself.

Wth! Did they move induction into the prelim course. Dw If I do well this year, get ready for a motivational/success thread

 

[Carrotsticks]

Wth! Did they move induction into the prelim course. Dw If I do well this year, get ready for a motivational/success thread

Different schools follow different order of topics.

 

[Joshmosh2]

The question said a/x-2 + b/x-3 , so you had to find the values of a and b.
With the polynomial, did you look for another root, to get it to simultaneous equations, solve for m and n, used one of the roots using factor theorem to find the remaining roots?

Weirdly enough, I had exactly the same question in my prelim test today, it was basically this a/x-2 + b/x-3
For the polynomial question, since it's a double root, P(1) = 0 but also P'(1) = 0
So by solving simultaneously, I got m = -68 and n = 90
If you sub the function into a graphing calculator, there should be a double root at x=1

 

[mreditor16]

Different schools follow different order of topics.

second that.

 

[jkerr138]

Yes, we weren't going to even learn induction in prelim, until I looked at the mapping grid and one of the questions had induction, so we had to learn the concept a couple of days before the exam.

We only have 4 days of Maths Ext 1 in the two week cycle. How about the rest of you? Do I have enough lessons to do well in the course?