Level 2 Further Maths - Post some hard questions (Includes unofficial practice paper)

Reply 200

16

Original post

by notnek

Yes I'll post some questions between now and Paper 2. I'll probably make the difficulty level closer to the real exam since I've realised that students already find Level 2 FM hard so I don't need to increase the difficulty by much. But I'm sure there will still be some tough questions.

Can you think of any big topics that didn't appear in Paper 1? I haven't seen the paper yet.

There wasn't a lot of:
Trig / Trig identities
Matrices
Differentiation / Calculus
Dividing a line in a given ratio to find points
There was no circle theorems, completing the square or cosine rule.

There was lots of:
Factorising
Surds / Rationalising the denominator
Drawing graphs (There were 3 graphs to draw)
Quadratics / Quadratic sequences

Reply 201

TheMightyBadger

13

Original post

by notnek

Yes I'll post some questions between now and Paper 2. I'll probably make the difficulty level closer to the real exam since I've realised that students already find Level 2 FM hard so I don't need to increase the difficulty by much. But I'm sure there will still be some tough questions.

Can you think of any big topics that didn't appear in Paper 1? I haven't seen the paper yet.

As already said, circle theorems and algebraic proofs. Differentiation. 3D Trig and Pythagoras. Midpoints. Equations of circles. Matrix simultaneous equations. Hard matrix transformations. Trig graphs. Trig identities. Rearranging to make one variable the subject. Factor theorem. Inequalities (possibly, quite prominent in today's paper). Some sort of ratios.

Reply 202

Notnek

OP

21

I've added links to all questions posted so far at the start of this thread for people who are new to the thread or haven't seen all the questions.

If any of you want to make up your own question then that would be really good and others can try it. You may find that coming up with your own question helps you understand a topic better.

Reply 203

Notnek

OP

21

(Calculator allowed but this can be done without a calculator)

The graph of $y=x^3-6x+4$ is shown below, where $P$ and $Q$ are stationary points of the curve.

The tangent to the curve at $Q$ and the normal to the curve at $P$ intersect at the point $R$ . Find the area of triangle $PRQ$

Reply 204

TheMightyBadger

13

Original post

by notnek

(Calculator allowed but this can be done without a calculator)

The graph of $y=x^3-6x+4$ is shown below, where $P$ and $Q$ are stationary points of the curve.

The tangent to the curve at $Q$ and the normal to the curve at $P$ intersect at the point $R$ . Find the area of triangle $PRQ$ .

Looks like a really neat question, although I will have to try it tomorrow because I'm currently focused on acing Physics tomorrow.

Reply 205

thekidwhogames

18

Original post

by notnek

(Calculator allowed but this can be done without a calculator)

The graph of $y=x^3-6x+4$ is shown below, where $P$ and $Q$ are stationary points of the curve.

The tangent to the curve at $Q$ and the normal to the curve at $P$ intersect at the point $R$ . Find the area of triangle $PRQ$

Spoiler

(edited 8 years ago)

Reply 206

Notnek

OP

21

Original post

by thekidwhogames

Spoiler

Out of interest, are there topics in Level 2 Further Maths that you don't know? E.g. matrices?

Reply 207

Loci Pi

16

Original post

by notnek

(Calculator allowed but this can be done without a calculator)

The graph of $y=x^3-6x+4$ is shown below, where $P$ and $Q$ are stationary points of the curve.

The tangent to the curve at $Q$ and the normal to the curve at $P$ intersect at the point $R$ . Find the area of triangle $PRQ$

Is it:

Spoiler

Reply 208

thekidwhogames

18

Original post

by notnek

Spoiler

Out of interest, are there topics in Level 2 Further Maths that you don't know? E.g. matrices?

Oh yeah I will add spoilers next time, I forgot to.

Also, I'm not sure which topics are in FM as I'm only doing these for fun - I haven't learnt the spec. I can only do these questions since these are core 1/core 2 topics so they're quite accessible for me. I'll just do any that you put on.

Oh yeah by the way, do you have any links to any video tutorials that cover modular arithmetic? Like an introduction to it, congruence rules, using it to find last few digits of an exponent?

Reply 209

Notnek

OP

21

Original post

by Loci Pi

Is it:

Spoiler

That's right.

Reply 210

Loci Pi

16

Original post

by notnek

That's right.

Thanks. That question was fun :smile:

Do you have any questions on matrices or 3d trig / Pythagoras?

Reply 211

Pastelx

18

Original post

by notnek

(Calculator allowed but this can be done without a calculator)

The graph of $y=x^3-6x+4$ is shown below, where $P$ and $Q$ are stationary points of the curve.

The tangent to the curve at $Q$ and the normal to the curve at $P$ intersect at the point $R$ . Find the area of triangle $PRQ$

Nice question! Won't post the answer because I still don't know how to use the "spoiler" setting on my phone XD
I did the same method as Loci Pi though

Reply 212

Notnek

OP

21

Original post

by thekidwhogames

Oh yeah by the way, do you have any links to any video tutorials that cover modular arithmetic? Like an introduction to it, congruence rules, using it to find last few digits of an exponent?

Finding resources for degree level topics is tricky since the best things would be lecture notes but these will be aimed at university students so the style and notation may be strange to you. Try looking for videos e.g. "introduction to modular arithmetic lecture".

Is there a specific reason why you are learning this topic?

Reply 213

thekidwhogames

18

Original post

by notnek

Finding resources for degree level topics is tricky since the best things would be lecture notes but these will be aimed at university students so the style and notation may be strange to you. Try looking for videos e.g. "introduction to modular arithmetic lecture".

Is there a specific reason why you are learning this topic?

There's this Math cup thing in Serbia was on the 26th and my school has enrolled me to go compete there but the topics are mad; modular math, Fermet's last theorem, diphantine equations, etc.

http://www.cup.mg.edu.rs/mgsc/mgsc-2016

I've tried searching for videos but none explain how you can use it to find last digits of powers e.g. 7^9^9^9 (question 1-2 on paper 2016 iirc).

Reply 214

stochasym

12

can complex numbers tricky questions or inverse trig integrals be posted in this thread?

Reply 215

Notnek

OP

21

Original post

by thekidwhogames

There's this Math cup thing in Serbia was on the 26th and my school has enrolled me to go compete there but the topics are mad; modular math, Fermet's last theorem, diphantine equations, etc.

http://www.cup.mg.edu.rs/mgsc/mgsc-2016

I've tried searching for videos but none explain how you can use it to find last digits of powers e.g. 7^9^9^9 (question 1-2 on paper 2016 iirc).

I'm not really sure where the best place to learn this stuff is, sorry. It may be a good idea to post one of these question on the forum and someone will help you with it then you could ask them for resources.

Reply 216

Notnek

OP

21

Original post

by depymak

can complex numbers tricky questions or inverse trig integrals be posted in this thread?

No they're not in the spec :smile:

Reply 217

Notnek

OP

21

Can be done without a calculator:

a) Factorise $\ \ \ 2x^2-3x-14$

b) Hence or otherwise solve the equation

$\displaystyle \ \ \ 2(4x^2+9x-2)^2-3(4x^2+9x-2)-14 = 0$

Reply 218

thekidwhogames

18

Original post

by notnek

I'm not really sure where the best place to learn this stuff is, sorry. It may be a good idea to post one of these question on the forum and someone will help you with it then you could ask them for resources.

Alright good idea, thanks! I posted a question on the forum, awaiting responses and explanations haha

Reply 219

stochasym

12

ok

Original post

by notnek

No they're not in the spec :smile:

Level 2 Further Maths - Post some hard questions (Includes unofficial practice paper)

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