!! Maths HL paper 1 2016 - Before and After

123zxc

does anyone have any predictions for maths paper 1 this year? i dont know how to begin studying, and i want to start with something that there is a good chance will come up

Curb Your Enthusiasm

123zxc wrote: »

does anyone have any predictions for maths paper 1 this year? i dont know how to begin studying, and i want to start with something that there is a good chance will come up

Predictions are pointless.

Ovomos

Don't think you can predict maths questions.. But there are certain topics that are examined in p1 each year. Calculus,complex numbers, algebra, patterns and sequence, functions and numbers I think

skippy1977

As a minimum I would make sure to be solid on the few things that can be learned off....that way if they get asked you'll get 5% (ish) of the paper. No learned proof was asked on Paper 1 last year so the likelihood is that something is due??

1. De Moivre's Theorem by Induction
2. Proof by Contradiction (Root 2 is Not rational)
3. Constructions of Root 2 and Root 3 (and the tricks they could ask....construct root 8 or root 2 minus 1)
4. Sum of a Finite Series by Induction
5. Sum of an Infinite Series by Limits
6. Derive the Amortisation formula (expressing as Geometric Series)

Also (not so much learned off...but def. the headings...and the start)
1. Differentiation by 1st Principles
2. De Moivres to Prove Special Trig Identities...

In all likelihood no more than 1 if any of the above will come up on the day...but simple marks if you know them and difficult to bluff on the day if you don't.

Absolutely guessing I would say...
Some type of Binomial question would be due up...
Complex Number question had no Polar Form aspect last year so it would be likely...
They will ask either NO Financial Maths...or a really hard one (as last year's was unbelievably easy)...
Inverse and Composite functions, Limits and Continuity of functions...this stuff has hardly been examined at all
A proof by induction (possibly as one of the proofs above)...none asked last year...
Contexts and Application questions with e's and logs...area and volume question with max/min aspect?

Sorry I'm just wildly guessing now...to get a really good grade you'll need to have the work done by now...but looking over the papers and identifying things that you don't know (and practising them) is the best bet the next few days.

aunt aggie

skippy1977 wrote: »

As a minimum I would make sure to be solid on the few things that can be learned off....

Great advice from Skippy if and only if, you're studying HIGHER level.

I don't think the OP specified which level they're studying which makes it a bit more difficult to give advice.

If the OP does study Ordinary Level, I'd say he/she had a minor heart attack looking at that list

For OL, do questions from the papers!! and if you have done very little up to now there are some revision tips below. These are just the basics and not an exhaustive list of what you should be revising.

• Algebra, you need to know how to factorise and solve quadratics and how to solve simultaneous equations as these topics can also appear in Functions and Differentiation Qs
• Differentiation, you need to be able to find first and second derivatives and use this information to find min and max values/ turning points
• Sequences, you need to know how to find the general rule (nth term rule) of a sequence and also find the Sum of the first however many terms. Most student do well continuing the pattern but struggle with formulas.
• Functions, know how to find and plot points, and use your graph to estimate values including roots. Simultaneous equations and solving can also pop up here.
• Complex Numbers, you need to know how to calculate with complex numbers, plot on argand diagram and find the modulus
• Applied Arithmetic is almost impossible to predict, but definitely be sure you know how to calculate percentages.. you'd assume that was a given at LC but no, its not!

This is just the bare bones for LCOL Paper 1. It's the basics and they appear often on papers. It's not a prediction, or a complete list of what you should study. Best advice you'll ever get is write something for every question and the examiner will do their best to find you marks. Leave it blank and you're getting nothing!

If really confused, attempt the same question twice. BUT never cross out or tippex over work.

Bring a calculator and construction set to both exams and know which pages of the log tables are relevant. You should also know how to use the formulas in the log tables. At this stage, if you need extra help revising any particular topic, youtube has some great tutorial videos geared towards mostly gcse students but many are also relevant to LCOL

CreepyOnion

skippy1977 wrote: »

3. Constructions of Root 2 and Root 3 (and the tricks they could ask....construct root 8 or root 2 minus 1)

How do you construct root 8 or root 2 minus 1?

skippy1977

CreepyOnion wrote: »

How do you construct root 8 or root 2 minus 1?

So they could ask you to do the root of 2 which everyone will have learned but as an extension to that they might add...hence draw root 8....well root 8 is 2root2...so twice as far as root 2...

The construction of root 2 begins with a line of one unit length....so if you measure this with the compass and swing it on the root 2 line you will have split the root 2 line into a piece that is 1 and a piece that is root 2 minus 1.

Both these questions have appeared in Mocks in recent years so whilst not state issued this is higher level and they will expect you to take what you know and be able to adapt it.

daraghwal

skippy1977 wrote: »

As a minimum I would make sure to be solid on the few things that can be learned off....that way if they get asked you'll get 5% (ish) of the paper. No learned proof was asked on Paper 1 last year so the likelihood is that something is due??

1. De Moivre's Theorem by Induction
2. Proof by Contradiction (Root 2 is Not rational)
3. Constructions of Root 2 and Root 3 (and the tricks they could ask....construct root 8 or root 2 minus 1)
4. Sum of a Finite Series by Induction
5. Sum of an Infinite Series by Limits
6. Derive the Amortisation formula (expressing as Geometric Series)

Also (not so much learned off...but def. the headings...and the start)
1. Differentiation by 1st Principles
2. De Moivres to Prove Special Trig Identities...

In all likelihood no more than 1 if any of the above will come up on the day...but simple marks if you know them and difficult to bluff on the day if you don't.

Absolutely guessing I would say...
Some type of Binomial question would be due up...
Complex Number question had no Polar Form aspect last year so it would be likely...
They will ask either NO Financial Maths...or a really hard one (as last year's was unbelievably easy)...
Inverse and Composite functions, Limits and Continuity of functions...this stuff has hardly been examined at all
A proof by induction (possibly as one of the proofs above)...none asked last year...
Contexts and Application questions with e's and logs...area and volume question with max/min aspect?

Sorry I'm just wildly guessing now...to get a really good grade you'll need to have the work done by now...but looking over the papers and identifying things that you don't know (and practising them) is the best bet the next few days.

Please tell my binomial is paper 2 and also what is the continuity of functions!

skippy1977

A binomial expansion is Paper 1 where, for example they could ask you for the 4th term of the expansion of (2x+4)^5....A bernouilli trial is Paper 2, also called a Binomial trial...one is linked to Algebra and multiplying expressions (P1), the other to probability (P2).

A continuous function will have no break in it....some functions have no y values for certain x values and therefore on a sketch of the graph there is a break....for example if the denominator of a function was x-2....there could be no value for x=2 as this would give 0....and dividing by 0 is undefined.

Here is a nice little worksheet that will help.

http://www.projectmaths.ie/documents/PDF/ActivitiesOnLimitsAndContinuity.pdf?strand

daraghwal

skippy1977 wrote: »

A binomial expansion is Paper 1 where, for example they could ask you for the 4th term of the expansion of (2x+4)^5....A bernouilli trial is Paper 2, also called a Binomial trial...one is linked to Algebra and multiplying expressions (P1), the other to probability (P2).

A continuous function will have no break in it....some functions have no y values for certain x values and therefore on a sketch of the graph there is a break....for example if the denominator of a function was x-2....there could be no value for x=2 as this would give 0....and dividing by 0 is undefined.

Here is a nice little worksheet that will help.

http://www.projectmaths.ie/documents/PDF/ActivitiesOnLimitsAndContinuity.pdf?strand

So something like tan, something with asymptotes then?
I actually never thought of binomial expansion as paper 1. Thanks!

skippy1977

Exactly the graph of the Tan function is not continuous...asymptotes same idea...

Yeah the confusion is that Binomial was added to some books late and only included in supplements with inferential stats and other paper 2 stuff.

daraghwal

skippy1977 wrote: »

Exactly the graph of the Tan function is not continuous...asymptotes same idea...

Yeah the confusion is that Binomial was added to some books late and only included in supplements with inferential stats and other paper 2 stuff.

Inferential stats is definitely paper 2 though yeah? I just notices this today http://www.mathsdojo.ie/pdf/EP_LCH_P1_2015_Sample.pdf The maths tutor have this down in the Paper 1 section? That's not right is it?

skippy1977

No that's def Paper 2 stuff...well worth doing them questions at the weekend.

123zxc

Thank you, I will go over all these before Friday! Do you have any links to show me how to prove the amortisation formula by induction?

lostatsea

123zxc wrote: »

Thank you, I will go over all these before Friday! Do you have any links to show me how to prove the amortisation formula by induction?

I wonder if forums help or cause unnecessary panic - I think the latter. The chances of asking you to prove the amortisation formula are miniscule and then to do it by induction are non-existent. Please stop this unnecessary worry. Everybody will be fine.

daraghwal

lostatsea wrote: »

I wonder if forums help or cause unnecessary panic - I think the latter. The chances of asking you to prove the amortisation formula are miniscule and then to do it by induction are non-existent. Please stop this unnecessary worry. Everybody will be fine.

If it wasn't for the forum I'd probably be panicking more!

skippy1977

123zxc wrote: »

Thank you, I will go over all these before Friday! Do you have any links to show me how to prove the amortisation formula by induction?

That one doesn't have to be shown through induction (just De Moivre and the Sum of Finite Series). Amortisation is derived using a Geometric Series. If you want a look at that PM me and I'll send on last minute revision sheet with it and a few other bits and pieces.

ConorD21

How Much are the Theorems usually worth at OL? If you didnt learn them could you still pass maths easily?

skippy1977

ConorD21 wrote: »

How Much are the Theorems usually worth at OL? If you didnt learn them could you still pass maths easily?

Theorems don't have to be proven at Ordinary Level so you don't have to learn any off...just understand each one. For example you need to know that the 3 angles of a triangle sum to 180....or that opposite sides and angles of a parallelogram are equal...but you don't need to be able to prove that.

evolving_doors

CreepyOnion wrote: »

How do you construct root 8 or root 2 minus 1?

Use the wheel of theodorus, it'll cover you for any root up to root 18 I before it comes full circle (no biggy if it does though it just gets messy)

The important thing to remember is to go off 1 unit at right angles each time.

https://www.youtube.com/watch?v=tpAL-qgquUo

If you don't want to go all the way around to root 8, just reduce
root 8 = root 4 X root 2 = 2xroot2

So go to root 2 line and double it with compass.

- - - - - - - - - -- -- -

for root 2 minus 1 ... get your root 2 line (from the 1,1,root2 right angled triangle).. then mark of the length 1 on the compass from one side and mark it on the root2 line . The remainder is root 2 minus 1

- - - - - - - - - - - - -

This method is a little bit neater but not as 'pretty'.

https://www.youtube.com/watch?v=JywEjZNKSco

123zxc

skippy1977 wrote: »

That one doesn't have to be shown through induction (just De Moivre and the Sum of Finite Series). Amortisation is derived using a Geometric Series. If you want a look at that PM me and I'll send on last minute revision sheet with it and a few other bits and pieces.

Yea I don't know how to PM you, I'm new to board, could u tell me how haha

skippy1977

123zxc wrote: »

Yea I don't know how to PM you, I'm new to board, could u tell me how haha

Sent you a PM, you should see a red (1) beside your name in the top right. Click up there and you can view private messages. Best of luck.

TSMGUY

so happy that I wrote off maths, now if I do well it's just a pleasant surprise and if I f*** up it's already expected.

randomlad727

How do you prove the sum of an infinite series by limits??

skippy1977

randomlad727 wrote: »

How do you prove the sum of an infinite series by limits??

Very short proof, start with the sum of an infinite series and get the limit of it as n tends towards infinity.

Here is is straight from the horses mouth...

http://www.projectmaths.ie/documents/LCActivities/SumToInfinityOfAGeometricSequence.ppsx

Soolander

Does it matter which method you use to construct root 2 or root 3?
In my book its an incredibly simple way of just using pythagoras' theorem and drawing a right angled triangle but someone else posted a video of a big circle?
Also does anyone know how I could construct root 2 - 1 in that way?

skippy1977

Soolander wrote: »

Does it matter which method you use to construct root 2 or root 3?
In my book its an incredibly simple way of just using pythagoras' theorem and drawing a right angled triangle but someone else posted a video of a big circle?
Also does anyone know how I could construct root 2 - 1 in that way?

No the syllabus isn't specific about the method. Don't get too caught up on root 2 -1...I was kind of giving an example of how they could surprise people and ask things in a different way. If you have constructed root 2 using pythagoras then both the other sides are 1....so root 2 -1 is the length of your hypotenuse minus the length of one of your sides. So get the length of your side with your compass and swing that onto the hypotenuse, cutting a piece of 1....the piece left is root minus 1....again just an example of how they might twist something that people will know well.

emersyn

@Everyone: Before you go to sleep tonight make sure you have two calculators and your geometry set in your bag so you're not stressing at the last minute - for the junior cert mock I managed to forget my geometry set and 2.5 years later I'm still having nightmares about it
Make sure your calculators are in radians too, and put a reminder on your phone for after the exam to set them to degrees so you're ready for Monday

swagmire

What formulas have I too learn that arnt in log tables

skippy1977

Mmm maybe stuff like:

Polar Form
Headings for 1st Principles
Average Value of a Function
Headings for Induction

...in fairness there is a list of things you should know off (difference of cubes, forming a quadratic, nature of roots...even stuff like percentage error) but not really formula as such.

malnurtured

skippy1977 wrote: »

Mmm maybe stuff like:

Polar Form
Headings for 1st Principles
Average Value of a Function
Headings for Induction

...in fairness there is a list of things you should know off (difference of cubes, forming a quadratic, nature of roots...even stuff like percentage error) but not really formula as such.

Is there an exhaustive list of non-tables formulae anywhere? I don't want to get caught. Thing is, most people just say learn x y z formula and I get the feeling there's a list somewhere that says all the things you need off by heart (including nature of roots, forming quadratics, difference of cubes, etc.)