Working/method step in Exam 2

[YouAreNowReadingMyName]

In a two mark (or 3 or 4 or more) question, how do you show your working steps? In fact, what is a method step? Apparently stuff like f'(x)=0 so x=3.2 blah blah blah isn't enough. What do you have to do to get the method mark? In particular, could someone detail the method mark for these types of questions please:

simultaneous equations
finding maxima/minima/turning points
limiting a domain/range
'show that' questions

From what I've heard, formula + answer isn't enough. Is that true?

Then what happens if you just can't think of a method step? For 1c in the 2012 exam, it's find Dv/dx, and I can't think of any method step other than just putting it into your calculator to differentiate.

Any help would be greatly appreciated!

[Damoz.G]

Do not write calculator syntax as part of your answer as your working out. Just want to point this out.

If its worth more than a mark, you definitely need to show working out (Clearly :p). I've always learnt to just write down as much working out as you can until you can't do it any further in your head, and then use your CAS.

I'm on my phone at the moment, so I'll answer the rest of your question a bit later when I get home.

[Stevensmay]

Examples of questions you have trouble answering would help. I haven't seen any questions (yet) that give more than two marks for finding a domain and range. Same goes with simultaneous.

I generally write things like for minima/maxima.

Then what happens if you just can't think of a method step? For 1c in the 2012 exam, it's find Dv/dx, and I can't think of any method step other than just putting it into your calculator to differentiate.

For this I did.

[Damoz.G]

simultaneous equations
finding maxima/minima/turning points
limiting a domain/range
'show that' questions

* Simultaneous Equations - Write out all matrices, and then write the answer. Then interpret the matrix answer, and state what each number means.

* Max/Min TPs - state the f'(x) equation. Then state "let f'(x)=0". Then provide the answer.

* Domain and Range - No other working required. Usually if it asks for Domain and it has 2 marks, the examiner is looking for whether you have both the open/closed brackets used and whether the figures are correct.

* Show that - Write out as much working out as you can. You can write little explanations as well (If you want to, but not necessary).

As I mentioned before, the best way is to write out as much working out as you can, where you reach a limit that you can't do it by hand any further.

[BigAl]

It's really important to state what you're doing in show that question...list any theorem, identity you used along the way...you should be communicating with the assessor..maths is so boring otherwise

[JieSun92]

What about probability questions like Binomial, Normal Distributions or Inverse Normal. how do we show the working out?

[Stevensmay]

Depending on how many marks they are worth.
Binomial I normally write
If you are really struggling for things to write
 

As inverse normal often also makes reference to the standard normal distribution, writing down/using the z-score conversion formula should net a mark.
Drawing the distributions and marking on values/areas can also be worth a mark, especially in symmetry questions.

[Zealous]

What about probability questions like Binomial, Normal Distributions or Inverse Normal. how do we show the working out?

From Methods CAS Resource Thread:
Mathematical Methods CAS Resources

Have a good read below, this pretty much sums up what is required for probability working out =)

Spoiler

Guide to Probability Notation
luken93

So there's been a few questions regarding the proper notation to be used on the exam, so I thought it's probably time to make a thread

I'm assuming this is right, but feel free to pick me up on anything I've missed:

Normal Distribution
The range of scores on a particular test are such that they hold a mean of 60 with a standard deviation of 4.

NORMAL CDF
a) Find the probability of a student's scores lie between 55 and 62

On the TI-Nspire;
On the classpad;

On paper:
Let X be the range of scores of students on the test.




NORMAL PDF
b) Find the probability that a student's score is 61

On the calculator;

On paper:
Let X be the range of scores of students on the test.




INVERSE NORMAL
c) 75% of students passed the test. Find the score needed to pass the test.

On the calculator;

On paper:
Let X be the range of scores of students on the test.

Let a be the minimum value needed to pass, Find a such that


Therefore a score of 57.3020 is needed to pass.



Binomial Distribution
BinomPDF
d) The probability that a particular student passes the test is 0.4.
i) If this student sits 3 tests that are independent to the other, what is the probability that the student passes 2 out of 3 tests.

On the calculator;

On paper:
Let Y be the performance of the student in the 3 tests




BinomCDF
ii) This particular student needs to pass at least one of the tests to make his parents happy. What is the probability that his parents will be happy?

On the calculator;

On paper:
Let Y be the performance of the student in the 3 tests




Number of Trials
iii) The student is now getting very worried about his parents. To ensure that the probability that his parents are happy is 0.95, how many tests will he have to sit if he has to pass at least one of them?

On paper:
Let Y be the performance of the student in the m number of tests

Find m such that





the student will need to sit 6 tests.
Hopefully that's all correct!

[JieSun92]

From Methods CAS Resource Thread:
Mathematical Methods CAS Resources

Have a good read below, this pretty much sums up what is required for probability working out =)

Spoiler

Depending on how many marks they are worth.
Binomial I normally write
If you are really struggling for things to write
 

As inverse normal often also makes reference to the standard normal distribution, writing down/using the z-score conversion formula should net a mark.
Drawing the distributions and marking on values/areas can also be worth a mark, especially in symmetry questions.

wow thanks guys good stuff. I should read the rest of that post

[Damoz.G]

Using Binomial as an example, you could also write down what each thing is when you are entering it.

e.g. You could write "n=18, p= 0.18, lower bound=0, upper bound=5"

If you write that out, then its fine (That's what my teacher says). But writing "binomCdf(18,0.18,0,5)" (in other words, CAS Syntax) is not acceptable.

[achre]

For the distribution notation above, is it sufficient to state X~binom(n=10,p=0.4) alone? The worked solutions for my school's SACs required us to define it (as, 'let X be as binomially distributed random variable blah blah blah') and then state the X~ part.

[Stevensmay]

should be acceptable as I believe it is convention.

I haven't seen any of the assessors reports mentioning a need for students to write "let X be as", so I'm guessing no.
Was trying to find a copy of last years marking scheme but can't seem to locate it.

[YouAreNowReadingMyName]

Wow thanks everyone!

Writing out as far as much as possible...but that's so tedious and it takes so much time

lol @ Stevensmay isn't that just reordering the equation from step 2 to step 3?

I've got another question which is strictly spesh, but I'll ask anyway: what about force equations? When you do the simultaneous equations, should you write it in terms of u*N and g and T (pretend it's thrust in the question), or should you spell out the actual numbers?

[Stevensmay]

Yeah with the rearrangement I didn't want to risk losing a mark for it being not exactly in the form given. Figured it's safer to spend 5 seconds writing it than risking a mark.

With the forces one.
I set everything up in the terms given in the question first, to make it clear to the examiner what I'm doing. Parallel and perpendicular components clearly indicated.

Then I bring it all into one equation, still using the original terms given. Once I'm done to a single equation then I simplify all my numbers to give the final answer.

[YouAreNowReadingMyName]

So you can't just write two simultaneous equations and then the answer?