Student Written Methods Exam

[VanillaRice]

from what i know there is nothing saying combinatorics/permutations can't come up on exam 1 

which part of the study design says otherwise, I couldnt find it 

Very valid point indeed, I scanned the study design properly this time sourced from;

http://www.vcaa.vic.edu.au/Documents/vce/mathematics/MathematicsSD-2016.pdf

Combinations are listed Under Unit 2 Methods; AOS 4 Probability and Statistics pg.38; Where they state combinations are included within the topic. However they do not reappear again key knowledge or key skills. This is the contrary for Specialist where they appear on pg45 AOS 2 Arithmetic and Numbers and again on pg 48, where they are included in key knowledge and skills.

I too have found that companies such as MAV and TSM and Hefferman have used them in their past 2016 exams.

Obviously knowing how to apply them can't hurt, and they're something I am fine with. What are your thoughts though? For it is for my class I am worried for as my teachers are under the pretense that VCAA won't be assessing them this year.

It looks like a combinations calculation was required in Question 6aii of the 2017 Northern Hemisphere Exam 1 (current study design):
http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2017/nht/2017MM1-nht-w.pdf

[AlphaZero]

Hi, I'm a current year 12 student who did Methods 3/4 in year 11. I've been writing exams for methods since the end of last year (and now writing for Specialist). Here is my feedback:

Question 1: I like the style of this question, but it is quite difficult and is perhaps a bit of a stretch for the methods course as VCAA seems to not focus on changes of base with logs and exponential functions anymore (it was only 1 multiple-choice question). You would also have to note that it is possible to find the same answer by implicit differentiation by first taking the natural log of both sides.

Question 2: Again, this I think is a bit too difficult and asks too much of methods students. Remember that using the reciprocal circular functions are dedicated to the specialist maths course! Also, differentiation of sec(x) is not required. Therefore, most students (unless they have studied maths beyond methods and specialist) will use the quotient rule inside the chain rule, and then substitute x=pi/6.

Question 3: I really like this question. I don't have much else to say about it. Note: you should probably say "Let X be a normally distributed random variable...".

Question 4: Again - "Let". I like part a. For part b., 17 students is too higher of a number as you are expected to then calculate 17C3. VCAA usually limits these calculations to n<10. I would suggest changing the number of students to a number that cancels nicely with 0.5^3 and ask to leave the answer in a different form.

Question 5: I really like the style of part a. It takes a different turn to the standard VCAA ones and asks you to apply basic formulas in a different way - I like it. For part b. you must say "0<p<1", not "p is a positive real constant", as it suggests p can be larger than 1 (which is not possible for the context of the question). Otherwise, I really like the idea behind it.

Question 6: This is a bit of a borderline question. It almost crosses into specialist maths territory as you are asked to consider continuity (cancelling (x+2)'s). However, as you state a domain, of course cancelling is allowed and continuity is not affected. The second reason I say it is borderline is that VCAA does not expect you to simplify rules of functions where the denominator has a polynomial of a degree greater than 1 - (this is for specialist maths). I understand it is very easy (for most people), but I don't think this would be tested. I think part b. is a pointless question. Given the difficulty and "theme" of your exam, I feel like it has been 'chucked' in after you realised you only had 39 marks and needed one more.

Question 7: I like this because you tried to adopt a typical VCAA-style question, but unfortunately there is a big mistake! This function cannot possibly be a continuous random variable as F(B)<0 for 1<B<2! The definition of a continuous probability density function means F(B)>=0 for all the domain! Notice that if you evaluate Pr(1<B<2) you get a negative... So in short, this question doesn't work.

Question 8: Part a. is a cool question. Limits are not technically in the course, even in the form of derivatives by "first-principle" method. It is a cool question as it combines this with the fundamental theorem of calculus, but I don't think it will be tested in the methods course. I like part b. however (you have to take the negative of the answer to part a.) Part c. is good. I think part d. needs a bit of work. By definition the word "approximation" means it will be slightly different from the "actual" value. I looked at your solutions. Perhaps a better question to ask is "Explain why the approximated value is less than the actual value for the area of the region". Then, your solution works well.

Question 9: I have no problems with this question other than I don't think it is worth 4 marks.

Question 10: I think "-12" is an unnecessarily small coefficient considering the fractions work you must do to get the correct answer. I like part b. I like the idea behind part c., but I think it goes into some unnecessary depth. I think it is a bit unfair to ask a 4 mark question where if people have no idea on how to proceed, they lose all 4 marks. It lacks accessibility.

Overall, I think the exam is good, but needs a bit of work. Obviously, you must fix the mathematical conceptual error (question 7). As for the structure, I thought you stayed quite true to VCAA's style (question 1 is differentiation, question 2..., etc.) and I like that. However, I think you need to group the questions together properly. Question 1 and 2 should just be Question 1 a. and b. I also think for question 10, the parts are completely unrelated (they don't even use the same function), so I think you need to change this.

In terms of formatting, this needs work. Consider downloading MathType (VCAA uses this to write equations). I suggest looking at the VCAA exams to find out how they format their papers.

I really admire people who take it upon themselves to write their own questions as it requires a deeper understanding of maths than simply studying it in VCE. Well done

[MathMethdz99-R]

Hi, I'm a current year 12 student who did Methods 3/4 in year 11. I've been writing exams for methods since the end of last year (and now writing for Specialist). Here is my feedback:

Question 1: I like the style of this question, but it is quite difficult and is perhaps a bit of a stretch for the methods course as VCAA seems to not focus on changes of base with logs and exponential functions anymore (it was only 1 multiple-choice question). You would also have to note that it is possible to find the same answer by implicit differentiation by first taking the natural log of both sides.

Question 2: Again, this I think is a bit too difficult and asks too much of methods students. Remember that using the reciprocal circular functions are dedicated to the specialist maths course! Also, differentiation of sec(x) is not required. Therefore, most students (unless they have studied maths beyond methods and specialist) will use the quotient rule inside the chain rule, and then substitute x=pi/6.

Question 3: I really like this question. I don't have much else to say about it. Note: you should probably say "Let X be a normally distributed random variable...".

Question 4: Again - "Let". I like part a. For part b., 17 students is too higher of a number as you are expected to then calculate 17C3. VCAA usually limits these calculations to n<10. I would suggest changing the number of students to a number that cancels nicely with 0.5^3 and ask to leave the answer in a different form.

Question 5: I really like the style of part a. It takes a different turn to the standard VCAA ones and asks you to apply basic formulas in a different way - I like it. For part b. you must say "0<p<1", not "p is a positive real constant", as it suggests p can be larger than 1 (which is not possible for the context of the question). Otherwise, I really like the idea behind it.

Question 6: This is a bit of a borderline question. It almost crosses into specialist maths territory as you are asked to consider continuity (cancelling (x+2)'s). However, as you state a domain, of course cancelling is allowed and continuity is not affected. The second reason I say it is borderline is that VCAA does not expect you to simplify rules of functions where the denominator has a polynomial of a degree greater than 1 - (this is for specialist maths). I understand it is very easy (for most people), but I don't think this would be tested. I think part b. is a pointless question. Given the difficulty and "theme" of your exam, I feel like it has been 'chucked' in after you realised you only had 39 marks and needed one more.

Question 7: I like this because you tried to adopt a typical VCAA-style question, but unfortunately there is a big mistake! This function cannot possibly be a continuous random variable as F(B)<0 for 1<B<2! The definition of a continuous probability density function means F(B)>=0 for all the domain! Notice that if you evaluate Pr(1<B<2) you get a negative... So in short, this question doesn't work.

Question 8: Part a. is a cool question. Limits are not technically in the course, even in the form of derivatives by "first-principle" method. It is a cool question as it combines this with the fundamental theorem of calculus, but I don't think it will be tested in the methods course. I like part b. however (you have to take the negative of the answer to part a.) Part c. is good. I think part d. needs a bit of work. By definition the word "approximation" means it will be slightly different from the "actual" value. I looked at your solutions. Perhaps a better question to ask is "Explain why the approximated value is less than the actual value for the area of the region". Then, your solution works well.

Question 9: I have no problems with this question other than I don't think it is worth 4 marks.

Question 10: I think "-12" is an unnecessarily small coefficient considering the fractions work you must do to get the correct answer. I like part b. I like the idea behind part c., but I think it goes into some unnecessary depth. I think it is a bit unfair to ask a 4 mark question where if people have no idea on how to proceed, they lose all 4 marks. It lacks accessibility.

Overall, I think the exam is good, but needs a bit of work. Obviously, you must fix the mathematical conceptual error (question 7). As for the structure, I thought you stayed quite true to VCAA's style (question 1 is differentiation, question 2..., etc.) and I like that. However, I think you need to group the questions together properly. Question 1 and 2 should just be Question 1 a. and b. I also think for question 10, the parts are completely unrelated (they don't even use the same function), so I think you need to change this.

In terms of formatting, this needs work. Consider downloading MathType (VCAA uses this to write equations). I suggest looking at the VCAA exams to find out how they format their papers.

I really admire people who take it upon themselves to write their own questions as it requires a deeper understanding of maths than simply studying it in VCE. Well done

Hey there, thanks for the feedback!

Question 1: Yeah, I see that this question is a bit unfair, I intended it to be a unique style of question but I'll keep that in mind in the future.

Question 2: I suppose it's a bit beyond the scope of the course, I assumed it'd be fine because sec(x) is used in the methods course (namely deriving tan(x)) and deriving it is mainly using chain rule but VCAA tends not to go into this area for methods so I can see how it's not relevant.. I mean related rates was also merely an application of chain rule and that's not explicitly in the course anymore either

Question 3: yep, makes sense.

Question 4: yeah you're probably right, i figured 17C3 wouldn't be too difficult since a lot of terms cancel out but it's probably still a bit much arithmetic

Question 5: Well that's true.

Question 6: I guess I just wanted something different cuz all the inverse functions questions in VCAA exams are a bit boring but you're probably right there's a reason for it haha. and you're exactly right for part b) as well as the fact that I felt I should include composite functions for the sake of it. I'll try to integrate(no pun intended) it more smoothly next time if I decide to include it.

Question 7) Ouch, you're right. Yeah I was a bit slack with that sorry... I'll change the function to sin(pi/3 * b) since that's positive for 0<b<3 and adjust the other numbers accordingly. I just did the maths for the question without considering the graph oops.

Question yep.. gotcha. The limits question was just me being a bit cheeky and trying something new haha.

Question 9) the reason i did 4 marks was for finding a, b, c, d so 1 mark each.

Question 10) yeah I guess I just tried to introduce a harder question for the last question of the exam since VCAA tends to do this sometimes.

I'll be sure to definitely fix Question 7 and yeah the grouping wasn't the best since I wrote this exam fairly quickly and structure wasn't considered as much as it could have been. Yeah I know about the formatting haha Microsoft Word.. in fairness, it was probably the same quality as my school's SACS hahaha I didn't know what else to use.. but I'll look into MathType. If you wouldn't mind, would you be able to send a methods (and spesh if you could) exam you have written to me please? Since this is the first exam I've written and I'd like to continue improving.

Thanks again for all the feedback!

[TheInfamousJimsRightHandMan]

Hello,
It's good to have another exam to do, so cheers!
Just wondering, in question 5a), I got Pr(B) = (3)^(1/2)/(7)^(1/2), so how do you go from that to solving Pr(A)=(21)^(1/2)/(7) x 1/3 ?
I didn't think (3)^(1/2)/(7)^(1/2)=(21)^(1/2)/(7)

[MathMethdz99-R]

Hello,
It's good to have another exam to do, so cheers!
Just wondering, in question 5a), I got Pr(B) = (3)^(1/2)/(7)^(1/2), so how do you go from that to solving Pr(A)=(21)^(1/2)/(7) x 1/3 ?
I didn't think (3)^(1/2)/(7)^(1/2)=(21)^(1/2)/(7)

So when you have pr(b)=sqrt(3)/sqrt(7) you can rationalise it by multiplying top and bottom by sqrt(7) to get pr(b)=sqrt(21)/7 then multiplying by 1/3 to get pr(a)=sqrt(21)/21. Alternatively, you could have used pr(b) =3pr(a) from the start then 3 (pr(a))^2 = 1/7 divide by 7, square root both sides and rationalise

[TheInfamousJimsRightHandMan]

So when you have pr(b)=sqrt(3)/sqrt(7) you can rationalise it by multiplying top and bottom by sqrt(7) to get pr(b)=sqrt(21)/7 then multiplying by 1/3 to get pr(a)=sqrt(21)/21. Alternatively, you could have used pr(b) =3pr(a) from the start then 3 (pr(a))^2 = 1/7 divide by 7, square root both sides and rationalise

Oh... 😂😂 cheers!