As students prepare for their exams, questions that only assessors can answer often pop into mind. Unfortunately, most students don’t have access to assessors in most of their subjects, so we took your questions and presented them to a senior VCAA assessor who has extensive experience in marking the VCE exams that you will soon sit. Here are his/her answers.
We hope that your exam preparations are going well.
What is the importance of understanding Methods concepts rather than just doing the exercises?
The benefit of understanding concepts is that you are more likely to be able to adapt to unfamiliar exam questions such as those found in Exam 2 as well as the latter parts of Exam 1. The deeper your understanding the easier it is to see links with questions in different formats. Of course you need to practise this through doing exercises or practice examination papers.
How do I get full marks?
Good question! Apart from the obvious answer of getting everything correct you also need to have excellent “examination technique” such as being aware of the time; having a plan for the order of questions done; re-reading questions to make sure entire question is answered; having a set of notes where you can find what you are looking for quickly and being outstanding at using your CAS calculator.
How dependent are the exams on the CAS?
Past experience shows that there will be questions you can only do on CAS on the examination, and that proficient use is a massive advantage. CAS skills play an important role in you working more efficiently and hence increasing your chance of completing the examination in the two hours allotted. If you are a confident user then lots of marks in Exam 2 can be found correctly and quickly.
Is calculator syntax accepted for certain things such as binomCdf(10, 0.5, 1, 10) for the method mark? Or is the method mark awarded for just defining ie X~Bi(10, 0.5)? For example 2016 Exam 2 Q3a.
CAS syntax is not acceptable: you must either use mathematical notation or set up the question in a way that shows your understanding. As you suggest, in 2016 Ex 2 Q3a your setting out would be:
X~Bi(22, 0.1) (or Binomial: n = 22, p = 0.1)
Pr(X ? 1) = 0.9015
Do you have to state that dy/dx=0 before finding the derivative and equating it to zero (again) when solving for maxmin?
No: just write f ’(x) = …. = 0 and solve from there
For the bound reference, can I staple the worksheets to the back of my notebook? – Can I use pencil only in the exam ? – Will I be given any spare paper if I ask for it?
You can staple in worksheets so long as they do not protrude beyond the edge of your book.
Pencil is allowable but it is often harder to read and we can only mark what we can read. It also is tempting to erase workings – so be careful.
If you raise your hand and ask in the exam the supervisor will bring you working sheets. Just be aware anything you want marked should be in the exam booklet.
This question is from a NEAP 2016 exam 2. The population parameter p=0.2. I’m not at all sure how the 200 samples is relevant when the sample size n is 100. Their solutions use n=200 to find the SD in part iii. This makes me think they are seeing 200 p hat values as a sample of size 200 and finding the mean and SD of those 200 numbers??? please help!
When we have 200 p hat values (each taken from a sample of 100 people) then if you graphed those 200 p hat values you would get a pretty good normal curve – hence we can use a normal approximation when looking at the probability of p hat values lying in a particular range.
The normal approx. uses the population parameter as the mean and the n value is the number of sample p hat values you have – here, 200.
Xavier takes a further 200 samples of 100 children, calculating the sample proportion and 95% confidence intervals for each.
i. How many of these confidence intervals could Xavier expect to contain the population proportion of children with tooth decay? 1 mark
95% of those 200 ie 190
ii. Give the appropriate type of distribution that you would expect would be a good approximation for these sample proportions. 1 mark
Since np and np(1-p) are both more than 5 or 10 we can use the normal approx?
iii. What would the parameters (mean and standard deviation) of this distribution be, correct to two decimal places? 1 mark
Mean = p = 0.20 and sd = sqrt(.2*.8/200) = 0.03
In questions relating to “for what domain is the function strictly increasing/decreasing,” are we to include/not include end points and or turning points?
VCAA includes endpoints and turning points when looking at strictly increasing or decreasing.
For an event occurring with a probability, am I just allowed to write Pr=0.5 or do I need to write Pr(event occurring)=0.5 every time?
You should always write Pr(X>2) = 0.5 (for example).
When working on a Bound Reference, what would be the best stuff to add to the Bound Reference and how long should the Bound Reference be?
Only you know what you need in the bound reference, but the main things I would include are:
- an index at the front (with page numbers throughout) so you can find your section easily.
- a section (say on the back couple of pages) on the things you most commonly mix up or have difficulty with.
- some worked examples from text or practice examination.
Do you give consequential marks? If so, does it depend on how badly we stuffed up on the previous question?
In certain questions examiners will award marks when an incorrect result from a previously step is correctly used in a subsequent step.
Within reason it usually does not matter how far from the correct answer it is, but an obviously wrong number would not be rewarded – for example if in part (a) you found the probability to be 1.4 you could not use that in part (b).
When giving the domain for x values when the function is dealing with real life situations (where f(x)>0, do we include the values of x where f(x)=0?
Great question, but it depends on the particular question. For example if it was “for what times was the vehicle stationary” when it started after 4 seconds, then you would use [0, 4].
If the question was about when the vehicle was in motion, then you would use (4, …)
Mostly in VCAA exams they are pretty clear about what they want.
In exam 1, what should I do if I spent a long time on a question but still haven’t reached the answer? Should I abandon it or continue it since I’ve already worked so long on it?
Yes! If you have hit a road block definitely move on, and come back to it if you have time.
You are better to get on to other questions you can gain marks for, and also when you come back to a question after a break sometimes you can see what you could not earlier.
What questions should I do first in exam 2? Is the approach: 80 minutes for section b and 40 minutes for multiple choice a good approach? Also in section B, should I start from the last questions and then do the first questions?
In terms of marks per minute, Exam 2 is 80 marks in 120 minutes so 1.5 min per mark. This neatly works out to 30 min for m/c and 90 minutes for ext response. However if you find the 40/80 split better for you, that is fine. The main thing is to keep an eye on the clock – if you do M/C first, get engrossed and look up after 60 minutes you will not get the ext resp done.
The usual approach is to do the easiest questions/ones you are most confident of first.
If you mean first and last within an ext resp question I would definitely start at part a then work through it. The earlier parts are easier to get marks, and you generally need some of parts a-d to do latter parts pf the question.
Conditional probability, how much working out is required to gain full marks eg. find pr(x<6 | x>3) [2 marks] = pr(x<6 and x>3)/pr(x>3) – is this required? (stating the and) or can we go directly to the next line = pr(33) = pr4or equal to 4)
For a two-mark question, examiners are usually looking for a meaningful step of working for one mark, and the correct answer for the other.
So for cond prob show the intersection divided by the condition, then the answer
e.g. say we have Binomial; n = 8 and p = 0.5 find Pr(2 < x < 6|x > 3)
Pr(2 < x < 6|x > 3) = Pr(x = 4, 5)/Pr(x > 3) = 0.773
Sample proportion, how much working out is required to gain full marks eg. the manufacturer decides to take samples of 100 model Y phones from a number of different retail outlets that it has supplied. let P^ be the random variable of the distribution of sample proportions of model Y phones with a charge time greater than one hour for these samples of 100 model Y phones. it is known that 10% of the model Y phones that the manufacturer has in its stockpile have a charge time greater than 1 hour. find pr(P^>0.05| P^<0.15). give your answers correct to four decimal places. do not use normal approximation. [3 marks]
From this large population we can use the binomial distribution to solve this question.
It correlates to X~Bi(100, 0.1)
Hence Pr(p^ > .05 | p^ < .15) = Pr (X > 5 | X < 15)
= Pr(5 < X < 15)/Pr(X < 15)
= 0.9379 (Make sure you don’t include 15 etc in your binomcdf calculations)
Differentiation and anti-differentiation, what is the appropriate working out eg. let y=x*cos(x) a) find dy/dx [2 marks] b) hence, evaluate integral of 2x*sin(x) dx from pi/6 to 0 [2 marks] for b in particular, what are the answer marks typically allowed as my method is not the same as the ones usually given but I reach the same answer also, when finding the derivative in a two mark question, can I go straight to the answer or do I have to show that I have applied the chain/product/ quotient rule and when showing my application of these rules, is it okay to just say dy/dx of cos(2x)*5x = 5cos(2x)-10xsin(x) or do I need to show = 5*cos(2x) + (-2sin(x))(5x)
In terms of two marks for a diff: yes I would make sure of it and show the extra step as you have above i.e. dy/dx = 5*cos(2x) + (-2sin(x))(5x) = 5cos(2x)-10xsin(x)
So same above with xcos(x).
There is no one correct method for Integration by Recognition so as long as you clearly set out what you are doing you will get the marks. If you have done this legible working and you end up with the right answer you will be fine.