As someone who struggled with maths in school, and later went on to become a foundation exam writer, I 100% agree. Lots of people, like me, really try hard in maths but, despite being desperate to do it in VCE, ultimately find it way too hard. Foundation Maths solves that gap, by having an exam written by people who struggle with maths, for people who struggle in maths
Sigh. Thanks, FT, and honestly I was not trying to be rude or flippant.
I don’t pay much attention to either GM or FM, but also my sense was that people who read (or at least comment on) this blog also regard FM as in a different category. Isn’t there also something odd about FM, that the exam is optional or something?
There was also something a little odd about the FM commentary last year. Although there was a decent amount of commentary on the Secret FM post, I was frankly astonished when I later looked at the exam: it was a godawful mess, which I hammered here and itemised here.
I have trouble understanding the proper purpose of either GM or FM, but I still try to provide the platform for the discussion and I will look closely when people suggest I should. (I spent a decent amount of time last night, trying to untangle the GM Hungarian nonsense.)
I don’t know in what sense FM can possibly be considered an equally valid maths choice.
I think the question asking the limiting value of the surface area was very poorly worded. Especially since this year I was expecting the wording to be less ambiguous. Since I don’t have the paper with me, I cant remember the exact wording that was used, however for the surface area of a pond, I found the total surface area (
). But I think (not sure) that the intention was to find just the surface area of the top circular disc. I think the wording could have been much better, since to me I was unsure whether the question is referring to just the top circular disc or the total surface area. Will comment further once a copy of the exam is available.
I don’t know if this is the issue, but once VCAA bungled “surface area” in the sample questions, they made it difficult for themselves to then word things correctly (if they even knew how).
I really really hate Q B3, but I don’t see any ambiguity in (d). It is the surface of the lake in question and the area of that surface covered by pollutant.
All I can suggest is that VCAA’s idiotic “open hollow surface” from last year is making people jump at shadows this year.
I think would have been better worded if the question asked for the area of the circular disc or something, rather than referring to the “surface area of the pond would the coverage of the pollutant”. Maybe I was just overthinking in the exam to find the area of the cylinder.
it is very ambiguous question here, i think VCAA intends to only ask the top surface area. But if students work out the total surface area, it should be fine.
Question bi) The region bound by y=f(x), y=1 and y=6… Is the part “y=1” is necessary because it doesn’t make any sense to me as only y=f(x) and y=6 make a “closed area” and the line y=1 is tangential to y=f(x) and does not make any bound region with anything.
Huh, that’s a bit odd. Thanks, Victoria. No, the y = 1 is not needed and thus could well be confusing. A mistake to include it in the question.
My only thought is that the writers consciously put in the y =1 in order to flag the limit of integration. If that was the reason then it was too hand-holding (and anyway they shouldn’t have done it).
MCQ1 asks for the contrapositive of a quantified statement. The answer they intended (C) correctly contraposes the conditional contained in the statement, however none of the options as they are currently written are actually logically equivalent to the original statement.
Thanks, Daniel and yes, I saw that. A bad one. More precisely, the problem is that quantified statements do not have contrapositives. I hammered that here.
It seemed the writers tried to duck the issue, by the possible answers being conditionals only, but they obviously didn’t duck successfully.
I assume people are not going to be bothered by this, since students will know what is expected. So, once again, they wave the Psychometrician Magic Wand: no harm, no foul. But I’m bothered by it. It’s wrong.
Yes, of course. See points 2 and 3 of my post on exam errors. (I could have made the point stronger, but my focus there was on the administration of errors.)
Where are monash maths professors?
Were we not promised they would take care of merits of questions?
Did not deputy premier announce vic (vce ?) to have world class education?
Down to plant Earth. Pls.
a few points
(1) long and too much on CAS, for those who have programs on CAS would have so much advantage.
(2) nothing really new, all routine kind of questions we have seen before.
(3)Q3(c), use substitution u=root 5 t^2, what is the point to this question, you can do the following question by CAS.
(4)Q3 (d), the most unclear question, total surface area or only the top one? do we also assume t approach infinite?
(5) Q4, the yacht question, is the worst, nothing new, but just type lots of things on CAS.
(6)Q5, vector question, is just too easy with lots of CAS, the last part , you can use Heron’s formula to work out area.
This could be for many reasons. None of them sit well with me…
Most years, CAS has played a lesser role in SM papers compared to MM papers, which is why I liked them better. This year, it felt like the amount of CAS-bashing required was a lot closer between MM and SM.
And I do not like this. For many reasons. Most of all because this is meant to be a test of Mathematics, not button-pushing.
I believe multiple choice Q19 had no correct answer either. Presumably their intended definition for a Type 2 error was “a null hypothesis is not rejected when the alternative hypothesis is true”, however, the correct definition would be “a null hypothesis is not rejected when the null hypothesis is false”, because the null hypothesis being false does not necessitate that the alternative hypothesis is true.
Considering an example: a drug company is testing a new drug to see if it is successful in reducing the recovery time for a certain disease.
Here, VCAA’s definition of a type 2 error would read “the drug was successful, but we concluded it was not”, but the correct statement would read “the drug did make a difference, but we concluded that it did not”.
For mathematical working:
H_0: µ = µ_0
H_1: µ < µ_0
Here, the type 2 error would be if we accept µ = 12 but in reality µ ≠ 12, so by saying “the drug was successful [in reality]” we ignore the possibility that µ > µ_0, which is shown in the attached image.
I don’t believe so. If we define P as H_0 i.e. µ = µ_0, and Q as “we conclude that the drug had no effect” (fail to reject H_0), a Type 2 error is (¬P ∧ Q). This has no contrapositive because it is not a conditional statement, rather just a scenario.
Sorry the last bit was removed due to HTML formatting:
H_0: µ = µ_0
H_1: µ < µ_0
Here, the type 2 error would be if we accept µ = 12 but in reality µ ≠ 12, so by saying “the drug was successful [in reality]” we ignore the possibility that µ > µ_0, which is shown in the attached image.
I agree that the question was/is crap. I was/am hoping students just picked the answer that I assume VCAA intended. Spoiler Alert – I chose option A.
You are correct though in that Type 1 and Type 2 errors have nothing to do with the alternative hypothesis and everything to do with the null hypothesis.
I think it is wrong. I think a Type 2 error is when you do not reject when it is wrong. This is different to accepting when is correct, because is not always correct when is wrong (unless it is a 2-tail test, in which case… I’m not so sure).
I am not a statistician. I cannot speak with authority on this matter.
The wording is not great, but option A is “technically correct”. A type II error does occur when H1 is true (implying H0 is not true) but H0 was not rejected.
The question does not necessarily imply that this is the only way a type II error can occur.
Thanks, Wilba. It’s still stats crap, and I still don’t do stats crap. Is it possibly not poor wording, but is just a more subtle question than people are expecting?
After some reflection and discussion with a person who actually studied statistics to a high level, I withdraw my previous complaint that the question was/is wrong.
However, I think it was/is dangerously close to being wrong and I’m not sure the folks at VCAA quite understood the content they were/are trying to test here.
The exam setter(s) got lucky.
But hey – at least there was no pseudocode rubbish on these papers…
The alternative hypothesis being true does necessitate the null hypothesis being false. Agree the question is crap and should’ve been worded as Garv says, but I don’t see a major problem. Other than the general problem with stats.
VCAA uploaded (slightly blurry) photos of the exam, instead of uploading the original file. I’m guessing that they’re temporarily avoiding uploading original files while they review how the cover sheets leaks occurred (for all we/they know, uploading the original exam file could leak deleted questions that were pushed to next year’s exam, for example)
Didn’t notice any mistakes, long with lots of cas work and 1 marks though
Thanks, RA.
(not counting Foundation)
Bit rude there, Marty? I thought Foundation is an equally valid Maths choice?
As someone who struggled with maths in school, and later went on to become a foundation exam writer, I 100% agree. Lots of people, like me, really try hard in maths but, despite being desperate to do it in VCE, ultimately find it way too hard. Foundation Maths solves that gap, by having an exam written by people who struggle with maths, for people who struggle in maths
Sigh. Thanks, FT, and honestly I was not trying to be rude or flippant.
I don’t pay much attention to either GM or FM, but also my sense was that people who read (or at least comment on) this blog also regard FM as in a different category. Isn’t there also something odd about FM, that the exam is optional or something?
There was also something a little odd about the FM commentary last year. Although there was a decent amount of commentary on the Secret FM post, I was frankly astonished when I later looked at the exam: it was a godawful mess, which I hammered here and itemised here.
I have trouble understanding the proper purpose of either GM or FM, but I still try to provide the platform for the discussion and I will look closely when people suggest I should. (I spent a decent amount of time last night, trying to untangle the GM Hungarian nonsense.)
I don’t know in what sense FM can possibly be considered an equally valid maths choice.
I think the question asking the limiting value of the surface area was very poorly worded. Especially since this year I was expecting the wording to be less ambiguous. Since I don’t have the paper with me, I cant remember the exact wording that was used, however for the surface area of a pond, I found the total surface area (
). But I think (not sure) that the intention was to find just the surface area of the top circular disc. I think the wording could have been much better, since to me I was unsure whether the question is referring to just the top circular disc or the total surface area. Will comment further once a copy of the exam is available.
Thanks vce.m.s. I’ll look.
I don’t know if this is the issue, but once VCAA bungled “surface area” in the sample questions, they made it difficult for themselves to then word things correctly (if they even knew how).
You raise an excellent point.
I agree that it is not clear.
It was Q3d and it simply asked “What surface area of the pond would the coverage of the pollutant approach?”
I took this to mean surface of the pond, not the pollutant, and so height is not a consideration but now I’m not so sure…
I really really hate Q B3, but I don’t see any ambiguity in (d). It is the surface of the lake in question and the area of that surface covered by pollutant.
All I can suggest is that VCAA’s idiotic “open hollow surface” from last year is making people jump at shadows this year.
I really hate Q B3.
I think would have been better worded if the question asked for the area of the circular disc or something, rather than referring to the “surface area of the pond would the coverage of the pollutant”. Maybe I was just overthinking in the exam to find the area of the cylinder.
I don’t think the wording was great, but I don’t think it is ambiguous.
it is very ambiguous question here, i think VCAA intends to only ask the top surface area. But if students work out the total surface area, it should be fine.
Thanks, WW. I disagree. I do not think the question is ambiguous.
Question bi) The region bound by y=f(x), y=1 and y=6… Is the part “y=1” is necessary because it doesn’t make any sense to me as only y=f(x) and y=6 make a “closed area” and the line y=1 is tangential to y=f(x) and does not make any bound region with anything.
Huh, that’s a bit odd. Thanks, Victoria. No, the y = 1 is not needed and thus could well be confusing. A mistake to include it in the question.
My only thought is that the writers consciously put in the y =1 in order to flag the limit of integration. If that was the reason then it was too hand-holding (and anyway they shouldn’t have done it).
Multiple choice Q19 reminded me of the 2016 specimen paper in that it was basically a “do you know the definition of Type 1/2 errors?” question.
Was expecting something a bit more difficult by that point.
The more token the stats, the happier I am.
MCQ1 asks for the contrapositive of a quantified statement. The answer they intended (C) correctly contraposes the conditional contained in the statement, however none of the options as they are currently written are actually logically equivalent to the original statement.
Thanks, Daniel and yes, I saw that. A bad one. More precisely, the problem is that quantified statements do not have contrapositives. I hammered that here.
It seemed the writers tried to duck the issue, by the possible answers being conditionals only, but they obviously didn’t duck successfully.
I assume people are not going to be bothered by this, since students will know what is expected. So, once again, they wave the Psychometrician Magic Wand: no harm, no foul. But I’m bothered by it. It’s wrong.
Except harm is done if students are learning “facts” that are not actually facts and universities then have to un-teach things.
Maybe not a huge time loss and maybe very few people care. This does not excuse the error.
Yes, of course. See points 2 and 3 of my post on exam errors. (I could have made the point stronger, but my focus there was on the administration of errors.)
Where are monash maths professors?
Were we not promised they would take care of merits of questions?
Did not deputy premier announce vic (vce ?) to have world class education?
Down to plant Earth. Pls.
They vetted. They did not write.
a few points
(1) long and too much on CAS, for those who have programs on CAS would have so much advantage.
(2) nothing really new, all routine kind of questions we have seen before.
(3)Q3(c), use substitution u=root 5 t^2, what is the point to this question, you can do the following question by CAS.
(4)Q3 (d), the most unclear question, total surface area or only the top one? do we also assume t approach infinite?
(5) Q4, the yacht question, is the worst, nothing new, but just type lots of things on CAS.
(6)Q5, vector question, is just too easy with lots of CAS, the last part , you can use Heron’s formula to work out area.
Thanks, WW. Others also appear to be of the opinion that the exam was too CAS-heavy. Of course I have a slightly stronger stance …
The exam felt CAS heavier than in the past.
This could be for many reasons. None of them sit well with me…
Most years, CAS has played a lesser role in SM papers compared to MM papers, which is why I liked them better. This year, it felt like the amount of CAS-bashing required was a lot closer between MM and SM.
And I do not like this. For many reasons. Most of all because this is meant to be a test of Mathematics, not button-pushing.
I believe multiple choice Q19 had no correct answer either. Presumably their intended definition for a Type 2 error was “a null hypothesis is not rejected when the alternative hypothesis is true”, however, the correct definition would be “a null hypothesis is not rejected when the null hypothesis is false”, because the null hypothesis being false does not necessitate that the alternative hypothesis is true.
Considering an example: a drug company is testing a new drug to see if it is successful in reducing the recovery time for a certain disease.
Here, VCAA’s definition of a type 2 error would read “the drug was successful, but we concluded it was not”, but the correct statement would read “the drug did make a difference, but we concluded that it did not”.
For mathematical working:
H_0: µ = µ_0
H_1: µ < µ_0
Here, the type 2 error would be if we accept µ = 12 but in reality µ ≠ 12, so by saying “the drug was successful [in reality]” we ignore the possibility that µ > µ_0, which is shown in the attached image.
Thanks, Gary. It’s stats crap. I don’t do stats crap. Could it be a contrapositive thing?
I don’t believe so. If we define P as H_0 i.e. µ = µ_0, and Q as “we conclude that the drug had no effect” (fail to reject H_0), a Type 2 error is (¬P ∧ Q). This has no contrapositive because it is not a conditional statement, rather just a scenario.
Sorry the last bit was removed due to HTML formatting:
H_0: µ = µ_0
H_1: µ < µ_0
Here, the type 2 error would be if we accept µ = 12 but in reality µ ≠ 12, so by saying “the drug was successful [in reality]” we ignore the possibility that µ > µ_0, which is shown in the attached image.
I agree that the question was/is crap. I was/am hoping students just picked the answer that I assume VCAA intended. Spoiler Alert – I chose option A.
You are correct though in that Type 1 and Type 2 errors have nothing to do with the alternative hypothesis and everything to do with the null hypothesis.
It is pretty simple, definition level stuff.
But as Marty said, it is not really Mathematics…
Is the question merely crap, or also wrong?
I think it is wrong. I think a Type 2 error is when you do not reject
when it is wrong. This is different to accepting 
when 
is correct, because 
is not always correct when 
is wrong (unless it is a 2-tail test, in which case… I’m not so sure).
I am not a statistician. I cannot speak with authority on this matter.
I can ask a (retired) statistician if you want.
The wording is not great, but option A is “technically correct”. A type II error does occur when H1 is true (implying H0 is not true) but H0 was not rejected.
The question does not necessarily imply that this is the only way a type II error can occur.
Thanks, Wilba. It’s still stats crap, and I still don’t do stats crap. Is it possibly not poor wording, but is just a more subtle question than people are expecting?
ah, that is true! I didn’t consider that but I believe you’re right, bad wording but not incorrect for sure
After some reflection and discussion with a person who actually studied statistics to a high level, I withdraw my previous complaint that the question was/is wrong.
However, I think it was/is dangerously close to being wrong and I’m not sure the folks at VCAA quite understood the content they were/are trying to test here.
The exam setter(s) got lucky.
But hey – at least there was no pseudocode rubbish on these papers…
Thanks, RF.
The alternative hypothesis being true does necessitate the null hypothesis being false. Agree the question is crap and should’ve been worded as Garv says, but I don’t see a major problem. Other than the general problem with stats.
Both exams are now up. Also is it just me or is the text sort of blurry on some pages?
Thanks very much, Craig. Links added.
VCAA uploaded (slightly blurry) photos of the exam, instead of uploading the original file. I’m guessing that they’re temporarily avoiding uploading original files while they review how the cover sheets leaks occurred (for all we/they know, uploading the original exam file could leak deleted questions that were pushed to next year’s exam, for example)