VCAA 2000 exam 1 question 1

[Mattjbr2]

Does anyone know why only 7% of students got this question correct? Is it an error in VCAA's reporting? They don't mention it at all in the general comments.
Sorry if this has been asked before, I tried checking but it seems as though it hasn't been.

[Sine]

Does anyone know why only 7% of students got this question correct? Is it an error in VCAA's reporting? They don't mention it at all in the general comments.
Sorry if this has been asked before, I tried checking but it seems as though it hasn't been.

nah it's no error just a very good question which seems almost too basic when you look at it.
so we have two x intercepts a and b make sure to note that a is a negative number and b is positive (as well as quadratic)
the general x-intercept form is y = (x-a)(x-b)(x-c) where the x intercepts are at a,b and c.
So our x-intercepts are x=a, x=b and x =b (repeated solution)
So we get y = (x-a)(x-b)(x-b) = (x-a)(x-b)^2

[Mattjbr2]

nah it's no error just a very good question which seems almost too basic when you look at it.
so we have two x intercepts a and b make sure to note that a is a negative number and b is positive (as well as quadratic)
the general x-intercept form is y = (x-a)(x-b)(x-c) where the x intercepts are at a,b and c.
So our x-intercepts are x=a, x=b and x =b (repeated solution)
So we get y = (x-a)(x-b)(x-b) = (x-a)(x-b)^2

But what makes this question so difficult that only 7% got it correct? Where's the difficult and tricky part that stumped almost everyone? Was it just pure chance that so many people chose the wrong solution or some other reason?

[Sine]

But what makes this question so difficult that only 7% got it correct? Where's the difficult and tricky part that stumped almost everyone?

people thinking that "a" being a negative number actually mattered I'd assume the most people who got it wrong put down B as the answer

[keltingmeith]

Building on to Sine's answer, this is an old question. Like, next year, this question can legally drink.

In those years, the course has changed to include calculators, have multiple exams, had content added, had content removed, moved to the internet, and the amount and type of practice questions has changed dramatically. Something that was difficult during that exam may not be difficult now because people now know to look out for it.

Seeing where people did poorly isn't really useful more than 5 years ago, so be careful when checking that section of reports.

[Mattjbr2]

Ah yes that makes sense

[Maths Forever]

A very similar question was asked in 2015 exam 2. It was question 3 of multiple choice and was answered almost just as poorly (I think around 20% got the answer right). So perhaps they do go back to old exams when making new questions!

[keltingmeith]

A very similar question was asked in 2015 exam 2. It was question 3 of multiple choice and was answered almost just as poorly (I think around 20% got the answer right). So perhaps they do go back to old exams when making new questions!

Oh no, don't get me wrong - they do. But poor performance on a question in 2000 doesn't necessarily mean poor performance on a question in 2018. In fact, in 2015, the proportion of people who got that question right was about 3x that of 2000, which is a massive statistic.

[Maths Forever]

Oh no, don't get me wrong - they do. But poor performance on a question in 2000 doesn't necessarily mean poor performance on a question in 2018. In fact, in 2015, the proportion of people who got that question right was about 3x that of 2000, which is a massive statistic.

It's funny how it works out! But, I agree. 7% to 20% does seem like quite an improvement on that question.