VCE Methods Question Thread!

[Sine]

I know that diagrams aren't generally drawn to scale in VCAA exams, but what do we do when they're RIDICULOUSLY off?
Example: VCAA 2017 Exam 1
(Image removed from quote.)
As you can see there is a VERY OBVIOUS gap between the x-intercept of the curve at (1,0) and point B, yet after doing the calculations it's found that they're actually the same point. I ended up rejecting x=1 for point B because I thought the diagram made it very clear that B>1.

If this comes up on the final exam do we just trust our own calculations and assume that the diagrams are wrong? Thanks.

I would firstly double check my own maths and if that is still correct there is not much you can do if VCAA put dodgy diagrams up.

I would be confident in my answer If I am using information that is explictly stated in the questoin and not inferred from the diagram.

[S_R_K]

I know that diagrams aren't generally drawn to scale in VCAA exams, but what do we do when they're RIDICULOUSLY off?
Example: VCAA 2017 Exam 1
(Image removed from quote.)
As you can see there is a VERY OBVIOUS gap between the x-intercept of the curve at (1,0) and point B, yet after doing the calculations it's found that they're actually the same point. I ended up rejecting x=1 for point B because I thought the diagram made it very clear that B>1.

If this comes up on the final exam do we just trust our own calculations and assume that the diagrams are wrong? Thanks.

That diagram is to illustrate the case when AC is tangent to the graph and forms some angle theta – which is not necessarily 45° – with the x-axis. If the angle is not 45°, then BC does not intersect the x-axis at the same point as the graph. So finding that x = 1 for the point B is not inconsistent with the diagram. There was some problems with that question (finding a derivative at an endpoint), but the diagram is fine.

In general, just be careful with not over-interpreting diagrams. Most of the time they exist to illustrate general features of the situation, not necessarily all the specific features that you'll find by doing calculus / algebra / whatever.

[DinWell]

If
and
Both on their maximal domains. How would I find range of
?
This is from a paper 1.

I guess you can do it by saying that the minimum will occur when is a minimum and that expression is minimum when is minimum. This has a minimum of 0, so the minimum value must be
And for maximum, as x->-inf 4-2x->inf so g(f(x))->inf.
So we conclude the range is [5, inf).
BUT, this is a 2 mark question, do they really expect this much thinking in a 2 mark question? There has to be a simpler way...
Also, is the above reasoning valid?
In the solutions, they give no reasoning They just sketch it and say the range. Secondary part of this question is: How would I sketch the graph of g(f(x)) without a calculator?

[Azim.m]

Would this explanation be sufficient?
Work out g’(x) and state that g’(x) > 0 for x = (-k, infinity).
Since the derivative function is always positive, g(x) is strictly increasing in the given domain, hence x2 > x1 implies that g(x2)> g(x1)

2016 exam 2 question 4d

[minhalgill]

for this quesitons why do we do dt/dx less than or equal to 0? why not equate it to 0?

thanks in advance!!

[darkz]

So I was doing this question from 2016 MAV Exam 2, but for some reason, when I solve the equations given by the question, it simply won't give me the exact values for some odd reason :/. However the solutions show that it does work so not too sure why this is the case? (When I solve it, I just get random equation =0, then I ctrl+enter for decimals lol)

[Lear]

So I was doing this question from 2016 MAV Exam 2, but for some reason, when I solve the equations given by the question, it simply won't give me the exact values for some odd reason :/. However the solutions show that it does work so not too sure why this is the case? (When I solve it, I just get random equation =0, then I ctrl+enter for decimals lol)

I remember this.
This was a very weird case. Try putting your cas on ‘auto’ instead of ‘exact’

Oddly enough, for me putting it on ‘auto’ gave me exact yet on ‘exact’ it refused to.

[DinWell]

Is there a way to make CAS simplify expressions like to

[Lear]

Try the expand function

[DinWell]

Try the expand function

Doesn't work unfortunately.

[integrationbyrecognition]

2017 methods exam 1 question 8c
How come 0 is not included but 1/40 is included?

[MB_]

2017 methods exam 1 question 8c
How come 0 is not included but 1/40 is included?

The sets would be disjoint if p=0

[integrationbyrecognition]

The sets would be disjoint if p=0

Can you please explain how?
Thanks

[MB_]

Can you please explain how?
Thanks

P(A∩B)=p, if p=0 then the sets have no common elements and are disjoint. Also, the whole question would be infeasible as you are given that Pr(A|B)=1/5 and Pr(B|A)=1/4

[Freddie Hg]

yes, a friend of mine and I both used limits for this question in the actual 2016 exam and we got marks.

sine, can you please provide an example of how limits can be used to solve this question? sorry im unfamiliar with limits (i dont do spesh, or have i used them in mm)