Maths Extension 1 solutions

[RuiAce]

Let's get started. Is now complete. Let me know of any further mistakes spotted, or any questions in the thread.

(Click the image to rescale it more nicely.)
Multiple choice

Questions 1-5

Questions 6-10

Short Answer

Question 11

Question 12

Question 13

Question 14

[black.mamba]

hi rui, for q13, dont you need to test on both sides of the discontinuity?

[RuiAce]

hi rui, for q13, dont you need to test on both sides of the discontinuity?

Good pickup. Yes you do. I'll be sure to fix that.

[Ookei]

Wow I got a lot of the hard question correct but the easy integration questions I got wrong. What is wrong with me?

[Fabrizio111111]

For 13c ii is using pythag to prove they are equal also a valid solution?

[HeyyyIts2xq]

For 13c ii is using pythag to prove they are equal also a valid solution?

arccos x has a range of 0 to pi. 1 triangle not enough.

[RuiAce]

For 13c ii is using pythag to prove they are equal also a valid solution?

Agree with above. You'd basically get the same amount of marks as if you only tested one side of y=f(x). At the end of the day, triangles are made for working with only angles between 0 and pi/2 (i.e. 0 and 90 degrees).

[Noomin]

if you applied the continuity correction is it still valid? thanks!

[HeyyyIts2xq]

think ur meant to put D not A for q6 lol

[RuiAce]

if you applied the continuity correction is it still valid? thanks!

Should still be fine. I get
\[ P(55\leq X \leq 65) \approx P \left( \frac{55 - 60 - \frac12}{\sqrt{24}} \leq Z \leq \frac{65 - 60 + \frac12}{\sqrt{24}} \right) \approx P(-1.12\leq Z \leq 1.12),\]
which can still be approximated by \(P(-1\leq Z \leq 1) \).

Edit: As an aside, I just found out that the continuity correction actually does estimate the probability more accurately. From statistical computing software, I found
\[ P(55\leq X \leq 65) =P(X\leq 65) - P(X\leq 54) \approx 0.73857,\]
which you might want to note is at least a bit far off from 0.68! But
\[ P \left( \frac{55 - 60 - \frac12}{\sqrt{24}} \leq Z \leq \frac{65 - 60 + \frac12}{\sqrt{24}} \right)\approx 0.7384278.\]

think ur meant to put D not A for q6 lol

Whoops.

[mrsc]

For question 12e) i put x^2+y^2=1. Would that be considered as the incorrect solution?

[BakerDad12]

I've heard a lot of people complaining about this exam and its difficulty. Can an unbiased person offer their opinion? Was it more difficult than other years, or was it around the same?

[yolthony yolksdee]

For 12biii I used P(-1.02<Z<1.02) and evaluated that, without simplifying it to P(-1<Z<1), will I lose marks for this?

[RuiAce]

For question 12e) i put x^2+y^2=1. Would that be considered as the incorrect solution?

I would've accepted it personally. Not sure about NESA.

I've heard a lot of people complaining about this exam and its difficulty. Can an unbiased person offer their opinion? Was it more difficult than other years, or was it around the same?

Just as I feel MX2 got underestimated, I feel this got overestimated. However, I'll agree that the perms and combs wasn't too friendly...

For 12biii I used P(-1.02<Z<1.02) and evaluated that, without simplifying it to P(-1<Z<1), will I lose marks for this?

May I ask how you evaluated that without a Z-table? Or did they give one in the exam somewhere.

[yolthony yolksdee]

I would've accepted it personally. Not sure about NESA.Just as I feel MX2 got underestimated, I feel this got overestimated. However, I'll agree that the perms and combs wasn't too friendly...May I ask how you evaluated that without a Z-table? Or did they give one in the exam somewhere.

I can do it on my calculator (fx100au) not sure if everyone else can. But do you reckon I'll lose any marks for having a more accurate answer compared to the "approximate" answer they wanted?