VCE Further Maths Exam 2 Discussion and Solutions

[Mojo Z]

What did we think for the final geometry question with the path length, I got 153 by finding the length of the triangle and minusing from radius 50 to get 12 which when adding the 50 times 2 and (65-12) gave me 153m

Yup!! i did that too! Hopefully it's right!

[jonathanelias123]

What did we think for the final geometry question with the path length, I got 153 by finding the length of the triangle and minusing from radius 50 to get 12 which when adding the 50 times 2 and (65-12) gave me 153m

affirmative

[hk9191]

I think what is creating the confusion is the following:

If you use the exact values provided on the exam paper e.g. 2.85, then 10^2.85 = 707.95 ~ 708.
But if you do it off the regression equation: -14.4 + 0.00854 * 2020 = 2.8508 and then 10^2.8508 = 709.25 ~ 709.
Since the answer is provided in the question, I think 708 is the better answer. Or am I wrong?

I think VCAA will only accept 708, but the regression equation is in part i of the same question and I guess it could be assumed that the predictions are supposed to stem from the regression line exactly? idk

[kirstfletch99]

What did we think for the final geometry question with the path length, I got 153 by finding the length of the triangle and minusing from radius 50 to get 12 which when adding the 50 times 2 and (65-12) gave me 153m

That's what I did as well!

[aussiegodx]

For the lid questiobon, did people do one side of both, talking about part a not c

[crackleking]

I did one because as they didn't give us the thickness of the lid so that wouldn't be the true total surface area anyway

[Paolo Grande]

Answers so far:
Core Q1ai 72
              aii 25%
              bi 84%
                ii 209
               c  105
            2a   place of capture
               b  20mm
               c  min 16mm  Q3 36mm
               d  52 is greater than upper fence 50 so it is an outlier
               e  The median wingspan of moths in grassland is 30mm when compared with median wingspan of moths in the
                    forest of 21mm. Wingspan is therefore associated with the location where they are caught.
             3a  egg density = -46.8 + 18.9 x number of male moths
               bi choose two points to input into equation given ie (10,504) and (60,2064) and draw line.
                ii for every additional female moth caught the egg density increases on average by 18.9.
               iii -412.5
               iv 74.3% of variation in egg density can be explained by the variation in number of female moths caught.
            4a   0.009
              b    log(area) = -14.4 + 0.009 x year
              ci  708 hectares
               ii  Extrapolated result
             5a 3375, 71625, 3375, 68250
               bi $3375
                ii 4.5%
               c  5.7%
              6a $203
                b Ao = 428, An+1= 1.015 x An
                c  $454.26
               7a  $1560
                 b  $805.65

[drepwns]

Answers so far:
Core Q1ai 72
              aii 25%
              bi 84%
                ii 209
               c  105
            2a   place of capture
               b  20mm
               c  min 16mm  Q3 36mm
               d  52 is greater than upper fence 50 so it is an outlier
               e  The median wingspan of moths in grassland is 30mm when compared with median wingspan of moths in the
                    forest of 21mm. Wingspan is therefore associated with the location where they are caught.
             3a  egg density = -46.8 + 18.9 x number of male moths
               bi choose two points to input into equation given ie (10,504) and (60,2064) and draw line.
                ii for every additional female moth caught the egg density increases on average by 18.9.
               iii -412.5
               iv 74.3% of variation in egg density can be explained by the variation in number of female moths caught.
            4a   0.009
              b    log(area) = -14.4 + 0.009 x year
              ci  708 hectares
               ii  Extrapolated result
             5a 3375, 71625, 3375, 68250
               bi $3375
                ii 4.5%
               c  5.7%
              6a $203
                b Ao = 428, An+1= 1.015 x An
                c  $454.26
               7a  $1560
                 b  $805.65

Some of these are wrong

[jonathanelias123]

Answers so far:
Core Q1ai 72
              aii 25%
              bi 84%
                ii 209
               c  105
            2a   place of capture
               b  20mm
               c  min 16mm  Q3 36mm
               d  52 is greater than upper fence 50 so it is an outlier
               e  The median wingspan of moths in grassland is 30mm when compared with median wingspan of moths in the
                    forest of 21mm. Wingspan is therefore associated with the location where they are caught.
             3a  egg density = -46.8 + 18.9 x number of male moths
               bi choose two points to input into equation given ie (10,504) and (60,2064) and draw line.
                ii for every additional female moth caught the egg density increases on average by 18.9.
               iii -412.5
               iv 74.3% of variation in egg density can be explained by the variation in number of female moths caught.
            4a   0.009
              b    log(area) = -14.4 + 0.009 x year
              ci  708 hectares
               ii  Extrapolated result
             5a 3375, 71625, 3375, 68250
               bi $3375
                ii 4.5%
               c  5.7%
              6a $203
                b Ao = 428, An+1= 1.015 x An
                c  $454.26
               7a  $1560
                 b  $805.65

I believe Q1bii is 975 and Q4a is 0.00854

[crackleking]

0.009 isn't 3 sig figs it is one

[superficious]

These are my answers for the exam correct me if i’m wrong thanks:

1)a)i) 72 ii) 25% b)i) 84% ii) 97.5%
c) 105

2)a)place of capture
b) 20
c) 16,36
d)32+(1.5x12)=50, 52 is an outlier
e) Median is greater for grasslands etc

3)a) -46.8+18.9
b)ii) number of moths increases by 1 results in an increase of egg density by 31.3
iii) -412.5
iv) 74.3% variation

4)a) 0.009 b)-14.4+0.009x
c)i) 416
ii)limited reliability bc of extrapolation

5)a) 3375, 71625-3375=68250
b)i) 3375 ii) 4.5%
c) 5.7%

6)a) $203
b) A•=428, An+1=1.015An
c) $454.26

7)a) $1560
b) $805.65

Matrices::

1)a) 159 b)Rolls sold in week 1
c)i) 3.8 ii) [ 0 1 1 ]
2)a) 40% b) 0.4, 0.6, 0.2
c) 750
3)a) 320 b) [250, 250, 300, 200]
c) 30% d) 250

Graphs::

1)a) 2 metres b) 8am till 6pm

2)a) 500 metres
b) 200=k x 5
k=200/5
k=40
d) 11 minutes

3) a) 2 b) number of junior lifeguards and senior lifeguards must be equal to or more than 12
c) 220
d)9.6=10
2.4=2



For Question 4 apparently its wrong so im not so sure, and 3)d) for graphs apparently has to be 9.6 and 2.4 instead of the rounded values of 10 and 2, I rounded them because it made sense as you typically dont see 9.6 lifeguards like??

[mathisfunlol]

Answers so far:
Core Q1ai 72
              aii 25%
              bi 84%
                ii 209
               c  105
            2a   place of capture
               b  20mm
               c  min 16mm  Q3 36mm
               d  52 is greater than upper fence 50 so it is an outlier
               e  The median wingspan of moths in grassland is 30mm when compared with median wingspan of moths in the
                    forest of 21mm. Wingspan is therefore associated with the location where they are caught.
             3a  egg density = -46.8 + 18.9 x number of male moths
               bi choose two points to input into equation given ie (10,504) and (60,2064) and draw line.
                ii for every additional female moth caught the egg density increases on average by 18.9.
               iii -412.5
               iv 74.3% of variation in egg density can be explained by the variation in number of female moths caught.
            4a   0.009
              b    log(area) = -14.4 + 0.009 x year
              ci  708 hectares
               ii  Extrapolated result
             5a 3375, 71625, 3375, 68250
               bi $3375
                ii 4.5%
               c  5.7%
              6a $203
                b Ao = 428, An+1= 1.015 x An
                c  $454.26
               7a  $1560
                 b  $805.65

Core
1bii is 975

Graphs
2a is 600
2d is 10.98

[giglim12]

In the last geometry question, did anybody else take the path to include every broken line instead of a the straight line directly from A to B?

[drepwns]

These are my answers for the exam correct me if i’m wrong thanks:

1)a)i) 72 ii) 25% b)i) 84% ii) 97.5%
c) 105

2)a)place of capture
b) 20
c) 16,36
d)32+(1.5x12)=50, 52 is an outlier
e) Median is greater for grasslands etc

3)a) -46.8+18.9
b)ii) number of moths increases by 1 results in an increase of egg density by 31.3
iii) -412.5
iv) 74.3% variation

4)a) 0.009 b)-14.4+0.009x
c)i) 416
ii)limited reliability bc of extrapolation

5)a) 3375, 71625-3375=68250
b)i) 3375 ii) 4.5%
c) 5.7%

6)a) $203
b) A•=428, An+1=1.015An
c) $454.26

7)a) $1560
b) $805.65

Matrices::

1)a) 159 b)Rolls sold in week 1
c)i) 3.8 ii) [ 0 1 1 ]
2)a) 40% b) 0.4, 0.6, 0.2
c) 750
3)a) 320 b) [250, 250, 300, 200]
c) 30% d) 250

Graphs::

1)a) 2 metres b) 8am till 6pm

2)a) 500 metres
b) 200=k x 5
k=200/5
k=40
d) 11 minutes

3) a) 2 b) number of junior lifeguards and senior lifeguards must be equal to or more than 12
c) 220
d)9.6=10
2.4=2



For Question 4 apparently its wrong so im not so sure, and 3)d) for graphs apparently has to be 9.6 and 2.4 instead of the rounded values of 10 and 2, I rounded them because it made sense as you typically dont see 9.6 lifeguards like??

6c asked for interest paid, not entire amount paid

[jonwil]

Answers so far:
Core Q1ai 72
              aii 25%
              bi 84%
                ii 209
               c  105
            2a   place of capture
               b  20mm
               c  min 16mm  Q3 36mm
               d  52 is greater than upper fence 50 so it is an outlier
               e  The median wingspan of moths in grassland is 30mm when compared with median wingspan of moths in the
                    forest of 21mm. Wingspan is therefore associated with the location where they are caught.
             3a  egg density = -46.8 + 18.9 x number of male moths
               bi choose two points to input into equation given ie (10,504) and (60,2064) and draw line.
                ii for every additional female moth caught the egg density increases on average by 18.9.
               iii -412.5
               iv 74.3% of variation in egg density can be explained by the variation in number of female moths caught.
            4a   0.009
              b    log(area) = -14.4 + 0.009 x year
              ci  708 hectares
               ii  Extrapolated result
             5a 3375, 71625, 3375, 68250
               bi $3375
                ii 4.5%
               c  5.7%
              6a $203
                b Ao = 428, An+1= 1.015 x An
                c  $454.26
               7a  $1560
                 b  $805.65

Bro your 0.009 is wrong
3 Sig figs is 0.00854 I think or 0.00853
Everything else tho is right!
Oh an that 30% for matrices the hard one is 25%