VCAA 2008 Exam 1 Q's

[gold104]

Hey guys. Just a few q's in regards to a couple of the questions in 2008 vcaa MC exam.
(Link to paper if you dont have one- http://www.vcaa.vic.edu.au/vce/studies/mathematics/further/pastexams/2007/2007furmath1.pdf)

`Core Q5. Looking at the results it seemed to be generally well answered but i cant seem to get the right answer. (I keep coming up with B). If someone could please take the time to explain why the answers C it would be greatly appreciated!

`I also dotn understand how to obtain the answers for-
  - Number Patterns (q8)
  - Graphs and Relations (q8)
If anyone knows how and could find the time to explain id be over the moon.

Cheers!

[samanthaw]

core question 5, you just put it into your calculator. I use the Ti-89 so i put like 0,0,0,1,1,2,2,2,2,3,3,4,4,5 into list1 and then used 1-var stat and i got C .__. also you need to use Sx, not that funny symbol x

for graphs and relations question 8, you just need to sub in all the points to see when the inequalities are true.. and then pick the point has all the 'true' inequalities

hope that helps (:

[gold104]

Thankyou! My stupidity of not being able to answer q4 is reflected in me posting the 2007 exam... haha.
Many thanks, for both explanations!

.. if you dont mind explaining - how would one approach question 9 of g&r of that same exam? this module is causing me headaches.

[milkcarton]

Hi gold104,
               You appear to be having trouble with this question?
               The firstst four terms of a sequence are
12, 18, 30, 54
A difference equation that generates this sequence is
A. tn + 1 = tn + 6        t1 = 12
B. tn + 1 = 1.5tn         t1 = 12
C. tn + 1 = 0.5tn + 12           t1 = 12
D. tn + 1 = 2tn - 6          t1 = 12
E. tn + 2 = tn+1 + tn             t1 = 12, t2 = 18

It's a method of substitution really, let's try A.

A) tn+1= tn+6
    t2 = 12+6 , t2= 18. Correct! BUT!
    t3 = 18+6, 24 = 30? Wrong!

B) tn + 1 = 1.5tn         t1 = 12
    t2 = 1.5x12
    t2= 18 Correct! BUT!
    t3 = 1.5 x 18 =   45. 3rd term is 30 though! WRONG!

C) tn+1 = 0.5tn + 12
    t2 = 0.5x12 +12 = 18! Correct! BUT!
    t3= 0.5x18 + 12 = 21.  21 = 30? WRONG!

D) tn+ 1 = 2tn - 6. t1= 12
    t2 = 2x12 - 6 = 18! Correct!
    t3= 2x18 - 6 = 30! Correct!
    t4 = 2x30 - 6 = 54 Correct!
     D!

Hope that helped!

[gold104]

Hi gold104,
               You appear to be having trouble with this question?
               The firstst four terms of a sequence are
12, 18, 30, 54
A difference equation that generates this sequence is
A. tn + 1 = tn + 6        t1 = 12
B. tn + 1 = 1.5tn         t1 = 12
C. tn + 1 = 0.5tn + 12           t1 = 12
D. tn + 1 = 2tn - 6          t1 = 12
E. tn + 2 = tn+1 + tn             t1 = 12, t2 = 18

It's a method of substitution really, let's try A.

A) tn+1= tn+6
    t2 = 12+6 , t2= 18. Correct! BUT!
    t3 = 18+6, 24 = 30? Wrong!

B) tn + 1 = 1.5tn         t1 = 12
    t2 = 1.5x12
    t2= 18 Correct! BUT!
    t3 = 1.5 x 18 =   45. 3rd term is 30 though! WRONG!

C) tn+1 = 0.5tn + 12
    t2 = 0.5x12 +12 = 18! Correct! BUT!
    t3= 0.5x18 + 12 = 21.  21 = 30? WRONG!

D) tn+ 1 = 2tn - 6. t1= 12
    t2 = 2x12 - 6 = 18! Correct!
    t3= 2x18 - 6 = 30! Correct!
    t4 = 2x30 - 6 = 54 Correct!
     D!

Hope that helped!

Hey, thanks for the explanation MC but thats the 07 paper which i accidently posted instead of the 2008 >.< So sorry!
Im sorry for wasting your time! .. if you arent too busy heres the one i meant to post. http://www.vcaa.vic.edu.au/vcaa/vce/studies/mathematics/further/pastexams/2008/2008furmath1-w.pdf

[samanthaw]

Thankyou! My stupidity of not being able to answer q4 is reflected in me posting the 2007 exam... haha.
Many thanks, for both explanations!

.. if you dont mind explaining - how would one approach question 9 of g&r of that same exam? this module is causing me headaches.

for question 9, we give M rough coordinates, so i said it looks about (20,50) .. we can also see that (0,60) and (40,0) are also within the feasible region

so then we just go along and sub in the points, and chose the objective function that gives a maximum for point (20,50) and not for the other 2 points

hope that makes sense (: