VCAA Exam 1 2008

[Hooligan]

Some more of my problems... 

Question 8c.
I did it the way the itute solutions proved it, but it just doesn't look sufficient enough to prove that the shape is a rectangle, 'cause all its proving is that is perpendicular to and hence makes a right angle with it... but how does that prove it is a rectangle? It could be a right angle triangle for all we know, if all we're saying is that one of the sides is a right angle....!

Question 9a.
This is what I did: .... how is my calculation wrong? ... and I don't get when all they do is simply ?

Question 10c.
I am completely confuzzled with this question... I again referred to itute solutions, however, the first line already confuses my poor little brain.... 

[TrueTears]

8c.

To prove something is rectangle you must prove all angles are right angles. To prove it I proved that two adjacent angles are right angles thus it is a rectangle. I wouldn't really do it any other way.

9a.

It is a rectangle and the two areas separated by the curve is equal



Blue area = Pink area

So you can see it's a rectangle with side length 2 and . Half of this is

[TrueTears]

10c

Since is a solution that means is also a solution.



Thus for

We know that

a must be a real number thus

if then

if then

Thus lets see what happens when



But question said b is non zero so

Thus

So 3 solutions are

[Hooligan]

8c.

To prove something is rectangle you must prove all angles are right angles. To prove it I proved that two adjacent angles are right angles thus it is a rectangle. I wouldn't really do it any other way.

I see... because if the question was more than 1 mark, I would have proved that all corners are 90 degrees + opposite sides are the same length....

9a.

It is a rectangle and the two areas separated by the curve is equal

So you can see it's a rectangle with side length 2 and . Half of this is

Oh! I see it now! Thank you!!!
However, with my way, I switched x and y etc... and did the integral I showed, how come that doesn't work also?

EDIT: Just figured out why my way didn't work. haha... this is the correct integral (I looked at the wrong side of the bit of the graph. haha): WHOOT! 

[TrueTears]

8c.

To prove something is rectangle you must prove all angles are right angles. To prove it I proved that two adjacent angles are right angles thus it is a rectangle. I wouldn't really do it any other way.

I see... because if the question was more than 1 mark, I would have proved that all corners are 90 degrees + opposite sides are the same length....

Remember a square is a special case of a rectangle so you don't have to prove opposite sides are same length

[Hooligan]

10c

Since is a solution that means is also a solution.



Thus for

We know that

a must be a real number thus

if then

if then

Thus lets see what happens when



But question said b is non zero so

Thus

So 3 solutions are

I get everything, except for this bit, which I don't entirely understand:
"a must be a real number thus "
why do we replace z with a, and then bracket the modulus, and then power it?

[Hooligan]

8c.

To prove something is rectangle you must prove all angles are right angles. To prove it I proved that two adjacent angles are right angles thus it is a rectangle. I wouldn't really do it any other way.

I see... because if the question was more than 1 mark, I would have proved that all corners are 90 degrees + opposite sides are the same length....

Remember a square is a special case of a rectangle so you don't have to prove opposite sides are same length

Hmmm... right, but if I don't prove opposite sides are the same length (thus, also proving that all sides are not the same), then how do they know it is a rectangle I am proving? 'cause it could be a square, 'cause a square also has 4 angles of 90 degree...

[TrueTears]

8c.

To prove something is rectangle you must prove all angles are right angles. To prove it I proved that two adjacent angles are right angles thus it is a rectangle. I wouldn't really do it any other way.

I see... because if the question was more than 1 mark, I would have proved that all corners are 90 degrees + opposite sides are the same length....

Remember a square is a special case of a rectangle so you don't have to prove opposite sides are same length

Hmmm... right, but if I don't prove opposite sides are the same length (thus, also proving that all sides are not the same), then how do they know it is a rectangle I am proving? 'cause it could be a square, 'cause a square also has 4 angles of 90 degree...

A square is a rectangle

[Hooligan]

8c.

To prove something is rectangle you must prove all angles are right angles. To prove it I proved that two adjacent angles are right angles thus it is a rectangle. I wouldn't really do it any other way.

I see... because if the question was more than 1 mark, I would have proved that all corners are 90 degrees + opposite sides are the same length....

Remember a square is a special case of a rectangle so you don't have to prove opposite sides are same length

Hmmm... right, but if I don't prove opposite sides are the same length (thus, also proving that all sides are not the same), then how do they know it is a rectangle I am proving? 'cause it could be a square, 'cause a square also has 4 angles of 90 degree...

A square is a rectangle

It is? So, a square is a special type of rectangle, not the other way around.... interesting.... so its only when they want me to prove it is a square when I have to prove that all the sides are the same + all angles are 90 degrees (by proving two opposite angles are 90 degrees).

[TrueTears]

z is all the solutions for values which satisfy the equation.

a must be a real number since

Which means

and d is a non zero real number so a must be one too.

You sub it in to work out what a is.

[TrueTears]

8c.

To prove something is rectangle you must prove all angles are right angles. To prove it I proved that two adjacent angles are right angles thus it is a rectangle. I wouldn't really do it any other way.

I see... because if the question was more than 1 mark, I would have proved that all corners are 90 degrees + opposite sides are the same length....

Remember a square is a special case of a rectangle so you don't have to prove opposite sides are same length

Hmmm... right, but if I don't prove opposite sides are the same length (thus, also proving that all sides are not the same), then how do they know it is a rectangle I am proving? 'cause it could be a square, 'cause a square also has 4 angles of 90 degree...

A square is a rectangle

It is? So, a square is a special type of rectangle, not the other way around.... interesting.... so its only when they want me to prove it is a square when I have to prove that all the sides are the same + all angles are 90 degrees (by proving two opposite angles are 90 degrees).

Correct.

Check here for the properties you need to prove in vectors. http://vcenotes.com/forum/index.php/topic,17229.msg176466.html#msg176466

[Hooligan]

8c.

To prove something is rectangle you must prove all angles are right angles. To prove it I proved that two adjacent angles are right angles thus it is a rectangle. I wouldn't really do it any other way.

I see... because if the question was more than 1 mark, I would have proved that all corners are 90 degrees + opposite sides are the same length....

Remember a square is a special case of a rectangle so you don't have to prove opposite sides are same length

Hmmm... right, but if I don't prove opposite sides are the same length (thus, also proving that all sides are not the same), then how do they know it is a rectangle I am proving? 'cause it could be a square, 'cause a square also has 4 angles of 90 degree...

A square is a rectangle

It is? So, a square is a special type of rectangle, not the other way around.... interesting.... so its only when they want me to prove it is a square when I have to prove that all the sides are the same + all angles are 90 degrees (by proving two opposite angles are 90 degrees).

Correct.

Check here for the properties you need to prove in vectors. http://vcenotes.com/forum/index.php/topic,17229.msg176466.html#msg176466

LOL... I printed that off and stuck it on my wall yesterday. haha. Kudos to you TT!!

[Hooligan]

z is all the solutions for values which satisfy the equation.

a must be a real number since

Which means

and d is a non zero real number so a must be one too.

You sub it in to work out what a is.

OHHHH LOL! It just 'clicked'! haha. Thanks TT. I think I owe you half my Spesh study score now. :laugh:

[TrueTears]

hahaha s'all cool!

[thethingexe]

i'm sure if you include, if rectangle is ABCD...

|vector(AC)|=|vector(BD)|

it would also help prove that it is a rectangle...

i think for that question, it's like root(38)