VCE Specialist 3/4 Question Thread!

[jono88]

Those questions are quite common.
The main point is to use cos(nt) = Re(cis(nt))=Re((cis(t))^n) and likewise for sines
Again, make sure the expansion is correct...don't forget that i^3 = -i, for instance.

Have you tried expanding it using your CAS and getting the right answer?

[Stevensmay]

Using a TI-nspire cx and entering


Which is the expansion I believe given in the answers.

[ahat]

What's the best method for doing these type of questions, by hand or CAS?

[lzxnl]

If you were to choose the answer by hand:
Firstly, the gradient is negative. A, C, E only viable choices.
Gradient independent of t. Eliminate A. Decrease V, decrease magnitude of gradient.
C


I can't do maths anymore -.-

[availn]

If you were to choose the answer by hand:
Firstly, the gradient is negative. A, C, E only viable choices.
Gradient independent of t. Eliminate A. Decrease V, decrease gradient. Answer is E.

I thought it would be C? When V is 0, gradient is 0.

[Bad Student]

From MAV exam 2 2006 Q2

A stone is projected upwards from the top of a 50m building at an angle of to the horizontal with a velocity of
m/s at time t, where t is greater than or equal to 0.

When I integrate this equation to find the displacement, do I integrate with respect to t or ?

[ahat]

Answer is C, did choose E first though

[Stevensmay]

Theta is a constant but t is not, so you would integrate with respect to t.

[ahat]

From MAV exam 2 2006 Q2

A stone is projected upwards from the top of a 50m building at an angle of to the horizontal with a velocity of
m/s at time t, where t is greater than or equal to 0.

When I integrate this equation to find the displacement, do I integrate with respect to t or ?

so you would integrate with respect to t (because vector is in terms of t)

[lzxnl]

I thought it would be C? When V is 0, gradient is 0.

Yep, typo there. Fixed.

[Bad Student]

Yep, typo there. Fixed.

Sure...

[lzxnl]

Sure...

Believe whatever you want.

[ahat]

Gradient independent of t.

How do you know this?

Ahhhh, I went back and did it on CAS, don't know how I got it wrong, do you guys have the "Plot differential equation" program on your CAS? Super useful.

Sure...

Calm down there bro, Nilu is a flipping beast at maths ♥

[lzxnl]

For the gradient, scan across the page. The gradient should appear to be the same regardless of what t value you are, if you move your eyes horizontally.

[kinslayer]

Suggestion for anyone worried about that complex expansion on the last page: Pascal's triangle.

Also if the sines and cosines make it difficult to keep track of everything, try expanding then let and . In fact, is something you should probably be able to recite from memory.

For powers of , remember that multiplication by is just rotation by 90 degrees anticlockwise on an Argand diagram. That gives you the first four powers immediately and it also shows that the first four powers are the only ones you need to know.