AQA A2 Mathematics MPC4 Core 4 - 9th June 2015 [Discussion & unofficial markscheme]

Can someone explain this to me without the use of a CAST diagram?
(My college never taught them)

Quick question! Does 2p^t = q^t equal

2 ln p^t = ln q^t

I'm just unsure what to do with the 2!

Thanks

Quick question! Does 2p^t = q^t equal

2 ln p^t = ln q^t

I'm just unsure what to do with the 2!

Thanks

i dont understand.. in the jan 2011 paper, Q1, we had to find R, but then didnt use it in the next part?? S

Could someone explain how to do part c


Posted from TSR Mobile

Hello again. You don't know CAST (I know it as SACT, because it seems more logical to remember it that way)? Well, you should probably learn it !.

QUICK LESSON ON CAST/SACT:
Draw a big +, label the quadrants clockwise from the top-left in the order S-A-C-T. Each quadrant represents 90 degrees starting from the right - and going in an anti-clockwise direction. The letters represent what graph is positive in this range of degrees (i.e. S = sin, A = all, C = cos and T = tan).

Therefore, the reason you know tan is negative when the angle is obtuse is that an obtuse angle is from 90-180 and only sin is positive in that quadrant.

WITHOUT CAST/SACT:
Consider the graph of tanx. If an angle is obtuse then it must be somewhere on the portion of the graph for 90 degrees <= x < 180 degrees. From a tan graph you know that this region is from 0 <= tanx <= -1 (where y = tanx) and therefore tanx must be negative for an obtuse angle .

NOTE: I am extremely tired by this point and becoming somewhat delirious.

Hello again. You don't know CAST (I know it as SACT, because it seems more logical to remember it that way)? Well, you should probably learn it !.

QUICK LESSON ON CAST/SACT:
Draw a big +, label the quadrants clockwise from the top-left in the order S-A-C-T. Each quadrant represents 90 degrees starting from the right - and going in an anti-clockwise direction. The letters represent what graph is positive in this range of degrees (i.e. S = sin, A = all, C = cos and T = tan).

Therefore, the reason you know tan is negative when the angle is obtuse is that an obtuse angle is from 90-180 and only sin is positive in that quadrant.

WITHOUT CAST/SACT:
Consider the graph of tanx. If an angle is obtuse then it must be somewhere on the portion of the graph for 90 degrees <= x < 180 degrees. From a tan graph you know that this region is from 0 <= tanx <= -1 (where y = tanx) and therefore tanx must be negative for an obtuse angle .

NOTE: I am extremely tired by this point and becoming somewhat delirious.

A diagram would be very useful, thank you!

I have no idea how to cast
I just remember an algorithm

Excellent response! Thank you So if they said cos(x) is obtuse, find sin(x), sin(x) would be positive and that would be almost a "trick question" by mentioning obtuse, as that only matters when working out cos(x) and tan(x)?

Could someone explain how to do part c


Posted from TSR Mobile

You have to ln both sides and then separate the LHS into ln2 + tlnp using the log rule that lnab = lna + lnb.

Also, it should be 2p^(t-10) .

How to you find the Cartesian equation in this form?
I got to the point where y=square root 36(1-cos^2thetacos^2theta)



Posted from TSR Mobile

Lmao fk :| you have good memory! I didn't mention t-10 just for simplicity but thanks!!

That not quite correct, no; cosx wouldn't be obtuse, the angle would. If it were a "trick question" in that form they would tell you that for angle x, cosx is negative which would indicate the angle is obtuse .