Cambridge Prelim MX1 Textbook Marathon/Q&A (1 Viewer)

[leehuan]

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Why is xcos(alpha)=xcos(2alpha)=xcos(3alpha) and AP+PQ+QR=AB?

 

[davidgoes4wce]

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

 

[leehuan]

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Oh that makes more sense. Knew I should've produced the sides and tried viewing it differently

 

[appleibeats]

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Not sure how to show cot(3pi/10) = tan(pi/5)

 

[Shuuya]

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Not sure how to show cot(3pi/10) = tan(pi/5)

Recall that cot(theta) = tan(pi/2 - theta)

LHS = cot(3pi/10)
= tan(pi/2 - 3pi/10)
= tan(pi/5)
= RHS

 

[eyeseeyou]

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Not sure how to show cot(3pi/10) = tan(pi/5)

You change cot into tan and then move everything all over to one side

 

[Nailgun]

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

You change cot into tan and then move everything all over to one side

it's a proof, you can't move everything to one side

 

[Paradoxica]

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

it's a proof, you can't move everything to one side

Actually you can, but that's only for algebraic identities, not numerical ones.

 

[appleibeats]

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

If v^2 = 24 - 6x -3x^2, find the acceleration of the particle at the particles greatest displacement from the origin.

My answer:

Greatest displacement at amplitude where v = 0

When v = 0

( x - 2) (x + 4) = 0

so x = 2 or x = -4

Now acceleration = -3 -3x

when x = -4 ( greatest displacement )

acceleration = 9 m /s^2

But the answers says Max displacement occurs when x = 2 so acceleration is -9m/s^2


Why is it when x = 2 and not x = -4. Isn't the displacement from the origin greatest when x = -4 ??

 

[Nailgun]

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Actually you can, but that's only for algebraic identities, not numerical ones.

what do you mean lel?

 

[InteGrand]

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

If v^2 = 24 - 6x -3x^2, find the acceleration of the particle at the particles greatest displacement from the origin.

My answer:

Greatest displacement at amplitude where v = 0

When v = 0

( x - 2) (x + 4) = 0

so x = 2 or x = -4

Now acceleration = -3 -3x

when x = -4 ( greatest displacement )

acceleration = 9 m /s^2

But the answers says Max displacement occurs when x = 2 so acceleration is -9m/s^2


Why is it when x = 2 and not x = -4. Isn't the displacement from the origin greatest when x = -4 ??

The distance from the origin is greatest at x = -4. The displacement includes the sign, so is greatest at x = +2.

 

[Paradoxica]

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

what do you mean lel?

When your identity is numerical, i.e there are no variables, you should be aiming to prove it without shifting anything.

When your identity has variables, you can shift things around, maybe prove it using calculus.

Or you could be me and do it by inspection.

 

[appleibeats]

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

The distance from the origin is greatest at x = -4. The displacement includes the sign, so is greatest at x = +2.

So displacement can be either positive or negative?
Whereas distance is positive or 0 only.

 

[leehuan]

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

So displacement can be either positive or negative?
Whereas distance is positive or 0 only.

Distance is a scalar (magnitude only) whereas displacement is a vector (magnitude and direction)

Therefore yes

 

[davidgoes4wce]

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

If v^2 = 24 - 6x -3x^2, find the acceleration of the particle at the particles greatest displacement from the origin.

My answer:

Greatest displacement at amplitude where v = 0

When v = 0

( x - 2) (x + 4) = 0

so x = 2 or x = -4

Now acceleration = -3 -3x

when x = -4 ( greatest displacement )

acceleration = 9 m /s^2

But the answers says Max displacement occurs when x = 2 so acceleration is -9m/s^2


Why is it when x = 2 and not x = -4. Isn't the displacement from the origin greatest when x = -4 ??

Do you mind if I ask where you got that question from? Can't seem to find that in the Cambridge text book.

 

[appleibeats]

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

Do you mind if I ask where you got that question from? Can't seem to find that in the Cambridge text book.

It's from the Grammar Trial 2015

 

[leehuan]

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

It's from the Grammar Trial 2015

Uhh

Sorry for nitpicking but can you please leave this thread for the textbook questions

 

[appleibeats]

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

.

 

[appleibeats]

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

 

[si2136]

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread

View attachment 33158

Have you learnt Implicit Differentiation?