Cambridge Prelim MX1 Textbook Marathon/Q&A (4 Viewers)

appleibeats · Apr 16, 2016

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

leehuan said:
Keep in mind T=2π/n so 8 = 2π/n
n = π/4

For SHM, when they give you these questions you're better off not finding the time but rather just using these equations:
$\ddot{x}=-{n}^{2}x\\{v}^{2}={n}^{2}\left({a}^{2}-{x}^{2}\right)$

And the amplitude is 10

Keep in mind that you do typically have to derive the latter though

Using n = pi/4 and a = 10

and x = 4

accel = -pi^2/4

velocity = +- piroot21/2

Answers says 2pi cm/s , +/- 3pi^2 / 8 cm/s^2

So I think its the x value that is wrong. But If O is the centre of AB ( ie at 10 cm) , then 6 cm from O means the particle has only traveled 4 cm.

Thats my logic.

leehuan · Apr 16, 2016

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

appleibeats said:
Using n = pi/4 and a = 10

and x = 4

accel = -pi^2/4

velocity = +- piroot21/2

Answers says 2pi cm/s , +/- 3pi^2 / 8 cm/s^2

So I think its the x value that is wrong. But If O is the centre of AB ( ie at 10 cm) , then 6 cm from O means the particle has only traveled 4 cm.

Thats my logic.

O is the centre of motion.

So O is when x=0

So we plug in x=6

appleibeats · Apr 16, 2016

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

leehuan said:
O is the centre of motion.

So O is when x=0

So we plug in x=6

It worked out.

Just unsure why there are two answers for the acceleration

I just got the negative answer ( -3pi^2/8 ). Why is there also a positive answer?

Also why is there only one answer for velocity (2pi). If you sub into v^2 , shouldn't you get two answer? ( +/- 2pi)

leehuan · Apr 16, 2016

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

Oh. For the acceleration I can say it's because x can also be negative 6. When x=-6 it's still 6 units away from the origin.

As for the next part, they said speed not velocity.

Blitz_N7 · Apr 17, 2016

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

Not sure on how to work this one out

Paradoxica · Apr 17, 2016

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

Blitz_N7 said:
Not sure on how to work this one out

Divide both sides of the question by n. You should be able to handle it from there.

InteGrand · Apr 17, 2016

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

Blitz_N7 said:
Not sure on how to work this one out

$\noindent The identity is equivalent to $\sum _{k=1}^{n-2} \binom{n-1}{k}=2^{n-1}-2$ (just dividing the given identity to-prove through by $n$). Now, from this,$

$\begin{align*} LHS &= \sum _{k=0}^{n-1}\binom{n-1}{k}- \binom{n-1}{0}- \binom{n-1}{n-1} \\ &= 2^{n-1} - 2 \\ &= RHS. \end{align*}$

$\noindent The second line came from the well-known result $\sum _{k=0}^{N}\binom{N}{k}=2^{N}$, which holds for any non-negative integer $N$, and can be proved by substituting $x=1$ into the binomial expansion of $\left(1+x\right)^{N}$.$

Blitz_N7 · Apr 17, 2016

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

Thank you!

pasq · Apr 17, 2016

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

Shuuya · Apr 17, 2016

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

pasq said:
View attachment 33118

EDIT: angle QPO should be angle QPS

appleibeats · Apr 19, 2016

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

Screen Shot 2016-04-19 at 8.35.43 pm.png

Unsure about part b) iii) Answer says 112 degrees

I get the answer 90 degrees.

davidgoes4wce · Apr 20, 2016

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

appleibeats said:
View attachment 33129

Unsure about part b) iii) Answer says 112 degrees

I get the answer 90 degrees.

This is my solution:

$$ With part (iii), do the inverse tan to find the angle $ tan \theta = \frac{\dot{y}}{\dot{x}}$

appleibeats · Apr 20, 2016

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

I understand your mathematics, I just have a tough time trying to visualise the angle being formed.

davidgoes4wce · Apr 20, 2016

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

appleibeats said:
I understand your mathematics, I just have a tough time trying to visualise the angle being formed.

$I look at the vertical velocity components of both particles and notice that $ \dot{y} $ is a negative value. This is a giveaway that both particles collide on their paths when going downwards (same direction as acceleration due to gravity which I treated as negative.) Here is my diagram below:$

pasq · Apr 21, 2016

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

I have a difficult questions I would like help with:

1. AP, PQ and QR are three equal intervals inclined at angles
α, 2α and 3α respectively to interval AB. Show that:
tan BAR =
sin α + sin2α + sin3α / cos α + cos2α + cos3α

X42xows.png

pasq · Apr 21, 2016

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

thanks!

leehuan · Apr 21, 2016

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

pasq said:
I have a difficult questions I would like help with:

1. AP, PQ and QR are three equal intervals inclined at angles
α, 2α and 3α respectively to interval AB. Show that:
tan BAR =
sin α + sin2α + sin3α / cos α + cos2α + cos3α

X42xows.png

Confusing. No brackets or diagram.

Textbook reference? That'll suffice

pasq · Apr 21, 2016

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

davidgoes4wce · Apr 21, 2016

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

pasq said:
I have a difficult questions I would like help with:

1. AP, PQ and QR are three equal intervals inclined at angles
α, 2α and 3α respectively to interval AB. Show that:
tan BAR =
sin α + sin2α + sin3α / cos α + cos2α + cos3α

X42xows.png

$Key to this question is to let AP=PQ=QR=x$

InteGrand · Apr 22, 2016

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

We can even just let them equal 1 instead of x (as seen, the x's just cancel. By arbitrariness of units, we can just let them be 1).

Cambridge Prelim MX1 Textbook Marathon/Q&A (4 Viewers)

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