4U Maths Question Thread

[RuiAce]

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what did i do wrong for part d)
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Nothing. Your answer is the exact same as what WolframAlpha said.

[amandali]

Nothing. Your answer is the exact same as what WolframAlpha said.

the ans is this  but it seems correct too

[RuiAce]

Edit: Slight breakdown

[Spencerr]

Hey there!

How can I prove inequalities with composite functions
e.g. How do i prove this: sin(x) - x + (x^2) / 2 > 0

[RuiAce]

Hey there!

How can I prove inequalities with composite functions
e.g. How do i prove this: sin(x) - x + (x^2) / 2 > 0

This proof uses a tiny bit of intuition, which is mostly trained at the university level. It also really tests if you know that a monotonic function satisfies the horizontal line test: it is one-to-one. It's perfectly understandable to a 4U student however calls on a bit above their skills required.




Let me know if something doesn't make sense here.

[katherine123]

Can i have a quick rundown of the conical pendulum?

Im not sure where normal (reaction force) comes in?
is the upward force(opposite mg) always (N+Tcosα) for ques like 4

[RuiAce]

Can i have a quick rundown of the conical pendulum?

Im not sure where normal (reaction force) comes in?
is the upward force(opposite mg) always (N+Tcosα) for ques like 4

For these questions you need to analyse where the forces actually are.

Note that a normal reaction only exists if the particle is touching a surface. If the particle is suspended in the air then this force is non-existent.

The normal reaction force is always perpendicular to the edge of the surface.

Always draw a vector diagram. Going by memory can lead to massive consequences.
However as you can see, if you resolved the vectors correctly for THIS question, you do have N + T cos 60^o = mg

Does this vector diagram make sense to you? If yes, then to do the question just correctly substitute your values. (Note that r = sqrt(3)/2 from trigonometry)

Also, for Q7, period is related to angular velocity by the relationship Period = 2π/ω

Q7 is not a conical pendulum question. It's just your ordinary (however really weird) circular motion question.

[willy-boy]

Was wondering if anyone had a set of all the proofs we need to know to replicate? I'm fine with most eqns, but when we get those fundamentals questions, you really just have to know... ta

[RuiAce]

Was wondering if anyone had a set of all the proofs we need to know to replicate? I'm fine with most eqns, but when we get those fundamentals questions, you really just have to know... ta

Most of the time if you know your actual content you will be able to make up the proofs on the spot without roting them. However from memory here are some important ones

- Induction proof for de Moivre's Theorem
- Centripetal acceleration for circular motion (examined in 2003 or 2004)
- 1+w+w²+...+w^n-1 = 0 for roots of unity
- PS+PS' = 2a for an ellipse (and as for hyperbola)
- Multiple root theorem corollary: alpha is a root of multiplicity k for P(x) => it is a root of multiplicity k-1 for P'(x)

[willy-boy]

Bless your cotton socks. I don't mind the ol' De Moivre//Mechanics, but that is a great list. Thank you kindly

[jakesilove]

Bless your cotton socks. Thank you kindly

Love how polite these forums are

[jamonwindeyer]

Love how polite these forums are

Indubitably 

[Spencerr]

Hey Rui, I have two questions

For reduction integrals, how do you know which one to put as u and which one to put as dv?Is there any general rule to choose? And also when the question usually asks e.g. Show I (n+1) = n/n+1 I(n) when would you recommend subbing in LHS or RHS or is it up to individual intuition.

[RuiAce]

Hey Rui, I have two questions

For reduction integrals, how do you know which one to put as u and which one to put as dv?Is there any general rule to choose? And also when the question usually asks e.g. Show I (n+1) = n/n+1 I(n) when would you recommend subbing in LHS or RHS or is it up to individual intuition.

Q1: Even with reduction formulae, you usually follow the rule of LIATE with integration by parts (assuming that IBP is necessary).

With I_n = sinⁿ(x), tanⁿ(x) and secⁿ(x) you just need to know how to do them though.

Q2: I_n+1 generally requires a bit more intuition. If I was given it out of the blue I would start on I_n+1, but if halfway through my working out, or by looking ahead I see something really dodgy, I will turn back and start using I_n.

The intuition method is that when you use I_n, you get something like x^n-1 * x² which becomes xⁿ⁺¹

Edit: as an extra rule of thumb, if you have nothing to integrate with LIATE just integrate the 1 into x like you have to for ln(x)

[katherine123]

why is the vertical component Ncosx=mg instead of N+Tcosx=mg