Mathematics Question Thread

[hansolo9]

Hi
Can someone help with these 4 trial questions?
TIA

[RuiAce]

Hi
Can someone help with these 4 trial questions?
TIA

I don't know what's confusing about the first question and all I'd be doing is regurgitating the answer.

[RuiAce]

Hi
Can someone help with these 4 trial questions?
TIA

__________________________

[katnisschung]

Bonjour!
needing help with this question
its ii) (also its from 2010 paper q 5)
I don't understand how I show that the graph has a minimum value.
should I find the stationary points?
(how do i do that for graphs in general? generally only know how to do it with a parabola and differentiate)
helppp

[Shadowxo]

Bonjour!
needing help with this question
its ii) (also its from 2010 paper q 5)
I don't understand how I show that the graph has a minimum value.
should I find the stationary points?
(how do i do that for graphs in general? generally only know how to do it with a parabola and differentiate)
helppp

First you differentiate, then you find the stationary point/s. To find out whether it's a max/min, find whether the second derivative is positive/neg for that value and that should show it's a min (*in VCE we use different methods usually). If it's a minimum, the gradient should be increasing at that point (going from neg to 0 to positive) meaning the rate of change of gradient is positive at that value ie second derivative is positive

[RuiAce]

Bonjour!
needing help with this question
its ii) (also its from 2010 paper q 5)
I don't understand how I show that the graph has a minimum value.
should I find the stationary points?
(how do i do that for graphs in general? generally only know how to do it with a parabola and differentiate)
helppp

As far as 2U goes, the "existence" of the minimum value is verified so long as you may find a local minimum.

That being said, this type of question is very standard and you have seen many instances of it in the geometrical applications of differentiation topic.

[Mymy409]

Hi, I've got a question that's confusing me quite a bit.

A particle is moving along the x-axis. The displacement of the particle at time t seconds
is x metres.
At a certain time, v = -3 m/s and a = 2m/s^2.                                     
Which statement describes the motion of the particle at that time?
(A)    The particle is moving to the right with increasing speed.
(B)    The particle is moving to the left with increasing speed.
(C)    The particle is moving to the right with decreasing speed.
(D)    The particle is moving to the left with decreasing speed.

The answer is D.

[Shadowxo]

Hi, I've got a question that's confusing me quite a bit.

A particle is moving along the x-axis. The displacement of the particle at time t seconds
is x metres.
At a certain time, v = -3 m/s and a = 2m/s^2.                                     
Which statement describes the motion of the particle at that time?
(A)    The particle is moving to the right with increasing speed.
(B)    The particle is moving to the left with increasing speed.
(C)    The particle is moving to the right with decreasing speed.
(D)    The particle is moving to the left with decreasing speed.

The answer is D.

The velocity is negative so it's moving to the left
The acceleration is positive so the 'velocity' is increasing but it's just becoming less negative. The 'speed' however is decreasing (as the initial speed is 3 m/s, speed doesn't have a direction). So it's slowing down (speed decreasing). It's just a terminology thing, does this help?

[1937jk]

Hey! Just need some help in understanding how to go about this question, like I think I get how to get the answer but I don't quite think I get the concept behind it,
A coin is tossed n times. Find the probability in terms of n of tossing,
a) all heads
b) no tails
c) at least one tails

Thanks!

[RuiAce]

Hey! Just need some help in understanding how to go about this question, like I think I get how to get the answer but I don't quite think I get the concept behind it,
A coin is tossed n times. Find the probability in terms of n of tossing,
a) all heads
b) no tails
c) at least one tails

Thanks!

Non-mathematical, only explanation:

Of course, the probability of tossing a head in the first turn does not impact the probability of tossing a head on the second turn, and so on. i.e. all the tosses are independent.

a) The probability of tossing a head on the first turn is 1/2. The probability of tossing a head on the second turn is still 1/2. And we keep going, and the probability of tossing a head on the n-th turn is still 1/2. So we just multiply them together.

b) If exactly zero of your tosses are tails, then all of them are heads. This is the same as above.

c) At least one tail implies exactly one + exactly two + exactly three + so on and that takes work. So we consider the complement, which is the probability of tossing no tails. This is essentially the opposite event, which you should recognise fairly easily.
The probability of no tails from part b) is (1/2)^n, so the probability of at least one tail is 1 minus (1/2)^n

[winstondarmawan]

Hello, would appreciate help with the following, TIA.
Mainly not sure on how the n from n-sided polygon gets incorporated into the angle.
https://scontent-syd2-1.xx.fbcdn.net/v/t34.0-12/20427880_1282466078548868_1386597183_n.png?oh=a54f49ae1c9642fa30bdf54ebbf9cd6d&oe=597C71D1

[jaskirat]

Need help with this question

[Natasha.97]

Need help with this question

Hi!

I've attached the solution below:



Hope this helps!

Note: Not 100% sure that this is correct, maybe someone below could check

[jaskirat]

Thankyou so much!

Hi!

I've attached the solution below:

(Image removed from quote.)

Hope this helps!

Note: Not 100% sure that this is correct, maybe someone below could check

[Shadowxo]

Hi!

I've attached the solution below:

(Image removed from quote.)

Hope this helps!

Note: Not 100% sure that this is correct, maybe someone below could check

Looks good