Mathematics Question Thread

[hansolo9]

Hey guys,
Can someone show how to do part B?
My teacher didn't explain the Simpson/Trapezoidal rotation very well and I'm confused.

[RuiAce]

Hey guys,
Can someone show how to do part B?
My teacher didn't explain the Simpson/Trapezoidal rotation very well and I'm confused.

It is all formula work. You can choose to apply Simpson's rule twice separately or use the generalised Simpson's rule. Which one do you want to use?

[katnisschung]

for series application questions how do i know how to round up or round down.
e.g. A scientific researcher was studying the population growth of insects
He knew the population grew at a rate of 1% compounding daily.
The insect population was 1000.
how many insects would be in the colony after 100 days? you may assume the mortality rate is
zero over this period

so they answer i got by applying the compound interest formula was
2704.8138...
so do u just round up as normal for these questions. kinda counter-intuitive 

[Sine]

for series application questions how do i know how to round up or round down.
e.g. A scientific researcher was studying the population growth of insects
He knew the population grew at a rate of 1% compounding daily.
The insect population was 1000.
how many insects would be in the colony after 100 days? you may assume the mortality rate is
zero over this period

so they answer i got by applying the compound interest formula was
2704.8138...
so do u just round up as normal for these questions. kinda counter-intuitive 

for any sort of question involving an organism I always round down and feel that is the correct method to do so. (answering VCAA questions I have found this to be correct). However I am not sure about HSC stuff.

So I would say 2704.81 insects is 2704 since you can't have .81 of an insect

[RuiAce]

for any sort of question involving an organism I always round down and feel that is the correct method to do so. (answering VCAA questions I have found this to be correct). However I am not sure about HSC stuff.

So I would say 2704.81 insects is 2704 since you can't have .81 of an insect

For this particular question yes.

In general, you will need some common sense for all of these questions.

[Sine]

For this particular question yes.

In general, you will need some common sense for all of these questions.

yup definitely a case by case thing

[12070]

I'm baffled. I have expanded to get: ax^2-4ax+4a+bx-2b+c

[jakesilove]

I'm baffled. I have expanded to get: ax^2-4ax+4a+bx-2b+c

You'll get used to questions like this; they're always attacked in exactly the same way.



Now, we factorise out such that we get a coefficient of each power of x.



Finally, we EQUATE the coefficients of each power of x on the 'right hand side' with that of the original function. So, in this case, we get three equations





The first one is already solved, and thus we can use it to solve the second




Subbing in these values into the third equation yields

[vandanac55555]

Hi:)
I was wondering if anyone could please help me with this extension 1 maths q i have attached.
I wanted to integrate the acceleration formula to get the velocity but is there an easy way to expand the formula for acceleration? Or do i use binomial theorem? Not sure:(
Does anyone know ?
Thankyou:)

[Shadowxo]

Hi:)
I was wondering if anyone could please help me with this extension 1 maths q i have attached.
I wanted to integrate the acceleration formula to get the velocity but is there an easy way to expand the formula for acceleration? Or do i use binomial theorem? Not sure:(
Does anyone know ?
Thankyou:)

See the trick here is the x out the front. The derivative of (x²-3) is 2x. If you've learned substitution use that trying u=x²-3.
If you still need help let me know
Edit: Believe the formula you have to use is   a = v * dv/dx

[MisterNeo]

Hi:)
I was wondering if anyone could please help me with this extension 1 maths q i have attached.
I wanted to integrate the acceleration formula to get the velocity but is there an easy way to expand the formula for acceleration? Or do i use binomial theorem? Not sure:(
Does anyone know ?
Thankyou:)

Remember these formulas for derivatives/integrals?


Just sub into the equation.

[RuiAce]

See the trick here is the x out the front. The derivative of (x²-3) is 2x. If you've learned substitution use that trying u=x²-3.
If you still need help let me know
Edit: Believe the formula you have to use is   a = v * dv/dx

Might want to note that v.dv/dx isn't required in 3U. They are allowed to use it but they are only expected to know d/dx v^2/2

Also, in the future, please put Ext 1 questions in the ext 1 section of the forum.

Hi:)
I was wondering if anyone could please help me with this extension 1 maths q i have attached.
I wanted to integrate the acceleration formula to get the velocity but is there an easy way to expand the formula for acceleration? Or do i use binomial theorem? Not sure:(
Does anyone know ?
Thankyou:)

[RuiAce]

Remember these formulas for derivatives/integrals?


Just sub into the equation.

Carefully note that you actually did not use these formulae as you're dealing with a squared term. Those formulae are for linear expressions only, NOT quadratics.

Shadowxo's strategy of integration by substitution should be employed, which is 3U.

But I will remind that this question was 3U posted incorrectly into 2U. 2U deal with accelerations in terms of \(t\), not \(x\)

[katnisschung]

x-intercepts for cubic curves???
eg. 1/3 x^3 - 3x^2 + 11x-9=0
also need to justify my answer?

[RuiAce]

x-intercepts for cubic curves???
eg. 1/3 x^3 - 3x^2 + 11x-9=0
also need to justify my answer?

You are not required to know how to deal with these in 2U.