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

Paradoxica · Feb 28, 2016

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

InteGrand said:
I know. It's just then we shouldn't say it's the value of the derivative there, since the derivative would technically be undefined there.

In that case, just say the angle of the tangent wrt the x-axis.

InteGrand · Feb 28, 2016

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

Paradoxica said:
In that case, just say the angle of the tangent wrt the x-axis.

What do you mean? We can't mention the 'tangent' in our definition of 'tangent', since that'd be a bit of a circular definition.

Paradoxica · Feb 28, 2016

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

InteGrand said:
What do you mean? We can't mention the 'tangent' in our definition of 'tangent', since that'd be a bit of a circular definition.

I was referring to the gradient of the vertical tangent.

davidgoes4wce · Feb 28, 2016

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

Circle Geometry, explain why in part (c) the triangle is a right angled triangle? (from Cambridge EX 4A Q15 (c))

InteGrand · Feb 28, 2016

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

davidgoes4wce said:
Circle Geometry, explain why in part (c) the triangle is a right angled triangle? (from Cambridge EX 4A Q15 (c))

This is due to the HSC Circle Geometry theorem "line from centre of circle to midpoint of chord is perpendicular to chord". This can be easily proved by proving that those triangles are congruent (use SSS, due to equal radii, common sides, and bisection assumption), corresponding angles in congruent triangles are equal, and then adjacent angles in a straight line are supplementary.

drsabz101 · Feb 29, 2016

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

Is chapter 7H rates of change worth doing? Is it in the hsc

davidgoes4wce · Feb 29, 2016

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

drsabz101 said:
Is chapter 7H rates of change worth doing? Is it in the hsc

Personally, think its worth doing. I have seen related rates questions in past years papers.

axwe7 · Feb 29, 2016

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

But it is Yr12 topic.

InteGrand · Feb 29, 2016

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

axwe7 said:
11B Q8

What is the question?

drsabz101 · Mar 1, 2016

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

I suck at rates and need help with this q.8 ex 7g

InteGrand · Mar 1, 2016

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

drsabz101 said:
I suck at rates and need help with this q.8 ex 7g

What is the question?

drsabz101 · Mar 1, 2016

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

AfroNerd · Mar 1, 2016

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

Use mathematical induction to prove that for all positive integers n:

a)

a)

davidgoes4wce · Mar 1, 2016

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

drsabz101 said:
I suck at rates and need help with this q.8 ex 7g

EXERCISE 7G Q8.

$8 (a)$
$\frac{dV}{dt}=5000 cm^{3} / min, \ h=60 \ cm$

$\frac{dV}{dt}=2000 \ h \ \frac{dh}{dt}$

$5000=2000 \times 60 \times \frac{dh}{dt}$

$\therefore \frac{dh}{dt}=\frac{1}{24} \frac{cm}{min}$

$\frac{dA}{dt}=2000 \times \frac{dh}{dt}$

$\frac{dA}{dt}=2000 \times \frac{1}{24}$

$=\frac{250}{3} \frac{cm^{2}}{min}$

$\therefore $ The Surface area is increasing at $ \frac{250}{3} \frac{cm^{2}}{min} $ and the height is increasing at $ \frac{1}{24} \frac{cm}{min}$

$Part \ 8 \(b)$

$h=40 cm , \frac{dh}{dt}=0.1 \frac{cm}{min}$

$V=1000h^2$

$\frac{dV}{dt}=2000 \ h \frac{dh}{dt}$

$= 2000 (40) \times 0.1$

$=8000 \frac{cm^3}{min} = 8 \frac{L}{min}$

$\frac{dA}{dt}=2000 \frac{dh}{dt}$

$=2000 \times 0.10= 200 \frac{cm^{2}}{min}$

$\therefore $ The volume increases at a rate of 8 $ \frac{L}{min} $ and the rate at which the Area increases is 200 $ \frac{cm^2}{min}$

davidgoes4wce · Mar 1, 2016

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

AfroNerd said:
Use mathematical induction to prove that for all positive integers n:

a) View attachment 32967

a) View attachment 32968

My way of doing Induction for Exercise 6N Q1 (i)

drsabz101 · Mar 1, 2016

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

What are the steps involved in solving this (using the chain rule)

davidgoes4wce · Mar 2, 2016

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

AfroNerd said:
Use mathematical induction to prove that for all positive integers n:

a) View attachment 32967

a) View attachment 32968

$I'm not sure how to go about the 2nd part to of this guys question.$

$1+2^1+2^2+2^3+....+2^n=2^{n+1}-1$

$$ I tried to substitute a positive integer such as 1 on the LHS and RHS but they are not equal.$

$LHS = 2^1= 2 . RHS = 2^{2}-1=3 . $ Is this an example where Induction fails? $$

InteGrand · Mar 2, 2016

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

davidgoes4wce said:
$I'm not sure how to go about the 2nd part to of this guys question.$

$1+2+2^1+2^2+2^3+....+2^n=2^{n+1}-1$

$$ I tried to substitute a positive integer such as 1 on the LHS and RHS but they are not equal.$

$LHS = 2^1= 2 . RHS = 2^{2}-1=3 . $ Is this an example where Induction fails? $$

$\noindent For $n=1$, the LHS should be $1+2$, since the general expression of the LHS starts with a 1 (as it is $1+2+2^2 + \cdots + 2^n$).$

davidgoes4wce · Mar 2, 2016

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

InteGrand said:
$\noindent For $n=1$, the LHS should be $1+2$, since the general expression of the LHS starts with a 1 (as it is $1+2+2^2 + \cdots + 2^n$).$

$What happens if we wanted to use the integer of say n=2?$

InteGrand · Mar 2, 2016

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

davidgoes4wce said:
$What happens if we wanted to use the integer of say n=2?$

$\noindent The LHS would be $1+2+2^2$. The RHS would be $2^3 -1$.$

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