Mathematics Question Thread

[liya1234]

Oh okay that makes sense thank you so much! Just a few more things I wanted to clarify - so if I was given a graph on acceleration, could I find velocity by finding the area under the graph then as well? Also I understand that from a displacement graph, velocity is given by the slope so I would find the gradient. But for acceleration, which is given by concavity, how exactly would I find the value for it?

[RuiAce]

Oh okay that makes sense thank you so much! Just a few more things I wanted to clarify - so if I was given a graph on acceleration, could I find velocity by finding the area under the graph then as well? Also I understand that from a displacement graph, velocity is given by the slope so I would find the gradient. But for acceleration, which is given by concavity, how exactly would I find the value for it?

Yes to the first question.

You wouldn't be able to find the actual value. You can only find the sign of the acceleration.

[bimberfairy]

Hi! I was doing a paper and this question suddenly popped in my head. I'm only up to 2012 so far and haven't checked the more recent ones, but do the questions go from easy to hard ?? Or are all the questions jumbled up in the exam.

[RuiAce]

Hi! I was doing a paper and this question suddenly popped in my head. I'm only up to 2012 so far and haven't checked the more recent ones, but do the questions go from easy to hard ?? Or are all the questions jumbled up in the exam.

Yes.

Math papers are specifically designed so that the difficulty goes in ascending order (with the exception of the multiple choice).

[bimberfairy]

Yes.

Math papers are specifically designed so that the difficulty goes in ascending order (with the exception of the multiple choice).

Thank you !! I'll most likely use my reading time to flip to those first haha

[wulverine]

For questions asking to draw the derivative of a graph f(x), how would you approach this? Is it stationary points of f(x) drawn as x-intercepts of f'(x) and inflexion points of f(x) drawn as max/min points of f'(x) and whatever is under the curve as a negative slope vice versa for above curve?

And if given the graph of f'(x), how do you draw f(x)?

[pokemonlv10]

Hello, would like to know how to solve this type of equation?

[RuiAce]

Hello, would like to know how to solve this type of equation?

I'm not lying when I say this.

You need to sketch a graph, drawn to scale. Because there IS no algebraic method of solving that equation.

[pokemonlv10]

And these two not sure about, i subbed in a, but didn't get any of the mc. Also not sure about the last question.

[RuiAce]

For questions asking to draw the derivative of a graph f(x), how would you approach this? Is it stationary points of f(x) drawn as x-intercepts of f'(x) and inflexion points of f(x) drawn as max/min points of f'(x) and whatever is under the curve as a negative slope vice versa for above curve?

And if given the graph of f'(x), how do you draw f(x)?

So yes, a S.P. on y=f(x) corresponds to an x-intercept on y=f'(x).

The same can be deduced from a similar analysis for inflexion points as you stated.

[RuiAce]

And these two not sure about, i subbed in a, but didn't get any of the mc. Also not sure about the last question.

Note: This question could've been done differently if you chose to raise everything to the power of 3/2, before taking logs of both sides.

[RuiAce]

And these two not sure about, i subbed in a, but didn't get any of the mc. Also not sure about the last question.

\[ \text{The common trick to these questions is the identity }\boxed{e^{\ln a} = a}\text{ for all }a > 0. \]
\begin{align*}\int_3^{10}3^x\,dx &= \int_3^{10} e^{\ln (3^x)}dx\\ &= \int_3^{10} e^{x\ln 3} \tag{log law}\\ &= \left[\frac{e^{x\ln 3}}{\ln 3}\right]_3^{10} \tag{ln 3 is a constant}\\ &= \left[\frac{3^x}{\ln 3}\right]_3^{10}\tag{reverse engineering some steps}\\ &= \frac{3^{10} - 3^3}{\ln 3}\end{align*}

[sidzeman]

For question 16 part i does my answer (1/tantheta) satisfy the question. The solutions said there are many forms x could take i just wanted to make sure mine was correct. Note: I used to proportional division theorem of a triangle, I just didnt write it out (hence why AD also equals x)

[pokemonlv10]

Hello, how would i factorise this completely: x^2 -9y^2 -x - 3y. Apparently completing the square would lose marks here

[RuiAce]

For question 16 part i does my answer (1/tantheta) satisfy the question. The solutions said there are many forms x could take i just wanted to make sure mine was correct. Note: I used to proportional division theorem of a triangle, I just didnt write it out (hence why AD also equals x)

I'm not sure how you got that answer. You assumed that C is the midpoint of AB and D is the midpoint of AE, but I don't see anything that permits this.