Mathematics Question Thread

[Deng]

Hey guys i was wondering how to effectively study maths in the sense that i do past hsc papers and review my mistakes but i feel like it isnt necessarily improving my maths skills. Like even doing maths everyday i manage to forget small details and concepts of questions, im not sure how to explain it but an example would be like one of my maths exams i did well in, when i sat the same exam again 2 months later i manage to forget how to do some of the questions despite doing at least 30mins to 2 hours of maths everyday.

Also, when a question asks for maximum velocity e.g attached how would i do part (ii)



Thanks

[jamonwindeyer]

Hey guys i was wondering how to effectively study maths in the sense that i do past hsc papers and review my mistakes but i feel like it isnt necessarily improving my maths skills. Like even doing maths everyday i manage to forget small details and concepts of questions, im not sure how to explain it but an example would be like one of my maths exams i did well in, when i sat the same exam again 2 months later i manage to forget how to do some of the questions despite doing at least 30mins to 2 hours of maths everyday.

Also, when a question asks for maximum velocity e.g attached how would i do part (ii)

Thanks

Hey Deng! To address your question first, the answer is to differentiate! We seek a maxima for the velocity function, so:



Any subsequent values will be irrelevant because they will give the same answer. Test those values in the original function:



Clearly, the second is larger, and you can use typical tests to deduce that there is a maxima at t equal to pi.

Note that you could, in this case, do this conceptually. A cosine function will always range between -1 and 1, and so, a -2cost function will always range between -2 and 2. Pick the case which maximises velocity, and you get the same answer as above:



As for your study dilemma, let me ask you something. When you do those papers and forget concepts, when was the last time you had studied that specific topic, rather than Mathematics in general? Often, if you haven't done something in a while, you'll mess things up. I do it all the time if/when I revisit old math concepts. Hell, not just math, it applies to pretty much everything (writing a bit of code in a coding language you've not used in ages, or driving a manual after a year of driving an auto, for example). Your brain will forget things, are you consistently revising the old concepts?

[jakesilove]

Hey guys i was wondering how to effectively study maths in the sense that i do past hsc papers and review my mistakes but i feel like it isnt necessarily improving my maths skills. Like even doing maths everyday i manage to forget small details and concepts of questions, im not sure how to explain it but an example would be like one of my maths exams i did well in, when i sat the same exam again 2 months later i manage to forget how to do some of the questions despite doing at least 30mins to 2 hours of maths everyday.

Also, when a question asks for maximum velocity e.g attached how would i do part (ii)



Thanks

Hey! I'm on the run so can only quickly answer your Maths question, will get to your study question a bit later (unless someone else jumps in!). I'll just quickly say that your experience with maths is not abnormal, and there are definitely techniques to help you out!

For your question, you just need to recall that



In this case, velocity will be at a MAXIMUM when cos(t) is at its most NEGATIVE (as it is a negative term). Therefore, when cos(t) is -1, velocity will be 3. This is the maximum value!

[Deng]

@Jamon, ah i assumed you had to differentiate since it said maximum however i had never seen a question like this so i was confused on what to do

I havent touched the topics individually since ive been taught them so i guess it does make sense, should probably get down with the basics before doing the HSC papers to be more effective?



@Jake, Thanks, but i suck with inequalities so ill stick with Jamon's way

[olivercutbill]

Specifically iii) please!

This one is a series/probability one, not sure how to get to the answer.

Thanks!

[jamonwindeyer]

@Jamon, ah i assumed you had to differentiate since it said maximum however i had never seen a question like this so i was confused on what to do

I havent touched the topics individually since ive been taught them so i guess it does make sense, should probably get down with the basics before doing the HSC papers to be more effective?

@Jake, Thanks, but i suck with inequalities so ill stick with Jamon's way

That absolutely makes sense then, so yep, perhaps tackle some old chapter reviews before hitting HSC past papers? I always did Paper first, review second if required, but it might work better the other way around for you!!

[jamonwindeyer]

Specifically iii) please!

This one is a series/probability one, not sure how to get to the answer.

Thanks!

Hey! This is a fairly common ace up the sleeve for BOSTES, the same style of question was at the end of my MX1 exam:

First question is fairly easy, remember that there are 36 possible outcomes for throwing two dice, and only one yields a win!



For the second bit, remember that for Pat to have a second turn, Chandra must not roll a double six on her turn, otherwise she would win, AND Pat must not roll a double six on his first turn either. This creates the following:



Now we get technical. For Pat to eventually win the game, we need to consider an infinite number of turns. After all, the game could go on forever, couldn't it? Let's look at the series for just the 1st-3rd turns:



Notice what's inside the brackets? An infinite series! We can find it's sum using the formula:



Note that we are allowed to use this formula because the common ratio is less than 1

Using that formula should get the answer you need!

[RuiAce]

@Jake, Thanks, but i suck with inequalities so ill stick with Jamon's way

Jamon's method is your standard method that you turn to when you're stuck. But something like this is something you should be able to cope with.

Hey! This is a fairly common ace up the sleeve for BOSTES, the same style of question was at the end of my MX1 exam:

First question is fairly easy, remember that there are 36 possible outcomes for throwing two dice, and only one yields a win!



For the second bit, remember that for Pat to have a second turn, Chandra must not roll a double six on her turn, otherwise she would win, AND Pat must not roll a double six on his first turn either. This creates the following:



Now we get technical. For Pat to eventually win the game, we need to consider an infinite number of turns. After all, the game could go on forever, couldn't it? Let's look at the series for just the 1st-3rd turns:



Notice what's inside the brackets? An infinite series! We can find it's sum using the formula:



Note that we are allowed to use this formula because the common ratio is less than 1

Using that formula should get the answer you need!

This looks good (y)

[anotherworld2b]

Hi i was wonering how do I solve these questions?

[jakesilove]

Hi i was wonering how do I solve these questions?

I'll just help you out with the first, one, because once you've done one you can definitely figure out the rest yourself! You need to start with the relevant formula for the type of sequence (ie. geometric or arithmetic). For arithmetic sequences;



Where n is the term number, a is the first term, and d is the difference between subsequent terms. So, we know two pieces of information.




We can quickly subtract one equation from the other (to eliminate the a term)




So, subbing back into an equation above



Giving us the final formula



We've already found the first term (a=2000). The 51st term will be



The same approach (simultaneous equations to fill in the relevant equation) should be taken for your other questions. If you can't get them, post up your attempt at a solution and I'll help you out!

Jake

[anotherworld2b]

thank you for your help with Q29 but for Q30 I'm not sure how to do it. I got a really large number that is completely off the correct answer

I'll just help you out with the first, one, because once you've done one you can definitely figure out the rest yourself! You need to start with the relevant formula for the type of sequence (ie. geometric or arithmetic). For arithmetic sequences;



Where n is the term number, a is the first term, and d is the difference between subsequent terms. So, we know two pieces of information.




We can quickly subtract one equation from the other (to eliminate the a term)




So, subbing back into an equation above



Giving us the final formula



We've already found the first term (a=2000). The 51st term will be



The same approach (simultaneous equations to fill in the relevant equation) should be taken for your other questions. If you can't get them, post up your attempt at a solution and I'll help you out!

Jake

[jamonwindeyer]

thank you for your help with Q29 but for Q30 I'm not sure how to do it. I got a really large number that is completely off the correct answer

Show us your working mate! wait, are you definitely using geometric sequence terms?



Try solving that simultaneously to find the parameters, then proceed! If you still have trouble then definitely pop up your working and we'll see if we can spot the problem

[anotherworld2b]

I found why I was getting it wrong yay 

[jamonwindeyer]

I found why I was getting it wrong yay 

Well done! glad to hear it

[anotherworld2b]

Thank you very much jamonwindeyer and jakesilove for your help