Mathematics Question Thread

[RuiAce]

Thank you! 

For exam prep, I mainly just go through each section and do questions from each topic and identify what I'm weak at, seek help and practice it.
My issue is that I feel somewhat confident when practising at home but when I get into the exam, I completely freak out and feel like I don't know anything... In the exam, I do the questions I know and guess the ones I think I don't know... Most of the time when I get back my paper, I am facepalming because I knew some the question but didn't do it correctly or made silly mistakes. It's so frustrating! 

When you practice each topic, how exactly are you practicing? Because you need to let past papers gradually take over this necessity.

It is perfectly fine to commence studying by taking out a textbook and making sure you know each corner of the topic. It lets you ensure you have all the foundations you need to go into the exam. But it is definitely insufficient. Questions in a textbook will never be the same as questions in a textbook; they can get close to, but they will never truly reflect what you will see on the day. You need to add lots and LOTS of past papers to this strategy.

If you are making silly mistakes, consider reading Jamon's article on common silly mistakes to look out for. Then, add to it any silly mistakes that relate to just you. Do past papers whilst looking at the silly mistakes, so that you know to not let that happen. Do enough past papers with this list in front of you so that by the time you walk into the exam, you already know what mistakes to watch out for. Then, when you're done writing and need to check your answers, you know what your checklist is.

Also, simulate exam conditions. Do some past papers as though you were in an exam - Find some place that's quiet and good for focusing. Set up your timer, and do the paper like you would do an exam. And mark it once you're done, clearly indicating to yourself where all the faults were.

[phebsh]

When you practice each topic, how exactly are you practicing? Because you need to let past papers gradually take over this necessity.

It is perfectly fine to commence studying by taking out a textbook and making sure you know each corner of the topic. It lets you ensure you have all the foundations you need to go into the exam. But it is definitely insufficient. Questions in a textbook will never be the same as questions in a textbook; they can get close to, but they will never truly reflect what you will see on the day. You need to add lots and LOTS of past papers to this strategy.

If you are making silly mistakes, consider reading Jamon's article on common silly mistakes to look out for. Then, add to it any silly mistakes that relate to just you. Do past papers whilst looking at the silly mistakes, so that you know to not let that happen. Do enough past papers with this list in front of you so that by the time you walk into the exam, you already know what mistakes to watch out for. Then, when you're done writing and need to check your answers, you know what your checklist is.

Also, simulate exam conditions. Do some past papers as though you were in an exam - Find some place that's quiet and good for focusing. Set up your timer, and do the paper like you would do an exam. And mark it once you're done, clearly indicating to yourself where all the faults were.

This is great advice, thank you very much. I will definately be using these techniques!

[bananna]

hi!
can someone pls help me with these qs:

q 9, q 13 (a and i) and q 10 (e)

thank you!

[Kekemato_BAP]

Hi, I need help with question b. I don't get these max-min questions for calculus

[jamonwindeyer]

hi!
can someone pls help me with these qs:

q 9, q 13 (a and i) and q 10 (e)

thank you!

Hey! I certainly can! For Q9, the hard bit is the differentiation, which requires the Product Rule:



So we want the equation of the tangent at \(x=2\), which means we need the gradient at \(x=2\) - Substitute \(x=2\) into our derivative to get:



The y-coordinate is obtained by substituting into the original function, and we get \(y=0\) - Having a set of coordinates and a gradient, we can now use the point gradient formula:



Isn't that crazy!

The first one from 13 is just product rule derivative like above! Hopefully you can follow the working (let me know if it doesn't make sense):



The next one is tougher, it's a chain rule derivative - Remember that the derivative of \(\ln{f(x)}\) is \(\frac{f'(x)}{f(x)}\) - That works even if \(f(x)\) happens to be another logarithm!



Then as the question states, 10E is the quotient rule:



Let me know if you need me to go through any of these in a little more detail!

[jamonwindeyer]

Hi, I need help with question b. I don't get these max-min questions for calculus

Hey! No worries, I'll step through this for you!

These questions always have a setup (part (i) in this case) and then the actual calculus itself.

So we've been given a formula linking speed to fuel consumption per hour. So given a speed, we know how many litres we guzzle per hour. So, we can link that to cost per hour, but remember we need to pay the drivers $20 each ($40 in total) as well! So let the hourly cost be \(H\), and it will be:



Multiplying the litres by 0.50 is because each litre is 50 cents! From there, we need to know how long the trip is! The time taken to complete the trip can be related to the velocity and the speed  by the speed/distance/time triangle:



So, the TOTAL cost will be the hourly cost, multiplied by the number of hours:



This matches the question, so we proceed! Remember that even if you don't get the proof in the first part of a question like this, you can still do the second bit!

The next bit is just a basic maxima question - We differentiate and put the derivative equal to zero. This allows us to find critical points (max/min) - We then use the second derivative test to classify them! In this question, we also have extra conditions to verify!



Setting \(y'=0\):



We need to check that this actually yields a minimum for the function - We do this using the second derivative.



When \(v=65.6\), \(y''>0\), so therefore, the critical point we have found is a minimum. But, does it satisfy the criteria? Well travelling at that speed, we can find that in 12 hours, we don't travel anywhere NEAR as fast as we need to to do the full 1000km. So this answer won't work.

From here, we have to simply deduce that we want to get as close to this minimum as possible. So, we should go as slow as possible to complete the trip in the allotted time of 12 hours. The velocity required, therefore, is:



I know that Calculus seems useless, but we have to do it to be allowed to make this final assumption!

I hope this makes sense - Let me know if you'd like any of it clarified

[laurenf58]

How do I simplify this? I'm terrible with surds!

Thank!

[jakesilove]

How do I simplify this? I'm terrible with surds!

Thank!

Hey! So,



Looks like we'll be working in threes, so I'm gonna start by breaking up our 27.



Now, if we have a square number inside a square root, we can just bring the number outside the square root! So,


Great! Now, let's attack the first part of the problem




Let me know if I can clarify any steps!

[laurenf58]

Thanks so much! That really helps

[12070]

For points of inflexion. When do you need to prove that it actually is one using the table thing. My math teacher always seems to prove that it is whereas my tutor only sometimes does.

[jakesilove]

For points of inflexion. When do you need to prove that it actually is one using the table thing. My math teacher always seems to prove that it is whereas my tutor only sometimes does.

In the Mathematics course, I would recommend proving it. You need to show that the point is a POI, not just another stationary point. The only way to prove that is quantitatively, using a table or the double derivative. It doesn't take much longer, and you will be sure to get full marks.

[12070]

In the Mathematics course, I would recommend proving it. You need to show that the point is a POI, not just another stationary point. The only way to prove that is quantitatively, using a table or the double derivative. It doesn't take much longer, and you will be sure to get full marks.

Okay thanks. My tutor said you only need to prove it's a point of inflexion if the first and second derivative equals 0 for the same x value or something. All it has done is confused me though.

[jakesilove]

Okay thanks. My tutor said you only need to prove it's a point of inflexion if the first and second derivative equals 0 for the same x value or something. All it has done is confused me though.

Yeah exactly; if you prove it in certain cases only, you'll just end up confusing yourself (should I prove it now? What if I don't? Argh what was the rule again!??!?!?!). Instead, prove it every time; you'll get really good at it, and you'll always get the marks

[RuiAce]

For points of inflexion. When do you need to prove that it actually is one using the table thing. My math teacher always seems to prove that it is whereas my tutor only sometimes does.

Honestly your teacher is right. You're supposed to always prove it (although a better word may be verify instead of prove).

Unless your tutor ignores it purely for saving some time, he/she is doing the maths incorrectly.

[12070]

        Topics covered:

1.   Rationalising denominators of surds
2.   Simple probability
3.   Derivative of function
4.   Minimum value of an expression
5.   Equations reducible to Quadratics
6.   Simpson’s Rule
7.   Area enclosed between 2 functions
8.   Geometric series: nth term and sum
9.   Increasing & decreasing functions
10.   Sign of first and second derivative
11.   Limiting sum
12.   Definite integrals
13.   Second derivative and concavity
14.   Finding primitives
15.   Arithmetic series: nth term and sum
16.   Tangent derivative
17.   Trapezoidal rule using function values
18.   Graphing functions
19.   Integrals as exact values
20.   Parabola vertex and focus
21.   Volume of revolution
22.   Find stationary points, determine nature,   
            sketch graph, state domain
23.   Problem question on sequences
24.   Maxima minima problem question

Hey again. Do you know any good sources of where I can get past papers for these sorts of questions.