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July 15, 2020, 10:41:21 pm

Author Topic: Mathematics Question Thread  (Read 713110 times)  Share 

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Coolmate

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Re: Mathematics Question Thread
« Reply #4410 on: January 20, 2020, 08:57:32 pm »
0
Hi Everyone, ;D

I have a test coming up regarding the syllabus topics of:

  • ✔Functions
    ✔Trigonometric Functions

I was just wondering whether anyone would have any tips for tests regarding these topics

Thanks in advance,
Coolmate 8)
« Last Edit: January 20, 2020, 09:01:21 pm by Coolmate »
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kauac

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Re: Mathematics Question Thread
« Reply #4411 on: January 20, 2020, 09:51:59 pm »
+2
Hi Everyone, ;D

I have a test coming up regarding the syllabus topics of:

  • ✔Functions
    ✔Trigonometric Functions

I was just wondering whether anyone would have any tips for tests regarding these topics

Thanks in advance,
Coolmate 8)

Hi Coolmate!

Not too familiar with the new maths advanced syllabus, but I had a look at my 2U notes for the same topics and have some (but definitely not exhaustive) general things that could help:

Trigonometric Functions
•   Take note of whether the question is asking for the answer in degrees or radians (and double check your calculator is in this mode) – easy marks can be lost there.
•   On a similar note: know how to convert radians to degrees and vice versa.
•   Know well and be able to draw your basic y= sin x, cos & tan graphs (and their inverse).

Functions:
•   Know the difference between domain & range
•   With a region question, check you have drawn it correctly by plugging a set of coordinates inside the region and making sure the inequality is true for this.
•   Be familiar with the format/wording of locus questions so that you can easily work out what it’s meant to look like (e.g. a circle or a straight line).

I’m sure there are plenty more tips that others could add as well! :)
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Re: Mathematics Question Thread
« Reply #4412 on: January 25, 2020, 09:35:57 am »
0
Hi Coolmate!

Not too familiar with the new maths advanced syllabus, but I had a look at my 2U notes for the same topics and have some (but definitely not exhaustive) general things that could help:

Trigonometric Functions
•   Take note of whether the question is asking for the answer in degrees or radians (and double check your calculator is in this mode) – easy marks can be lost there.
•   On a similar note: know how to convert radians to degrees and vice versa.
•   Know well and be able to draw your basic y= sin x, cos & tan graphs (and their inverse).

Functions:
•   Know the difference between domain & range
•   With a region question, check you have drawn it correctly by plugging a set of coordinates inside the region and making sure the inequality is true for this.
•   Be familiar with the format/wording of locus questions so that you can easily work out what it’s meant to look like (e.g. a circle or a straight line).

I’m sure there are plenty more tips that others could add as well! :)

Thankyou kauac for the advice! :D
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shekhar.patel

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Re: Mathematics Question Thread
« Reply #4413 on: February 09, 2020, 09:56:33 am »
0
Hi there. I need help in this question. If anyone can assist much appreciated.
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Re: Mathematics Question Thread
« Reply #4414 on: February 09, 2020, 01:03:27 pm »
+3
Hey there!

Given that the sums of three different sections need to be the same, we should automatically be considering a sort of inverse to that statement ie. that the three different sections need to each have a sum a third of the total, which is 78. Therefore, each section should have a total of 26. Also, note that each number can be paired up with one other to form 13, ie. two pairs form 26. It's a similar sort of idea to summing arithmetic series quickly by adding the first and last terms, the second and second last, etc. Therefore, any two pairs will work, but given that two lines need to be drawn as opposed to randomly picking two pairs, the following would be a good solution.

Spoiler
Hope this helps!
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shekhar.patel

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Re: Mathematics Question Thread
« Reply #4415 on: February 10, 2020, 04:16:43 pm »
0
Hey there!

Given that the sums of three different sections need to be the same, we should automatically be considering a sort of inverse to that statement ie. that the three different sections need to each have a sum a third of the total, which is 78. Therefore, each section should have a total of 26. Also, note that each number can be paired up with one other to form 13, ie. two pairs form 26. It's a similar sort of idea to summing arithmetic series quickly by adding the first and last terms, the second and second last, etc. Therefore, any two pairs will work, but given that two lines need to be drawn as opposed to randomly picking two pairs, the following would be a good solution.

Spoiler
Hope this helps!

Oh right!
That makes sense. Thanks a lot for your help.
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Tierney_P

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Re: Mathematics Question Thread
« Reply #4416 on: February 25, 2020, 02:50:12 pm »
0
Hey guys this is probably a dumb question......how do I integrate a square root???
like for example y=
?????
xx
T

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Re: Mathematics Question Thread
« Reply #4417 on: February 25, 2020, 04:06:03 pm »
+1
Hey guys this is probably a dumb question......how do I integrate a square root???
like for example y=
?????
This reads as \( 4\sqrt{2} - x\). Did you mean this or did you mean \(4\sqrt{2-x}\)?

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Re: Mathematics Question Thread
« Reply #4418 on: February 25, 2020, 04:48:52 pm »
0
This reads as \( 4\sqrt{2} - x\). Did you mean this or did you mean \(4\sqrt{2-x}\)?
Sorry  :-[ the second one!
xx
T

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Re: Mathematics Question Thread
« Reply #4419 on: February 25, 2020, 05:08:09 pm »
0
\[ \int 4\sqrt{2-x}\,dx = 4\int (2-x)^{\frac12}\,dx \]
\[ \text{Now apply the reverse chain rule result}\\ \int (ax+b)^n\,dx = \frac{(ax+b)^{n+1}}{a(n+1)}+c \]

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Re: Mathematics Question Thread
« Reply #4420 on: February 25, 2020, 05:16:26 pm »
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\[ \int 4\sqrt{2-x}\,dx = 4\int (2-x)^{\frac12}\,dx \]
\[ \text{Now apply the reverse chain rule result}\\ \int (ax+b)^n\,dx = \frac{(ax+b)^{n+1}}{a(n+1)}+c \]

Ok awesome! Thank you!
xx
T

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Re: Mathematics Question Thread
« Reply #4421 on: February 29, 2020, 10:13:40 pm »
0
Hello :)

How would I work out this question:

In an arithmetic series, T3 = -2 and T9 = 28. How many terms of this series are required to give a sum of 1092?

Thanks in advance!

fun_jirachi

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Re: Mathematics Question Thread
« Reply #4422 on: February 29, 2020, 10:23:55 pm »
+2
Hello :)

How would I work out this question:

In an arithmetic series, T3 = -2 and T9 = 28. How many terms of this series are required to give a sum of 1092?

Thanks in advance!

Hey there!

There are a few key steps to doing this question:

a) Consider that there are 9 - 3 = 6 'jumps' between T3 and T9, all with the same value. ie. \(T_i - T_j = (i-j)d, \ [i, j \in \mathbb{Z}^+, \ i > j]\). This step will enable you to find the common difference.
b) Use this common difference to find the first term in the sequence, then substitute the relevant values into the sum of an arithmetic sequence formula, to then solve for Sn = 1092.

Hope this helps :)
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Re: Mathematics Question Thread
« Reply #4423 on: March 11, 2020, 09:51:11 pm »
0
Hi!
My textbook has lots of questions that involve sketching graphs first and solving an equation graphically. This seems unreasonable to me. Isn't the idea of a sketch that it doesn't have to be accurate? Especially in exam scenarios. For example, how can we be expected to use our sketch of y=e^{x-1} - 2 to solve for e^{x-1} - 2 = 8, without doing is algebraically? Would we actually get such questions in an exam? Because so far, I've just sketched the graph and solved the given equation algebraically. I'd imagine they'd give us an accurately drawn graph in an exam and ask us to solve an equation or inequality using that.
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Re: Mathematics Question Thread
« Reply #4424 on: March 12, 2020, 07:41:46 am »
+1
Hi!
My textbook has lots of questions that involve sketching graphs first and solving an equation graphically. This seems unreasonable to me. Isn't the idea of a sketch that it doesn't have to be accurate? Especially in exam scenarios. For example, how can we be expected to use our sketch of y=e^{x-1} - 2 to solve for e^{x-1} - 2 = 8, without doing is algebraically? Would we actually get such questions in an exam? Because so far, I've just sketched the graph and solved the given equation algebraically. I'd imagine they'd give us an accurately drawn graph in an exam and ask us to solve an equation or inequality using that.

Usually in exams, graphs are used more for detecting if points of intersection exist, and for visualising inequalities. While textbooks do this as an exercise, its important to note it down as a decent technique to see if you algebraic answer is 'in the ballpark' of where the answer should be - does it make sense? Solving for the exact values of x would of course be done algebraically :) No exam will ever ask you to take values from your graph, though some more informal exams might ask you to take approximations.

Hope this helps :)
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