STEP Tricks and Hacks Thread
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@Zacken @Duke Glacia Can you add these?
level3
eliminate variables
2011,S3,Q8
There's nothing extremely hard or new ideas in this question. As long as you are familiar with complex, it is easy.
I'll just talk about (iv)
The standard answer gives a method using substitution tan(α/2). tan(α/2) is good, but not almighty---what if it
is not a circle? so the best method is:
simplified, we have u=2x/x^2+4, v=x^2/x^2+4
now what should we do? remind of your goal---we aim to find relationship between u and v, so we should
eliminate x.
but how? stupid idea is to "observe the relationship" . sometimes it is not easy to observe.
So, we need to express x in terms of u or v or both, and substitute x in this value, thus we can eliminate x.
Now either solve the first expression(treating it as a quadratic function as x), we get x in terms of u, and substitute
into the second, or it is easy to see that v/u=x/2, then substitute x=2v/u into the first of second, we are done.
level4
beautiful substitution
1998.3.7
I choose this question because the trick behind it is rare and beautiful.
To make it short, I'll just talk about the key of this question---how to find n.
Now b(x) is a function, with a ugly appearance. T is in the exp, and x3 looks useless
We aim to find Tn, so we should transfer T into the unmerator. obviously, Taylor expansion is not a good idea.
Using substitution u=x/T, then T will not occur in exp, and it will appear in the numerator.
done.
level3
eliminate variables
2011,S3,Q8
There's nothing extremely hard or new ideas in this question. As long as you are familiar with complex, it is easy.
I'll just talk about (iv)
The standard answer gives a method using substitution tan(α/2). tan(α/2) is good, but not almighty---what if it
is not a circle? so the best method is:
simplified, we have u=2x/x^2+4, v=x^2/x^2+4
now what should we do? remind of your goal---we aim to find relationship between u and v, so we should
eliminate x.
but how? stupid idea is to "observe the relationship" . sometimes it is not easy to observe.
So, we need to express x in terms of u or v or both, and substitute x in this value, thus we can eliminate x.
Now either solve the first expression(treating it as a quadratic function as x), we get x in terms of u, and substitute
into the second, or it is easy to see that v/u=x/2, then substitute x=2v/u into the first of second, we are done.
level4
beautiful substitution
1998.3.7
I choose this question because the trick behind it is rare and beautiful.
To make it short, I'll just talk about the key of this question---how to find n.
Now b(x) is a function, with a ugly appearance. T is in the exp, and x3 looks useless
We aim to find Tn, so we should transfer T into the unmerator. obviously, Taylor expansion is not a good idea.
Using substitution u=x/T, then T will not occur in exp, and it will appear in the numerator.
done.
Original post by Insight314
@Zacken, @Duke Glacia,
I was literally trying to find a thread/website with STEP Tips and Tricks yesterday. Thank you. I am really glad that you've decided to make one, and lucky that Duke Glacia accidentally tagged me in the OP (what is up with that?) since I do not regularly visit TSR to look for such thread.
Zacken, I think it is really helpful to give an "extension" problem like you did in "2. Trigonometrical symmetry and substitution for integration" since the main point of STEP questions is largely to learn a technique and then be able to apply it.
Recommendation: Do you have any Tricks and Hacks on questions with simultaneous equations, I often just skip them because I am not sure how to attempt them yet. Here is an example (Question 1 STEP III 2008) which I just tried doing before going to sleep and was easy at first (due to the hint) until you get all the equations and have no idea what to do with them. I know this is quite a general recommendation but I guess you could refer to different techniques of factorisation or whatever that is needed when attempting such questions.
I think it would be nice for people to recommend tricks on here, or maybe another thread linked to this.
If we get quite a few Tricks and Hacks on here, it is also possible to make it into a pdf through ShareLatex and type it out in LaTeX just like Stephen Siklos did; I wouldn't mind typing it out, if you want me to. It would be pretty useful to revise through on the day of the exam.
And, again, thank you for making this thread - you have no idea how useful this is going to be for me!
I was literally trying to find a thread/website with STEP Tips and Tricks yesterday. Thank you. I am really glad that you've decided to make one, and lucky that Duke Glacia accidentally tagged me in the OP (what is up with that?) since I do not regularly visit TSR to look for such thread.
Zacken, I think it is really helpful to give an "extension" problem like you did in "2. Trigonometrical symmetry and substitution for integration" since the main point of STEP questions is largely to learn a technique and then be able to apply it.
Recommendation: Do you have any Tricks and Hacks on questions with simultaneous equations, I often just skip them because I am not sure how to attempt them yet. Here is an example (Question 1 STEP III 2008) which I just tried doing before going to sleep and was easy at first (due to the hint) until you get all the equations and have no idea what to do with them. I know this is quite a general recommendation but I guess you could refer to different techniques of factorisation or whatever that is needed when attempting such questions.
I think it would be nice for people to recommend tricks on here, or maybe another thread linked to this.
If we get quite a few Tricks and Hacks on here, it is also possible to make it into a pdf through ShareLatex and type it out in LaTeX just like Stephen Siklos did; I wouldn't mind typing it out, if you want me to. It would be pretty useful to revise through on the day of the exam.
And, again, thank you for making this thread - you have no idea how useful this is going to be for me!
Hi, i know i'm 4 years late but for simultaneous equations 1) Gaussian elimination
2) and solution of sumltaneous eq degree 1 with 2 unknowns of form ax+by+c and a1x+b1y=c1
then x=(cb1-c1b)/(ab1-a1b) and y=(ac1-a1c)/(ab1-a1b)
Original post by calebs
Hi, i know i'm 4 years late but for simultaneous equations 1) Gaussian elimination
2) and solution of sumltaneous eq degree 1 with 2 unknowns of form ax+by+c and a1x+b1y=c1
then x=(cb1-c1b)/(ab1-a1b) and y=(ac1-a1c)/(ab1-a1b)
2) and solution of sumltaneous eq degree 1 with 2 unknowns of form ax+by+c and a1x+b1y=c1
then x=(cb1-c1b)/(ab1-a1b) and y=(ac1-a1c)/(ab1-a1b)
many thanks
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