Assorted questions related to A level Maths.
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edited.
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*opens eyes in the meditation room* Hi guys. After practicing school materials, i realize that i have some issues in certain topics, for some reason most of them have to do with graphs. 1) Parametic equations. Can someone give me the low down to approach this kind of question? A typical question would require the sketch of the cartesian curve from x=f(T) and y=f(T) given the range say 1 < T < 1. Yeah, the problem is, my answer when i punch the gc and when i do it manually is ALWAYS wrong (ie express X in terms of Y, and use the in gc to obtain the graph) I'm very sure this is not because of my window settings as the shape of the 2 graphs are drastically different. 2) Reciprocal graph ie 1/f(x). For some reason i can never get this right even though i know the steps involved. My main problem is determining the shape of the 1/f(x) graph. Increasing become decreasing and vice versa, but everytime i try to apply it my graph become very weird looking. :( 3)The graph of f'(x). My lecturer said that he cant penalize us with the shape of the graph, as the equation of the original curve is unknown. My question is, then when can he penalize us for the shape of the f'(x) graph. If the equation is given, we can just dy/dx and then g.c. what. Also, does d2y/dx^2 help us in determing the shape of the graph? 4)APGP story sums: Like they say the monkey chase the cow, covering eg 0.8m every step, the cow cover 0.6m every step and their dist apart is say 350m. How long will the monkey take to catch up with the cow? Or a ball bounce here bounce there, each subsequent bounce is 0.9 times of the previous bounce. Find the total height travelled after 100 bounce. Not exactly the best examples but i hope you all know what i mean. How do i approach this kind of questions? Like very chim leh. :( thanks guys. *waits for Mr Wee to enter meditation room*
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Originally posted by Lord dejavu:
opens eyes in the meditation room
Hi guys. After practicing school materials, i realize that i have some issues in certain topics, for some reason most of them have to do with graphs.1) Parametic equations. Can someone give me the low down to approach this kind of question? A typical question would require the sketch of the cartesian curve from x=f(T) and y=f(T) given the range say 1 < T < 1.
Yeah, the problem is, my answer when i punch the gc and when i do it manually is ALWAYS wrong (ie express X in terms of Y, and use the in gc to obtain the graph) I’m very sure this is not because of my window settings as the shape of the 2 graphs are drastically different.
2) Reciprocal graph ie 1/f(x). For some reason i can never get this right even though i know the steps involved. My main problem is determining the shape of the 1/f(x) graph. Increasing become decreasing and vice versa, but everytime i try to apply it my graph become very weird looking.
Hi,
For query 1:
Perhaps you should just use the Parametric mode, unless the question asks that you change it to cartesian equation. The default window settings for Tmin is 0 and Tmax is 2 pi, so do change them to suit the range of t given in the question.For query 2:
To sketch the graph of y = 1/f(x) from y = f(x), note that
(i) Vertical asymptote x = a on y = f(x) becomes x-intercept a on y = 1/f(x).
(ii) x-intercept a on y = f(x) becomes vertical asymptote x = a on y = 1/f(x).
(iii) Horizontal asymptote y = b on y = f(x) becomes horizontal asymptote y = 1/b on y = 1/f(x).
(iv) y = f(x) is increasing as x is increasing becomes y = 1/f(x) is decreasing as x is increasing.
(v) y = f(x) is decreasing as x is increasing becomes y = 1/f(x) is increasing as x is increasing.
(vi) Maximum turning point (a, b) on y = f(x) becomes minimum turning point (a, 1/b) on y = 1/f(x).
(vii) Minimum turning point (a, b) on y = f(x) becomes maximum turning point (a, 1/b) on y = 1/f(x).
The resulting curve can look wierd. Have confidence in your work if you have done the above steps correctly.Thanks!
Cheers,
Wen Shih
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Originally posted by Lord dejavu:
3)The graph of f’(x). My lecturer said that he cant penalize us with the shape of the graph, as the equation of the original curve is unknown. My question is, then when can he penalize us for the shape of the f’(x) graph. If the equation is given, we can just dy/dx and then g.c. what.
Also, does d2y/dx^2 help us in determing the shape of the graph?
4)APGP story sums: Like they say the monkey chase the cow, covering eg 0.8m every step, the cow cover 0.6m every step and their dist apart is say 350m. How long will the monkey take to catch up with the cow? Or a ball bounce here bounce there, each subsequent bounce is 0.9 times of the previous bounce. Find the total height travelled after 100 bounce. Not exactly the best examples but i hope you all know what i mean. How do i approach this kind of questions? Like very chim leh.
Hi,
Query 3:
To sketch y = f ' (x) from y = f(x), we take some points along the curve of y = f(x) to obtain the curve given by y = f ' (x). The marker can penalise a student if the behaviour of y = f ' (x) is not consistent with that of y = f(x). Take for example, a student draws a downward sloping curve for y = f '(x) when the gradient of y = f(x) is increasing as x is increasing.Query 4:
Make use of the pieces of information (one at a time patiently) given in the problem statement.
Write out some results and conclude AP/GP.
Also, one needs to translate the given information to mathematical expressions. These expressions are usually concerned with sums to be evaluated or inequalities to be established and solved.
Take the ball bouncing problem as an example.
Say it was dropped from height h. Let T_i be height reached AFTER ith bounce.
After 1st bounce, T_1 = 0.8 h.
After 2nd bounce, T_2 = 0.8^2 h.
After nth bounce, T_n = 0.8^n h.
So we can see a GP for this problem.
The second portion of the problem concerns the sum of GP, since the keywords are "total height". Do note that we are looking at this sum:
h + 2(0.8 h) + ... + 2(0.8^99 h).Take the chasing problem as an example. We see AP sequences.
For monkey, distance covered u_n = 0.8 n, where n is number of steps.
For cow, distance covered v_n = 350 + 0.6 n, where n is number of steps.
We want u_n >= v_n, so that the monkey catches up with the cow.Thanks!
Cheers,
Wen Shih -
Originally posted by Lord dejavu:
opens eyes in the meditation room
Hi guys. After practicing school materials, i realize that i have some issues in certain topics, for some reason most of them have to do with graphs.1) Parametic equations. Can someone give me the low down to approach this kind of question? A typical question would require the sketch of the cartesian curve from x=f(T) and y=f(T) given the range say 1 < T < 1.
Yeah, the problem is, my answer when i punch the gc and when i do it manually is ALWAYS wrong (ie express X in terms of Y, and use the in gc to obtain the graph) I’m very sure this is not because of my window settings as the shape of the 2 graphs are drastically different.
2) Reciprocal graph ie 1/f(x). For some reason i can never get this right even though i know the steps involved. My main problem is determining the shape of the 1/f(x) graph. Increasing become decreasing and vice versa, but everytime i try to apply it my graph become very weird looking.
3)The graph of f’(x). My lecturer said that he cant penalize us with the shape of the graph, as the equation of the original curve is unknown. My question is, then when can he penalize us for the shape of the f’(x) graph. If the equation is given, we can just dy/dx and then g.c. what.
Also, does d2y/dx^2 help us in determing the shape of the graph?
4)APGP story sums: Like they say the monkey chase the cow, covering eg 0.8m every step, the cow cover 0.6m every step and their dist apart is say 350m. How long will the monkey take to catch up with the cow? Or a ball bounce here bounce there, each subsequent bounce is 0.9 times of the previous bounce. Find the total height travelled after 100 bounce. Not exactly the best examples but i hope you all know what i mean. How do i approach this kind of questions? Like very chim leh.
thanks guys. waits for Mr Wee to enter meditation room
Professor Wee has entered the room! Toss the pokeball XD
Pardon my lame joke, Sir...
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Hi,
No worry :) This forum needs some humour to ease the stresses of our students.
Cheers,
Wen Shih