Ho Ho... No

[blacksanta62]

Can someone help me with this question please?
"find the antiderivative of the following"
2x - 1/(x - 1)Squared

Using u-sub but can't seem to get the right answer
(sorry phone doesn't have power thing)
Thank you

[JellyBeanz]

Here is my solution. Sorry it's so messy lol. But basically what I did was split up the fractions so it would be easily integrable. I made 2x-1 = 2(x-1) + 1. Sometimes you have to make subtle changes like this to make it integrable lol. Hope I helped and please ask If you don't understand anything.

[blacksanta62]

Hey Jelly, is that partial fractions? Or did you make the subtle changes solely on the fact that it would be easier? If that's the case, I don't understand where the "+1" came from after you factorised"2x-1". And is u-sub possible at all with this question? Other than that thank you

[JellyBeanz]

Hey Jelly, is that partial fractions? Or did you make the subtle changes solely on the fact that it would be easier? If that's the case, I don't understand where the "+1" came from after you factorised"2x-1". And is u-sub possible at all with this question? Other than that thank you

Yes, as you can see i did use u-sub for one part of the expression. Basically,  what i did was realise that the i can make the numerator similar to the denominator and hence i can simplify. the +1 is there because 2(x-1) + 1 is the same as 2x - 1 (2x-2 +1 = 2x-1). and you want to keep this expression. I didn't really factorise it, rather i just changed the way it was written.

[blacksanta62]

I have a mid year trial exam coming up for specialist and then my first specialist SAC. The SAC will cover a variety of things like vectors, calculus & integral calculus and their applications but I want some suggestions on how I should relearn the material that I haven't used since last term (vectors).Should I ask my teacher for her past resources and do all the Cambridge extended response questions I didn't do? Recommendations would be greatly appreciated. 

[blacksanta62]

With my spesh SAC approaching I would just like to know what should I include in my spesh notes? The whole SAC is tech enabled and I want to take in my own notes. My main empty areas are: Vectors; what must/should I include? I currently have some basics like the addition of vectors and how to find the magnitude of vectors. Trig: Haven't typed up much for this area of maths, more in my methods notes but not in great detail 
Any suggestions will be greatly appreciated

[blacksanta62]

Just a quick query: When given the graph of f(x) and told to sketch it's anti derivative what happens to the stationary points and stuff? What I mean is if given f(x) = x^3 + 3x^2 + 1 and told to sketch it's derivative then the stationary points become x-ints and the TP will be half way between the two stationary points: -b/2a, a parabola

Why doesn't seem to follow with the anti derivative? 1/4 x^4 + x^3 +x?? (not the symmetry, the x-intercepts and the TPs etc)
It seems to be strictly decreasing then strictly increasing then a point of inflection occurs while it's still increasing. Graphing these on desmos too

Thank you

Edit: Link to my notes on the graphs - https://www.desmos.com/calculator/kokfknmrtf

[lzxnl]

In general, there's no relationship between the intercepts and the turning point. Parabolas are just special/lucky.

[blacksanta62]

In general, there's no relationship between the intercepts and the turning point. Parabolas are just special/lucky.

Ahh, thanks IzxnI
Could anyone help me with B & C?
Thank you

[zsteve]

Ahh, thanks IzxnI
Could anyone help me with B & C?
Thank you

I'll give you *pointers*, but you can do the maths yourself!
You want to integrate (upper graph)-(lower graph) between the terminals. What is the 'upper graph'/'lower graph' really depends on which region you're integrating.

The terminals should be easy enough to find.

[blacksanta62]

Thanks zsteve

A question to anyone who is using the Cambridge spesh book: Are your worked solutions still available under 'more resources' or have they been removed? I've messaged them twice now and haven't gotten a response so I would like to know if this has only happened to me or to others.

Thanks

[blacksanta62]

Really don't want this thread to die (kinda dead rn, nothing but tumbleweeds)
Some questions:
1) With most kinematics question, like the one attached, will these bee more prominent in exam 2? I haven't run into any in exam one papers yet
2) With the attached question, I would love some help
3) With kinematics, did anyone else struggle with it a bit, and if so, how did you get better at it? Practice, extra help from teachers or peers? My next SAC is on mechanics and kinematics so I would like to do well and hopefully grasp rank one 
4) "Find the distance traveled"- In kinematics, we find the area underneath a curve, if it's a triangle, we use A=1/2b*h, I have forgotten some of these rules, should I go over them and try to remember them?

Sorry for all the questions, thank you

[Sine]

Really don't want this thread to die (kinda dead rn, nothing but tumbleweeds)
Some questions:
1) With most kinematics question, like the one attached, will these bee more prominent in exam 2? I haven't run into any in exam one papers yet
2) With the attached question, I would love some help
3) With kinematics, did anyone else struggle with it a bit, and if so, how did you get better at it? Practice, extra help from teachers or peers? My next SAC is on mechanics and kinematics so I would like to do well and hopefully grasp rank one 
4) "Find the distance traveled"- In kinematics, we find the area underneath a curve, if it's a triangle, we use A=1/2b*h, I have forgotten some of these rules, should I go over them and try to remember them?

Sorry for all the questions, thank you

1) you should be able to do these both tech free and tech active, they will just have "nicer" numbers for tech free
2)Draw a velocity time graph
3)kinematics is probably best done with a practical mind so just think of each question in a practical sense. With constant acceleration questions the hardest thing would be deciding whether your allowed to use those formulae once your certain just search for 3 known variables and find the required 4th. With variable acceleration the most important thing is finding what formulae  you need to use, this is best done by checking what the final answer requires.
4)yeah learn how to find areas using rectangles,triangles and trapeziums

[blacksanta62]

Thank you
Has anyone else found kinematics a challenge and overcome it? Looking for more anecdotes I guess 

[blacksanta62]

Can anyone help with these questions please:
1) 8A - How do you find the value of K?
2) With question 10, I integrated but don't know what to do next-hints would be appreciated
I'm thinking when v=0, t=? but I don't know how to find the value of K first
3) With differential equations involving kinematics, is the '+c' still required?

Thank you