Revision [Question and Answers Provided] Need help understanding ASAP

Alive · 2011-03-08 12:56:52

Do we use binomial theorem for this?

I understand a and b.. But for c) how do you get (-5,-16) ? Also for e) The question for the revision paper wasn't printed out properly, but I've seen the teacher do lots of things like this, what do you think the question would be or if you could do another example that looks like it?

I know how to do all of them except:
For 3b) What does linear factors mean? and how did the answer become x^3 + 2x^2 -5x - 6? Did they use long division?
For 4b) How do we sketch this? How do we know it has a shape like that?

I also have one more question but don't have the time to upload, I can't stress enough how important these questions are so please if you can answer them with detailed answers... I know how to do all except the ones that I pointed out above. Thank you very much

bobbym · 2011-03-08 14:26:49

Hi Alive;

Alive wrote:

Do we use binomial theorem for this?

I really would not waste my time with using the binomial expansion. You could make the substitution b = x^2 / 2 and with 2 multiplications you are done.

2c) Substitutions to the rescue again!

Solve that like any other quadratic. You will get roots x = -5 and x = 3. Plug those into 1) to get both y's.

2e) I cannot read that at all, sorry.

3b) (x + 3) is a linear factor. No powers of x greater than 1 and it is a polynomial. Linear comes from meaning if I graphed y = x + 3, I would get a straight line.

Alive wrote:

and how did the answer become x^3 + 2x^2 -5x - 6?

For 4b) How do we sketch this? How do we know it has a shape like that?

Listen to me for a second because you have to apply yourself a bit more. Supposing you do not know anything about the shape of that polynomial. Supposing you know nothing about extrema, turning points , roots and continuous functions. What you never want to do is leave an answer blank. Teachers mark you with a big fat zero and bosses fire you. You should still be able to have done this without any knowledge at all:

Remember your x,y tables? If all else fails use it.

Now just graph those points and draw a smooth line between them. See the graph below. That is good enough to answer the question of why it looks like that. Because it is a polynomial you know that it never does anything wild between any 2 points. That is why you can be sure of that graph.

Please go here to see a clever way.

http://www.mathsisfun.com/algebra/polyn … ehave.html
http://www.purplemath.com/modules/polyends.htm

Alive · 2011-03-08 20:17:47

Hey;

No I meant 4b) I don't know how to sketch that. I can find the domain and range... + asymptotes... but I don't know how to do it when x equals zero... I don't know how to re arrange it to get (-1(-1/4) and also when the f(x) equals zero... to get 2+√ 3/2 . I'm really not good at getting the x intercepts for things like that.. How do we get to the solution? I don't know the steps. This can be basic algebra but please if you have the time to...

Last question... How do we do this? Getting the x intercepts for the absolute value?

Last edited by Alive (2011-03-08 20:22:47)

bobbym · 2011-03-08 20:30:47

Hi Alive;

To get that - 5 / 4 you just plug into the function x = 0.

Alive · 2011-03-08 20:40:59

Could you explain it the same way to get 2+-√ 3/2 (x intercepts) for the same question please.

bobbym · 2011-03-08 20:58:05

Hi;

Times both sides by (x-2)^2

Expand it.

Can you solve that quadratic?

Alive · 2011-03-08 21:12:22

Solving the quadratic...
-8 +- √ 8^2 - 4(-2)(-5)
--------------------------
-4

-8 +- √ 64 - 40
-----------------
-4

-8 +- √ 24
------------
-4

I don't know how to do what is in the square root.? So 2x3x2x2 = 24... Do we use them in some way?

bobbym · 2011-03-08 21:24:15

Does that help?

Alive · 2011-03-08 21:58:11

No I still don't know the method to use here...

bobbym · 2011-03-08 22:02:27

You try split the square root into parts that are perfect squares.

Bob · 2011-03-08 22:04:33

hi Alive,

For 4b) How do we sketch this? How do we know it has a shape like that?

I wrote a set of sketching steps recently at

http://www.mathisfunforum.com/viewtopic.php?id=15139

post #7

Some practice questions too.

What exam course are you studying for? Maybe I can find some past papers.

Bob

Alive · 2011-03-08 22:40:53

Okay but... How do we end up having 2 -+ √3/2

Hey bob bundy;
It's for a functions test.. (without calculator) but there's going to be one with calculator for matrices later.

Bob · 2011-03-08 22:49:14

hi Alive,

But what exam board? Is this for C3 ?

Here's a start but I need more information to get the right questions for you.

http://www.pearsonschoolsandfecolleges.co.uk/Secondary/Mathematics/16+/AdvancingMathsForAQA2ndEdition/Samples/SampleMaterial/Chap02%20023-041.pdf

http://www.purecoder.net/sixthworksheets/OCR%20Functions.pdf

http://www.scribd.com/doc/48799935/Quadratic-Function-Set3-2011

Hope that helps,

Bob

Last edited by Bob (2011-03-08 22:49:48)

bobbym · 2011-03-08 22:53:37

Hi;

Okay but... How do we end up having 2 -+ √3/2

Please be careful in how you parenthesize things that 3 / 2 is inside the radical.

Continue to solve the problem the way you are going and do not worry about matching up with his answer.

Answers do not always look the same. 1 + 1 / 4 and 5 / 4 and 1.25 are all the same but look quite different. Each time you get stuck it is on an algebraic move. We need to strengthen those.

Alive · 2011-03-09 00:09:56

You're left with

-8 2√6
---------
-4

-2 2√6 ???

Hey Bob Bundy;
they are excellent tutorials, thanks for that! I'm doing Maths Methods in high school (Australia) so I don't know what C3 is?

Last edited by Alive (2011-03-09 00:10:40)

bobbym · 2011-03-09 00:13:47

Hi Alive;

You have forgotten the plus and minus sign in between.

Alive · 2011-03-09 00:19:24

Hey bobbym;

so what did we find here? Are they the x intercepts? If so.. I don't understand what that means... As in how will we know to where we are going to plot it? -8...+2...Square root of 6... and divided by -4..??

Bob · 2011-03-09 00:35:38

hi Alive

I see you are on-line now. Reply and we'll get a two way chat going to sort the maths out.

I think the x values are from question 4. You put f(x) = 0 and solved for x.

So it's the x values to make y coordinate zero => when the curve crosses the x axis. (= the intercepts)

Bob

Last edited by Bob (2011-03-09 00:41:27)

bobbym · 2011-03-09 00:40:10

Hi Alive;

Please reduce the two fractions down for me. Yes, those are the x intercepts or the roots of the equation. Your problem is not theory. You have very little manipulative skills, this is where you need help. Reduce the fractions to lowest terms.

Alive · 2011-03-09 00:41:04

Yeah I'm online The questions to the worksheet you gave is kind of different to what we are studying. It has tan etc. We are also doing cubic function, hyperbola, truncus, square root, absolute value.. More of transformations like dilation reflection etc, finding aymptotes and axis' and domain + range + Sketching them accordingly to what is being asked.

Hey bobbym;

You're right, I'm mostly comfortable with what is being asked but when it gets to fractions, I'm really bad at it. That's cause I don't know the steps to do these things as I havent practice them for a long time. I really don't know what to do next to get the solution...

Last edited by Alive (2011-03-09 00:43:34)

Bob · 2011-03-09 00:44:30

ok great.

You are asked to sketch the curve = show it's main features without doing an accurate plot.

You have got where it crosses the x axis.

Put x = 0 and the resulting f(0) is where it crosses the y axis.

Bob

bobbym · 2011-03-09 00:45:30

Hi;

The first one can be split like this:

Can you reduce the -8 / -4 ?

Alive · 2011-03-09 00:49:12

Yes it becomes 2

bob bundy;
Yeah I found the y int. need help with the x axis

Last edited by Alive (2011-03-09 00:49:27)

bobbym · 2011-03-09 00:52:30

Hi;

Look at the next term. Notice that the numerator and the denominator have a common factor. Use that to reduce both.

Alive · 2011-03-09 00:55:51

They can both be divided by 2 ?
2 + (√6 / -2) maybe?

Last edited by Alive (2011-03-09 00:56:50)

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Revision [Question and Answers Provided] Need help understanding ASAP

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