Edexcel C3,C4 June 2013 Thread

OP

Can someone please explain on Solomon Press Paper J - Rep for help!

Question 7
Paper: http://www.tomred.org/uploads/7/7/8/3/778329/c3_qp_solomon_j.pdf
MarkScheme: http://www.tomred.org/uploads/7/7/8/3/778329/c3_ms_solomon_j.pdf

f : x→ 2x − 5, x ∈ , (MODULUS FOR THE WHOLE FUNCTION)
g : x→ ln (x + 3), x ∈ , x > −3

(d) Show that the equation
f(x) = g(x)
has a root, α, in the interval [3, 4].

WHY DO YOU DO?
h(x) = f(x) − g(x)

Why can't you do
h(x) = g(x) - f(x)

I was confused here.

Question 6

I didn't follow exactly what they did instead I did

2cot 2x + tan x ≡ cot x(b) Solve, for 0 ≤ x < π, the equation 2cot 2x + tan x = cosec2
x − 7,

I did cot x = cosec^2x - 7

Then I expressed cot in terms of cosex and squared out instead of the other way round.

Why was my answer wrong?

I ended up with (x-10)(x-5)
where x - cosec^2x ....why did I get the wrong answer for one of the values surely algebraically its the same thing?

(edited 10 years ago)

Reply 1581

AndyBoughton

Can someone please explain to me part A. Not just telling me how to do it but explaining it.

I understand that -cosec^2 A goes to 1/sin^2 A but do not understand the other part.

Please can someone explain

Reply 1582

usycool1

19

Original post by AndyBoughton

Can someone please explain to me part A. Not just telling me how to do it but explaining it.

I understand that -cosec^2 A goes to 1/sin^2 A but do not understand the other part.

Please can someone explain

4 \csc^2 2\theta = \dfrac{4}{\sin^2 2\theta}

.

Then use double angle formulae. :smile:

Reply 1583

Nilsdejongh

Guys in regards to exam preparation? What's your views on past papers? Do the Solomon first? Then edexcel? After each paper I look into the mistakes and do Afew Q's from the book to solidify myself up on it

Reply 1584

MedMed12

21

Original post by Nilsdejongh

Guys in regards to exam preparation? What's your views on past papers? Do the Solomon first? Then edexcel? After each paper I look into the mistakes and do Afew Q's from the book to solidify myself up on it

thats what I'm doing/have done :smile:

solomon first then edexcel (which I've only done one of) as I'm doing afew solomon again

Reply 1585

usycool1

19

Original post by Better

f : x→ 2x − 5, x ∈ , (MODULUS FOR THE WHOLE FUNCTION)
g : x→ ln (x + 3), x ∈ , x > −3

(d) Show that the equation
f(x) = g(x)
has a root, α, in the interval [3, 4].

WHY DO YOU DO?
h(x) = f(x) − g(x)

Why can't you do
h(x) = g(x) - f(x)

I was confused here.

Both should be fine.

Question 6

I didn't follow exactly what they did instead I did

2cot 2x + tan x ≡ cot x(b) Solve, for 0 ≤ x < π, the equation 2cot 2x + tan x = cosec2
x − 7,

I did cot x = cosec^2x - 7

Then I expressed cot in terms of cosex and squared out instead of the other way round.

Why was my answer wrong?

I ended up with (x-10)(x-5)
where x - cosec^2x ....why did I get the wrong answer for one of the values surely algebraically its the same thing?

Avoid squaring when you're solving an equation; you'll end up with extra, invalid solutions.

For example, say you had:

x = 5

And for some reason you decided to square it:

x^2 = 25

You'd then get

x=\pm 5

, but -5 is an extraneous solution.

So you can use the method you used, but then check your answers by plugging them into the original equation to get rid of the extraneous solutions. Or, I'd just stick with the method they used in the markcheme (i.e. replace cosec^2 x with 1 + cot^2 x). :smile:

(edited 10 years ago)

Reply 1586

Nilsdejongh

C3 - been looking at validity of Binomials and their ranges/limits when N isn't a positive integer the .

If you have a 2 part inequality such as -1<-2x<1 and obviously need to rearrange to get just X.. You used to have to swap the sign Arround if you did something but I can't remember what! Haha

Reply 1587

super121

5

Do we need to know the half angle formulae?

Posted from TSR Mobile

Reply 1588

masryboy94

8

Original post by Tikara

Hey guys? Does anyone know if you have to be able to prove any formulas for C4?

not that i can think of, except maybe they might ask you to prove how

y= 2^t

differentiated becomes

\frac{dy}{dx} = 2^t ln2

Reply 1589

MedMed12

21

http://www.edexcel.com/migrationdocuments/QP%20GCE%20Curriculum%202000/Maths/49_C4_June_2005.pdf so I've got the right answer for question 4, but I just ignored the 3/2, but I was wondering what actually happens to it. Looking at the mark scheme, they seem to have ignored it too :s-smilie:

just wanted to understand what I should be doing there haha
heres the mark scheme http://www.edexcel.com/migrationdocuments/QP%20GCE%20Curriculum%202000/Maths/C4_June_2005_mark_scheme.pdf

heres my working :

1/(1-x^2)^3/2 with the integrals

then putting sintheta for X

1/(cos^2)^3/2

1/cos^2 is sec^2 so did that

then integrated sec^2 to get tan and then changed the limits and got 1/root3

or is cube root cos^2 then squaring that the same as cos^2 so nothing changes :s-smilie:

Reply 1590

usycool1

19

Original post by MedMed12

http://www.edexcel.com/migrationdocuments/QP%20GCE%20Curriculum%202000/Maths/49_C4_June_2005.pdf so I've got the right answer for question 4, but I just ignored the 3/2, but I was wondering what actually happens to it. Looking at the mark scheme, they seem to have ignored it too :s-smilie:

just wanted to understand what I should be doing there haha
heres the mark scheme http://www.edexcel.com/migrationdocuments/QP%20GCE%20Curriculum%202000/Maths/C4_June_2005_mark_scheme.pdf

heres my working :

1/(1-x^2)^3/2 with the integrals

then putting sintheta for X

1/(cos^2)^3/2

1/cos^2 is sec^2 so did that

then integrated sec^2 to get tan and then changed the limits and got 1/root3

or is cube root cos^2 then squaring that the same as cos^2 so nothing changes :s-smilie:

Firstly, you need to find

\dfrac{dx}{d\theta}

too.

And use power rules to get "rid" of the 3/2:

(\cos^2 \theta)^{\frac{3}{2}} = \cos^3 \theta

(multiply the powers).

But as I said, you need to find

\dfrac{dx}{d\theta}

too to see how it simplifies down to

sec^2 \theta

.

Reply 1591

m4ths/maths247

7

Original post by Nilsdejongh

Guys in regards to exam preparation? What's your views on past papers? Do the Solomon first? Then edexcel? After each paper I look into the mistakes and do Afew Q's from the book to solidify myself up on it

There is always the option of getting the 'exam questions' from your teacher that Edexcel have produced and going through the topics you are less at ease with.
I personally don't think there is one set approach that fits all students when it comes to the best way of prepping for an exam.

Reply 1592

kronca

0<= X <= Pi

cos\dfrac{1}{2}\theta +

2cos\dfrac{3}{2}\theta +

cos\dfrac{5}{2}\theta = 0

someone help pls!

Reply 1593

Better

OP

8

Original post by usycool1

Both should be fine.

Avoid squaring when you're solving an equation; you'll end up with extra, invalid solutions.

For example, say you had:

x = 5

And for some reason you decided to square it:

x^2 = 25

You'd then get

x=\pm 5

, but -5 is an extraneous solution.

So you can use the method you used, but then check your answers by plugging them into the original equation to get rid of the extraneous solutions. Or, I'd just stick with the method they used in the markcheme (i.e. replace cosec^2 x with 1 + cot^2 x). :smile:

Wow thank you so much for taking the time to explain that.

I really appreciate it you hero!

Reply 1594

masryboy94

8

DAYUM !!! got 100% in soloman paper J :biggrin:

!!

nice paper that was .... but i have a question on it, basically there was a question in that paper which asked to prove that

2cot2x + tanx = cotx

the attachment to this post is what they had in the mark scheme. however i proved it a different way. would i get the 5 marks awarded for it? because if not then i didn't get 100% :frown:

Spoiler

Screen Shot 2013-05-28 at 15.42.47.png15.2KB

Reply 1595

usycool1

19

Original post by Better

Wow thank you so much for taking the time to explain that.

I really appreciate it you hero!

No problem! :smile:

Original post by masryboy94

DAYUM !!! got 100% in soloman paper J :biggrin:

!!

nice paper that was .... but i have a question on it, basically there was a question in that paper which asked to prove that

2cot2x + tanx = cotx

the attachment to this post is what they had in the mark scheme. however i proved it a different way. would i get the 5 marks awarded for it? because if not then i didn't get 100% :frown:

Spoiler

Looks fine to me :yep: