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AQA A2 Mathematics MPC3 Core 3 - Wednesday 15th June 2016 [Official Thread]

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Post your working then.

I tried using chain rule this time;

dy/dx = 4 + 4tan^2(4x)
the 4 differentiates to 0 so i did chain rule of 4tan^2(4x);
=4(tan^2(4x))
=4[ (tan4x)^2 ]

u= tan4x y = u^2
du/dx = 4 + 4tan^2(4x) (as worked out in part a) dy/du = 2u (2tan4x)

dy/dx = 4[ du/dx x dy/du]
= 4[ (4 + 4tan^2(4x) ) x (2tan4x) ]
= 4[ 8tan(4x) + 8tan^3(4x) ]
= 32tan(4x) + 32tan^3(4x)
= 32tan(4x) [ 1 + tan^2(4x) ]
y = tan4x so;
= 32y(1 + y^2)

Reply 121

Zacken

Original post by Abbas.13

Yeah, that's correct, what's the problem?

Reply 122

Abbas.13

Original post by Zacken

Yeah, that's correct, what's the problem?

I didn't get what you meant by use the rule tan^2(x) + 1 = sec^2(x)

Reply 123

Zacken

Original post by Abbas.13

I didn't get what you meant by use the rule tan^2(x) + 1 = sec^2(x)

...uhm, you used it several times in your answer.

Reply 124

Abbas.13

Original post by Zacken

...uhm, you used it several times in your answer.

I did? I don't recall making use of it??

Reply 125

Fudge2

June 2013 made me lose the will to live. There's like 20 marks based on sketching/interpreting graphs. Give me 20 marks of integration instead :frown:

Reply 126

C0balt

Original post by Fudge2

June 2013 made me lose the will to live. There's like 20 marks based on sketching/interpreting graphs. Give me 20 marks of integration instead :frown:

Yeah I bloody hated it

Reply 127

Ano123

Original post by Fudge2

June 2013 made me lose the will to live. There's like 20 marks based on sketching/interpreting graphs. Give me 20 marks of integration instead :frown:

Evaluate

\displaystyle \int_{1/4}^{1/2} \frac{1}{x^2\sqrt{ 1-x^2}} dx

.
May not be 20 marks. But it may be quite a few.

(edited 7 years ago)

Reply 128

Fudge2

Original post by Ano123

Evaluate

\displaystyle \int_{1/4}^{1/2} \frac{1}{x^2\sqrt{ 1-x^2}} dx

.
May not be 20 marks. But it may be quite a few.

How'd I do? :smile:

cool question

Reply 129

xs4

Original post by Fudge2

How'd I do? :smile:

cool question

I got the same as you (2.14093) 2.14 to 3 s.f :smile:

Reply 130

Ano123

Original post by Fudge2

How'd I do? :smile:

cool question

Original post by xs4

I got the same as you (2.14093) 2.14 to 3 s.f :smile:

Very good, but exact values are preferable - but I suppose it doesn't matter.
I used u=1/x sub. Transforms it into a very easy integral. The exact value is √15 -√3.

(edited 7 years ago)

Reply 131

Suits101

Hi,

I've literally just read the last page of this thread so I don't know if this question is considered difficult/easy so I might be posting inappropriately! And I've just had to look how to use LaTex...

I don't know if these types of questions are still on spec, but I tried to make it difficult by combining quite a few rules and identities.

Solve:

Unparseable latex formula:

\int\frac{4+x}\sqrt{(4-2x^{2})}

Giving your answer in the simplest rationalised form.

I have worked out the solution and will post it tomorrow!

(edited 7 years ago)

Reply 132

Fudge2

Original post by Ano123

Very good, but exact values are preferable - but I suppose it doesn't matter.
I used u=1/x sub. Transforms it into a very easy integral. The exact value is √15 -√3.

Yeah I tried to get an exact value but the lower limit of arcsin(0.25) isn't nice so my calculator wouldn't give me nice values :tongue:

u=1/x...I'd never spot that haha

(edited 7 years ago)

Reply 133

Ano123

Original post by Fudge2

Yeah I tried to get an exact value but the lower limit of arcsin(0.25) isn't nice so my calculator wouldn't give me nice values :tongue:

u=1/x...I'd never spot that haha

You could have still got an exact answer using your sub instead of mine. You just need to know what cot(arcsinx) is. :smile:

Reply 134

Ano123

Original post by Suits101

Unparseable latex formula:

\int\frac{4+x}\sqrt{(4-2x^{2})}

Giving your answer in the simplest rationalised form.

I have worked out the solution and will post it tomorrow!

Reply 135

Ano123

∫ √(1+sin2x) dx
This one is tricky.
[latex doesn't seem to be working properly.]

(edited 7 years ago)

Reply 136

Qcomber

Original post by Suits101

Unparseable latex formula:

\int\frac{4+x}\sqrt{(4-2x^{2})}

Giving your answer in the simplest rationalised form.

I have worked out the solution and will post it tomorrow!

This would not come up on C3, only fp2

Reply 137

Suits101

Original post by Qcomber

This would not come up on C3, only fp2

Hi.

In the AQA textbook these questions are in the Core 3 section, especially since it's just a u substitution mixed with arcsin formula which the chapter includes.

I haven't seen any come up, but just incase I posted it.

Reply 138

Qcomber

Original post by Suits101

If it does come up, they shouldn't have because knowledge of inverse trigonometrical integration is not on the spec for c3. Whereas the fp2 spec clearly states that you need to know that it even exists in the formula book.