# AH Maths 2004

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### #1james1

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Posted 21 May 2004 - 03:44 PM

How did everyone find it?

These are unofficial solutions subject to checking. There may be typing errors for example. Let me know if you find errors.

### #2james1

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Posted 21 May 2004 - 05:23 PM

Q1 a

e^tanx(1-sin2x)

0

(4 marks)

Q1 b

(2-8x invtan(2x))/(1+4x^2)^2

(3 marks)

### #3james1

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Posted 21 May 2004 - 05:41 PM

Q2

4a^8 -12a^6 +54a&4 -108a^2 +81

(3 marks)

### #4james1

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Posted 21 May 2004 - 05:42 PM

Q 3

-cot(theta)

y+x=0.5*root 10

(5 marks)

### #5james1

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Posted 21 May 2004 - 05:44 PM

Q4

-10+20i
Proof
-5, 1+2i, 1-2i

(6 marks)

### #6james1

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Posted 21 May 2004 - 05:47 PM

Q5

Very odd question for the second part.

0.2/(x-3) - 0.2/(x+2)

-0.162 (did anyone else get this)

(6 marks)

### #7james1

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Posted 21 May 2004 - 05:50 PM

Q6

M1 = 0 -1
1 0
M2 = 1 0
0 -1
M2M1 = 0 -1
-1 0

Geometrical effect:

### #8james1

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Posted 21 May 2004 - 05:51 PM

Q7

f(x) = x +x^2 + (1/3) x^3

(5 marks)

### #9james1

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Posted 21 May 2004 - 05:56 PM

Q8

Proof
x=-5
y=68

(4 marks)

### #10james1

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Posted 21 May 2004 - 06:01 PM

Q9 Fully simplified

(1/root x +1)[1/(root x+1) -1]

(5 marks)

### #11james1

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Posted 21 May 2004 - 06:03 PM

Q 10

Odd function

(3 marks)

### #12james1

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Posted 21 May 2004 - 06:04 PM

Q11

0.25Pi(1-e^-4) units^3

(5 marks)

### #13james1

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Posted 21 May 2004 - 06:05 PM

Q 12

Proof by induction using derivatives!

(5 marks)

### #14james1

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Posted 21 May 2004 - 06:09 PM

Q13

x=-2
y=1

f'(x) = 0
5 = 0 therefore no stationary points

No f'(x) does not equal zero and there is no change in concavity

x=1
y=-2
x member of set of real numbers, x does not equal one
OR x>1 and x<1

### #15james1

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Posted 21 May 2004 - 06:14 PM

Q13

x=-2
y=1

f'(x) = 0
5 = 0 therefore no stationary points

YES THERE IS A POINT OF INFLEXION!

x=1
y=-2
x member of set of real numbers, x does not equal one

### #16james1

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Posted 21 May 2004 - 06:15 PM

Q14
A)

2X+3Y+Z=5

51.9 degrees

(3,5,8)

(10 marks)

### #17james1

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Posted 21 May 2004 - 06:19 PM

Q15

a)

y=x^4+cx^3

y=x^4+x^3

y= root of (.4x^2 +3x^2 +0.6)

(11 marks)

### #18james1

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Posted 21 May 2004 - 06:20 PM

Q16

a)

544

11

c)

a=12/11

n=7

(10 marks)

### #19james1

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Posted 22 May 2004 - 09:30 AM

Let me know if you find any errors.

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