**1**

# HSN Maths Quiz

### #1

Posted 13 January 2005 - 05:29 PM

The thread will remain closed so as to allow others to chance to find the answers for themselves

users can PM me there answers if they wish or ask for help

Questions will be made up be me so cannot be found in textbooks

Qustion will follow this weekend

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### #2

Posted 14 January 2005 - 06:26 PM

^{1/2}find f'(5) to 3 sig fig

2) Solve {limits: 0-3} x

^{3}+ 3x dx

3) Fred keeps fish in his pond, initially he has 20 fish. fred assumes that each year he will lose 25% of his fish stock and so each year he adds 4 fish to his pond.

a) how many fish will Fred have after 3 years

b) for the recurrence relation to have a limit what condition must be met

c) how many fish will be in the pond in the long term

4) The graphs of 2cos x and 4 sin 2x are plotted on one axis. find the points of intersection

5) If tan = 4/5 find cos 2 and sin 2 as a fraction

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### #3

Posted 22 January 2005 - 02:03 PM

**answers**

1) f'(x) = 1/2(8x-5)

^{ -1/2}* 8

= 4* 1/ 8x-5

f'(5) = 4 * 1/ 35

2) {limits} 0 to 3 x

^{3}+ (3x)

^{1/2}dx

[x

^{4}/4 + 3x

^{3/2}/3/2]

[x

^{4}/4 + 6x

^{3/2}/3]

[x

^{4}/4 + 2x

^{3/2}]

3

^{4}/4 + 6

^{3/2}- 0

20.25 + 54

3)

a)

U

_{n+1}= 0.75 U

_{n}+ 4

U

_{3}= 17.69

(answer can be found by finding U

_{1}then U

_{2}to finally find U

_{3})

b) -1<a<1

c) L = b/1-a

L = 4/(1-0.75)

L= 4/0.25

L = 16

4)

2cos x = 4 sin 2x

cos x = 2sin2x

cos x = 2(2sinxcosx)

cos x = 4 sinxcosx

4sinxcosx-cosx = 0

cosx(4sinx-1)=0

cosx =0 4sinx-1=0

x = 90, 270 sinx = 1/4

x = 14.5,165.5

2cos 90 = 0 A(90,0)

2cos 270=0 B(270,0)

2cos 14.5 = 2 C(14.5,2)

2cos 165.5 = -1.9 D(-1.9)

5) if you draw the triangle you will find:

cos = 5/ 41

sin = 4/ 41

cos2 = cos

^{2}- sin

^{2}

= (5/ 41) - (4/ 41)

= 25/41- 16/41

= 9/41

sin2 = 2sin cos

2*(4/ 41) * (5/ 41)

40/41

i hope you all did ok in this

Dave

If i am not here i am somewhere else

### #4

Posted 22 January 2005 - 02:25 PM

1) Express 3-6x - x in the form a(x+p) + b

2) Prove that sin 2 1 + cos 2[theta] = tan

3) Find k if 2x + x + kx -8 is divisible by x+2

4) Find P given (P+1)x[^2] -2(P+3)x + 3P = 0 has equal roots

5)Solve the trignometric equation for 0 x 360

cos 2x - 3cosx + 2 = 0

Happy mathing

dave

If i am not here i am somewhere else

### #5

Posted 07 February 2005 - 05:24 PM

1) 3 - 6x - x

^{2}

= -x

^{2}- 6x + 3

= -(x

^{2}+6x) +3

= -(x

^{2}+6x+9)-9+3

= -(x+3)

^{2}-6

2) sin 2 /1 + cos 2[theta]

= 2sin[theta]cos[theta]/2cos

^{2}

= sin[theta]/cos[theta] = tan[theta]

3) using remander theorem on (x+2)

solve what you get -20-2k = 0, k = -10

4) as equal roots b

^{2}-4ac = 0

sub in values you should get after simplifiing

4(p

^{2}+ 6P +9) = 0

4(p+3)(P+3) =

P=-3

5)

cos2x -3cosx + 2 =0

2cos

^{2}x -1 -3cosx+2 = 0

2cos

^{2}x - 3cosx +1=0

(2cosx - 1)(cosx -1)=0

2cosx-1 =0 , cosx - 1= 0

cosx = 1/2 , cosx x = -1

x = 60,300 , x = 0

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### #6

Posted 04 January 2006 - 04:42 PM

### #7

Posted 04 January 2006 - 04:44 PM

Thanks

### #8

Posted 04 January 2006 - 05:16 PM

Think it's unit 2, something about sin and cos rules and stuff like that.

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### #9

Posted 04 January 2006 - 08:17 PM

These are all very common type questions and arent particularly easy ones either. Mostly adapted from the kind of homework questions i got as "formal homework exercises" which were very good exam practice for me back then

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### #11

Posted 10 January 2006 - 02:52 PM

I know it was almost a year ago but your answer to question 4 on 22 Jan 2005 is wrong. I suggest you try the integration again.

### #12

Posted 10 January 2006 - 02:53 PM

### #13

Posted 10 January 2006 - 03:50 PM

fixed now

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### #14

Posted 10 January 2006 - 04:16 PM

Integrating (3x)^1/2 is not the same as integrating 3(x)^1/2 which is what you have done.

### #15

Posted 10 January 2006 - 04:22 PM

### #16

Posted 10 January 2006 - 04:24 PM

Ditto.

edit: I was being stupid.

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### #17

Posted 10 January 2006 - 04:38 PM

or

(3x)^1/2

is the same as 3^1/2 * x^1/2

whereas 3(x)^1/2 is 3*x^1/2

### #18

Posted 10 January 2006 - 07:43 PM

it is correct what you say, however 3

^{1/2}is no more than a constant and isnt effected by the integration

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### #19

Posted 10 January 2006 - 08:30 PM

I was confused as to what the integral was though, or . This is what I get:

and:

For the first one, you could also do:

which is the same answer.

### #20

Posted 11 January 2006 - 06:29 AM

Could someone tell me how I can type in the math symbols please.

Thank you

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