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# Official thread FP1, 1st Febraury 2010 watch

• View Poll Results: How do you rate this paper (on a scale of 1-10 with 10 being the best)?
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1. (Original post by quietlyconfidant)
no one fancy doing a mark scheme then????
I think everyone's over the exam now.
2. (Original post by cambo211)
which would be surprising as the paper was out of 75...
sorry 74/75
3. did everyone get -8 and 6 for the coordinates of the very last question?
4. (Original post by Khodu)
[latex] z_{1} = 2+8i , z_{2} = 1-i [/l

9. Matrices

My first ever attempt with latex, do not laugh lol
Would You or someone please do question 3, and break down the marks,? , also how much marks do you think i will losr for not saying , because it it ture for n=1, true for all R,

5. (Original post by Rough Inclined Plane)
did everyone get -8 and 6 for the coordinates of the very last question?
For 9e I think it was (-4(sqrt)2 , 3(sqrt)2).
Would You or someone please do question 3, and break down the marks,? , also how much marks do you think i will losr for not saying , because it it ture for n=1, true for all R,

You could look at the mark scheme for Jan 09, there's a very similar question to the one we got.
7. well i dont think anyone is that bothered to make a mark scheme cus it was a straight forward exam
8. (Original post by Robofish)
well i dont think anyone is that bothered to make a mark scheme cus it was a straight forward exam
No I mean the exam from last year January 2009.
9. (Original post by Mastercard)
For 9e I think it was (-4(sqrt)2 , 3(sqrt)2).

That's what I got.
10. (1) Complex numbers

Find:
Credit to 2710 i think
a)

ans=

b)

c)

(2) Root Intervals

(a) Write down, to 3 decimal places, the value of f(1.3) and the value of f(1.4).

The equation f(x) = 0 has a root α between 1.3 and 1.4
(b) Starting with the interval [1.3, 1.4], use interval bisection to find an interval of width
0.025 which contains α.

(c) Taking 1.4 as a first approximation to α, apply the Newton-Raphson procedure once to
f(x) to obtain a second approximation to α, giving your answer to 3 decimal places.

3. Proof by induction
4. Co-ordinate systems- parabola
5. Matrices

Credit to Mastercard

Given Matrix A, which I think looked like this . But I'm not sure about the -2 and 5.

(a) Find Det A. Det A =

(b) Prove that Matirix A is non-singular for all values of a.

and therefore the Matrix is non-singular.

(c) Find given that a=0.

6.Complex numbers

Credit to Mastercard

Given that two roots of the equation are find:

(a) The third root. Answer .

(b) Find the values of a and b. Answer .

(c) Display the three roots on an Argand diagram.

7.Co-ordinate systems rectangular hyperbola
8. Proof by induction and summation

a) = =
Prove true for all positive integers.

Prove that is true

= (4)= 1

Therefore true for

Assume true for

Prove true for

=

= +

=

= =

=

Therefore true for if is true. True for , therefore by induction true for all positive integers.

9. Matrices
11. (Original post by Khodu)
(1) Complex numbers

Find:
Credit to 2710 i think
a)

ans=

b)

c)

(2) Root Intervals

(a) Write down, to 3 decimal places, the value of f(1.3) and the value of f(1.4).

The equation f(x) = 0 has a root α between 1.3 and 1.4
(b) Starting with the interval [1.3, 1.4], use interval bisection to find an interval of width
0.025 which contains α.

(c) Taking 1.4 as a first approximation to α, apply the Newton-Raphson procedure once to
f(x) to obtain a second approximation to α, giving your answer to 3 decimal places.

3. Proof by induction
4. Co-ordinate systems- parabola
5. Matrices

Credit to Mastercard

Given Matrix A, which I think looked like this . But I'm not sure about the -2 and 5.

(a) Find Det A. Det A =

(b) Prove that Matirix A is non-singular for all values of a.

and therefore the Matrix is non-singular.

(c) Find given that a=0.

6.Complex numbers

Credit to Mastercard

Given that two roots of the equation are find:

(a) The third root. Answer .

(b) Find the values of a and b. Answer .

(c) Display the three roots on an Argand diagram.

7.Co-ordinate systems rectangular hyperbola
8. Proof by induction and summation

a) = =
Prove true for all positive integers.

Prove that is true

= (4)= 1

Therefore true for

Assume true for

Prove true for

=

= +

=

= =

=

Therefore true for if is true. True for , therefore by induction true for all positive integers.

9. Matrices
i think 6 is wrong....
12. (Original post by fredbraty)
i think 6 is wrong....
Why do you say that?
13. (Original post by 2710)
Why do you say that?
a was 49 but b was 100 and something i think
14. can some do question 9
15. (Original post by fredbraty)
a was 49 but b was 100 and something i think
No. Given that one of the roots is 2, if you sub in 2 for x, and 49 and -58, you get 0, which is correct. On the other hand, if you sub in 100 something....

Sorry mate
16. (Original post by 2710)
No. Given that one of the roots is 2, if you sub in 2 for x, and 49 and -58, you get 0, which is correct. On the other hand, if you sub in 100 something....

Sorry mate
hm...as i said i am not sure
17. (Original post by quietlyconfidant)
can some do question 9
9a) Find the transformation represented by Matrix .

b) =

Therefore, and
Which gives .

c) Distance between and the origin =

e) Transform using matrix squared.

I hope I haven't made any stupid errors here. Had to do it from memory since the paper's been taken down.
18. thanks very much. i think thats what i got. repped bam!
19. thank youuu nice paper i thought

20. any maths people around... Getting scared. Going to have to do S1,S2,M1,C4 in June. And that's the minimum.

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