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# AQA Maths FP1 - 15 June 2016 [Exam discussion] watch

1. (Original post by Hjyu1)
I thought that tanx=root 3 as pi(n) +pi/3 are the only possible general solution for it and as tanx had a period of pi you always get root 3. And you matrices question seemed fine as cos/sine have periods of 360 degrees so cos(-60)=cos(300) same for sine
Ahhh actually I think I got root 3!!!
I'm getting mixed up with questions lol
I'm all confused
2. (Original post by Chickenslayer69)
I can't remember exactly :/ But there was an equation with " i + qi " in it and it asked to explain why q must be -1 for it to be real
Basically as the roots were conjugate pairs the cofficent a are all real so the imaginary need to cancel out and only possible real solution for q would be -1
3. (Original post by Hjyu1)
Basically as the roots were conjugate pairs the cofficent a are all real so the imaginary need to cancel out and only possible real solution for q would be -1
Oh, right... I put that imaginary parts had to cancel, would I get a mark for that? Not sure what the other mark is for, stating the roots were conjugate pairs?
4. How many marks was the part b) of the trigonometry question)

And anyone remember what their inequalities were for question 9 last part?
5. Messed up on the summations series question and complex numbers ((((((
6. This is what the graph sketching shouldve looked like, (if the equation i typed in is correct)
7. (Original post by An1998)
Messed up on the summations series question and complex numbers ((((((
Both were a pain in the ass. Lots of people got them wrong so don't worry.
8. (Original post by An1998)
This is what the graph sketching shouldve looked like, (if the equation i typed in is correct)
Omg yes thank god!! I was sure i got that wrong, what did people get for the inequality thing after that? Think I got that wrong lool
9. Q= -12i-1 and 4i-1
P(root 3 over 2, 2)
10. Thought all the questions were easy except all the 6 marker Q's lol
Hardest Fp1 paper personally, all other years papers were a lot easier
11. (Original post by OturuDansay)
Thought all the questions were easy except all the 6 marker Q's lol
Hardest Fp1 paper personally, all other years papers were a lot easier
Agreed, I'm sure a lot of people feel the same People in my class found it hard
12. (Original post by Chickenslayer69)
I think I got -2<k<0.5
What was the equation of C the parabola? I can't remember what it was.
13. (Original post by B_9710)
What was the equation of C the parabola? I can't remember what it was.
This?
14. (Original post by Chickenslayer69)
This?
No the one with the parabola where you had to find possible k values.
15. (Original post by B_9710)
No the one with the parabola where you had to find possible k values.
forgot lol
16. (Original post by B_9710)
What was the equation of C the parabola? I can't remember what it was.
(Y-3)^2=4a(x-2)
17. Here is what I can remember. Someone make an unofficial mark scheme.
I need to focus on M1 & M2 now. I can't dwell on this.
arkhglsigh its going to drive me crazy...

2x^2 + 6x + 3 = 0 ??
alpha + beta= alphabeta=
Roots are alpha/beta & beta/alpha,
Find a quadratic equation with integer coefficients [5 marks]
7x^2 -4x + 7 =0

Linear laws
(a) y=a(b^x)so logy=loga + logb^xlogy=loga + xlogb
You are given that Y= logy and they gave us the graph of Y against x
With the intercept being 2.25??
(b) gradient is -0.4?? I've forgot :/
(i) Values of a & b to 3sf
a is 10^intercept,

General solutions to trigonometric equations
(a) If sin(pi/3) = cos (x/k), find k, k=6 [1 mark]
(b) Find general solution to cos(2x - pi/2) = sin(pi/3) ??
Ended up getting npi + pi/2 and npi + pi/3 ??
(c) Hence find the only finite value for tanx [2 marks]
Can't be pi/2 as tan(90) gives an infinite valueSo pi/3 therefore
tan(60)=root 3

Matrices
Given matrix A(a) Find A^2 [ marks]
(i) What is A^2 geometrically [2 marks]
Stretch in the x-direction by scale factor 4.
(b) Given that the reflection in line x + (root3)y so in the line y=(-1/root 3)x
Find the reflection matrix with everything in its exact trig values. [3 marks]
I found Cos(300) = 1/2 & Sin(300) = -root3/2
(c) Finding coordinates? After A^2 followed by reflection matrix to P(0,-4) [6 marks]
Root 3/2 and 2??

Complex numbers
Quadratic equation z^2 + 4z ... something like that It is given that a root is w= p + 3i ?
For z^2 + (4 + i + iq)z + 20 = 0
(a) Explain why q=-1 [2 marks]
Gets rid of imaginary parts so the coefficient of z is real.

(b) Given that w= p - 3i ?
Find other values for q
Q= -12i-1 and 4i-1

Parabola y^2=4ax, given that it is translated by [2,3] and passes (4,7) ??
(a) Show that a=2 [2 marks] (y-3)^2=4a(x-2), (4)^2=4a(2)16=8a
(b) Show values of k when it does not intersect line ky=x ? [6 marks]

Series question
(a) Show that question [ marks] 3n(4n^2-1) ??
(b) Find four linear factors [6 marks] ??
Sum from r=1 to 2n was in the question.

Graphs of rational functions
Graph: y=(x-1)/(x-2)(2x-1) ??
(a) Find asymptotes [3 marks]y=0, x=2, x=1/2 ??
(b) Sketch the graph [ marks]
y=1/2(x-1) intersects the graph(c) By forming a cubic find values where it intersects?? [ marks]
(d) Hence solve the inequality intersects the graph [3 marks]
18. Same I think although one was a minus on the i
19. (Original post by Pentaquark)
Here is what I can remember. Someone make an unofficial mark scheme.
I need to focus on M1 & M2 now. I can't dwell on this.
arkhglsigh its going to drive me crazy...

2x^2 + 6x + 3 = 0 ??
alpha + beta= alphabeta=
Roots are alpha/beta & beta/alpha,
Find a quadratic equation with integer coefficients [5 marks]
7x^2 -4x + 7 =0

Linear laws
(a) y=a(b^x)so logy=loga + logb^xlogy=loga + xlogb
You are given that Y= logy and they gave us the graph of Y against x
With the intercept being 2.25??
(b) gradient is -0.4?? I've forgot :/
(i) Values of a & b to 3sf
a is 10^intercept,

General solutions to trigonometric equations
(a) If sin(pi/3) = cos (x/k), find k, k=6 [1 mark]
(b) Find general solution to cos(2x - pi/2) = sin(pi/3) ??
Ended up getting npi + pi/2 and npi + pi/3 ??
(c) Hence find the only finite value for tanx [2 marks]
Can't be pi/2 as tan(90) gives an infinite valueSo pi/3 therefore
tan(60)=root 3

Matrices
Given matrix A(a) Find A^2 [ marks]
(i) What is A^2 geometrically [2 marks]
Stretch in the x-direction by scale factor 4.
(b) Given that the reflection in line x + (root3)y so in the line y=(-1/root 3)x
Find the reflection matrix with everything in its exact trig values. [3 marks]
I found Cos(300) = 1/2 & Sin(300) = -root3/2
(c) Finding coordinates? After A^2 followed by reflection matrix to P(0,-4) [6 marks]
Root 3/2 and 2??

Complex numbers
Quadratic equation z^2 + 4z ... something like that It is given that a root is w= p + 3i ?
For z^2 + (4 + i + iq)z + 20 = 0
(a) Explain why q=-1 [2 marks]
Gets rid of imaginary parts so the coefficient of z is real.

(b) Given that w= p - 3i ?
Find other values for qQ= -12i-1 and 4i-1

Parabola y^2=4ax, given that it is translated by [2,3] and passes (4,7) ??
(a) Show that a=2 [2 marks] (y-3)^2=4a(x-2), (4)^2=4a(2)16=8a
(b) Show values of k when it does not intersect line ky=x ? [6 marks]

Series question
(a) Show that question [ marks] 3n(4n^2-1) ??
(b) Find four linear factors [6 marks] ??
Sum from r=1 to 2n was in the question.

Graphs of rational functions
Graph: y=(x-1)/(x-2)(2x-1) ??
(a) Find asymptotes [3 marks]y=0, x=2, x=1/2 ??
(b) Sketch the graph [ marks]
y=1/2(x-1) intersects the graph(c) By forming a cubic find values where it intersects?? [ marks]
(d) Hence solve the inequality intersects the graph [3 marks]
Yes !! I think I got the same as you except I flopped the tan question cause I didn't understand what it was asking at the time but I got the same coordinates for p and the same equation for q.
20. Yes I got exactly that

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