AQA Maths FP1 - 15 June 2016 [Exam discussion]

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

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

Messed up on the summations series question and complex numbers ((((((

This is what the graph sketching shouldve looked like, (if the equation i typed in is correct)

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

I think I got -2<k<0.5

What was the equation of C the parabola? I can't remember what it was.

This?

No the one with the parabola where you had to find possible k values.

What was the equation of C the parabola? I can't remember what it was.

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...

Roots of quadratic equations
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,
b is 10^grad,

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]