My answers for this morning's exam, please let me know if you agree/disagree on answers!
Q1 Roots of Polynomials
(a) alpha+beta=6 [2marks]
alpha*beta=14
(b) 7X^2-4X+7=0 [5 marks]
Q2 Gradients using h
(a) -h-3 [3 marks]
(b) as h-->0 gradient-->-3 [2 marks]
when h=0 gradient= -3
Q3 Log graph
(a) show linear relationship log(Y)= Xlog(B) + Log(A) [2 marks]
(b)gradient was -0.4 [1marks]
(c) a= 316 [4 marks]
b=0.398
Q4 General Solutions
(a) k=6 [1 marks]
(b) x= πn+ π/2 [4marks]
x= πn+ π/3
(c) root 3 [2 marks]
Q5 summations
(a) show it equal to 3n(4n^2-1) [5 marks]
(b) n(2n+1)(2n-3)(n-1) [4marks]
Q6 parobola
(a) show a=2 [3 marks]
(b) k= 1/2 [6 marks]
k= -2
k=0
Q7 Complex Numbers
(a) -2+4i [3 marks]
-2-4i
(bi) i+qi=0 therefore q must beequal to -1 [2 marks]
(bii) p=4 q= -12-i [5marks]
p=-4 q= 4-i
Q8 Matrices
(a) matrix 4 0 [1 marks]
0 1
(b) stretch in x-direction SF4 [1 marks]
(c)matrix 0.5 -root3/2 [2marks]
-root3/2 -0.5
(d) matrix p= -2root3 [6marks]
-2
Q9 graph
(a) Asymptotes: x=0.5 x=2 y=0 [2 marks]
(b) Intersections: x=5/2 x=1 x=0 [3 marks]
(c) a sketch [3 marks]
(d) x<equal to 0 [3marks]
0.5< to x<equal to1
2<x<equal to 2.5