C3 Jan 06 MS
C3 Jan 06 MS
C3 Jan 06 MS
1) Graphical questions (I don't have a working scanner, so I can't scan a graph into
the computer).
= (x + 3)/(x + 1)
y = ln(x/3) = ln x - ln 3
dy/dx = 1/x
At P, dy/dx = 1/3.
y = -3x + 9
4ai) x²e3x + 2
4aii) cos(2x³)/3x
= -2xsin(2x³) - cos(2x³)/3x²
4b) x = 4sin(2y + 6)
dx/dy = 8cos(2y + 6)
x² = 2/x + 0.5
x³ = 2 + 0.5x
2x³ - x - 4 = 0
R = √160 = 4√10
(4√10)sin a = 4
sin a = 1/√10
a = 18.4349488...
x° = 37.9645...°, 285.165...°
6ci) -4√10
(x + 18.4349488...)° = 180°
x° = 161.565...
x° = 161.57° (2 d.p.)
2cosθ(cosθ - sinθ) - 1 = 0
2cos²θ - 2sinθcosθ - 1 = 0
sin2θ = cos2θ
sin2θ/cos2θ = 1
tan2θ = 1
= e2(2x + ln2)
= e4x + ln4
= e4x.eln4
= 4e4x
8b) Graphical question (I don't have a working scanner, so I can't scan a graph into
the computer).
16e4x = 3
e4x = 3/16
4x = ln(3/16)
x = 0.25ln(3/16)
x = -0.418494...
x = -0.418 (3 s.f.)