Advanced level 2023 northwest regional mock further mathematics 2
Advanced level 2023 northwest regional mock further mathematics 2
1. Show tljiatt,^ Vl+ Ax2dx —
Hence W,Qtlicr^j:sc.:.find the length of arcLofthe Darabola y2
Further show that the area of the surface
— 7T. generate* when the arc
V2+il„( 4 marks
= a:,for which 0 < y<
L is rotated completely aboutthe x-
3 marks
axis is
4 4marks
§
I
2. Given the differential equation
-Ay — 2e~2x-f-1.
Find the complementary function ofthis differentialequation.
Hence findthe solution ofthe differential equation for which when s
3. a)Solvc 4tanh completely x — sinh the 2xequationju = 0. ^^
Given that y-sinhAa;),
prove by Mathematical induction that
dx^_
1/4.Find thegcd(40321,35287). .
Hence find the values of aand b for which
40321a+352876 =1.
c) Solve the congruence
7x = 2(modl5)
Hence,using the Chinese remaindertheorem or otherwise solve the system
7x = 2(modl5)
3a:=l(mod4)
5.The Cartesian equation ofaHyperbolaHis
i-.i
y
d2y
dx2
2marks
0,^-= 0=f. 6 marks
1/
3 marks
-4 nsinhI( a:),neN. 4marks
2 marks
3 marks
1 mark
3 marks
x2
16 4
Find
i) thefoci andthedirectriceofH.
ii) theequationofthetangentatthepoint P(xvyl)
iii) the equation ofthe normal at P.
1. Show tljiatt,^ Vl+ Ax2dx —
Hence W,Qtlicr^j:sc.:.find the length of arcLofthe Darabola y2
Further show that the area of the surface
— 7T. generate* when the arc
V2+il„( 4 marks
= a:,for which 0 < y<
L is rotated completely aboutthe x-
3 marks
axis is
4 4marks
§
I
2. Given the differential equation
-Ay — 2e~2x-f-1.
Find the complementary function ofthis differentialequation.
Hence findthe solution ofthe differential equation for which when s
3. a)Solvc 4tanh completely x — sinh the 2xequationju = 0. ^^
Given that y-sinhAa;),
prove by Mathematical induction that
dx^_
1/4.Find thegcd(40321,35287). .
Hence find the values of aand b for which
40321a+352876 =1.
c) Solve the congruence
7x = 2(modl5)
Hence,using the Chinese remaindertheorem or otherwise solve the system
7x = 2(modl5)
3a:=l(mod4)
5.The Cartesian equation ofaHyperbolaHis
