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⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⣴⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣵⣄⠀⠀⠀
⠀⠀⢾⣻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡀⠀
⠀⠸⣽⣻⠃⣿⡿⠋⣉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣏⡟⠉⡉⢻⣿⡌⣿⣳⡥⠀
⠀⢜⣳⡟⢸⣿⣷⣄⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣠⣼⣿⣇⢸⢧⢣⠀
⠀⠨⢳⠇⣸⣿⣿⢿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡟⢆⠀
⠀⠀⠈⠀⣾⣿⣿⣼⣿⣿⣿⣿⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣽⣿⣿⠐⠈⠀⠀
⠀⢀⣀⣼⣷⣭⣛⣯⡝⠿⢿⣛⣋⣤⣤⣀⣉⣛⣻⡿⢟⣵⣟⣯⣶⣿⣄⡀⠀
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣶⣶⣴⣾⣿⣿⣿⣿⣿⣿⢿⣿⣿⣧
⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡿
4x 2 – y3 – 4xy + 2y
= 0
The point P with coordinates (–2, 4) lies on C.
(a) Find the exact value of d
d
y
x
at the point P.
(6)
The normal to C at P meets the y-axis at the point A.
(b) Find the y coordinate of A, giving your answer in the form p + qln2, where p and q
are constants to be determined.
(
Water is leaking from a hole P on the side of the tank.
At time t minutes after the leaking starts, the height of water in the tank is h cm.
The height h cm of the water in the tank satisfies the differential equation
d
d
h
t = − k h( ), 9
1
2 9 < h -200
where k is a constant.
Given that, when h = 130, the height of the water is falling at a rate of 1.1cm per minute,
(a) find the value of k.
(2)
Given that the tank was full of water when the leaking started,
(b) solve the differential equation with your value of k, to find the value of t when h = 50
(6)
standard deviation 7.5 cm.
(a) Find the probability that a randomly chosen adult female is taller than 150 cm
May Allah bless you,
with love, wisdom and joy.
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░░░░░░▐▌▀▄▀▄▀▐▄SPOOKY SKELETON
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░░░░░░▐▌▀▄▀▄▀▐▄SPOOKY SKELETON
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