H2 Further Mathematics Topical Questions - … Further Mathematics Topical Questions Compiled by Wee...

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H2 Further Mathematics Topical Questions Compiled by Wee WS (wenshih.wordpress.com) Q1

Q2

Q3

Q4

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Q5

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Q7

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Q8

Q9

Repeat the question by using the improved Euler’s method. Q10

Q11

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Q15

If ( )cos , sinP a bθ θ , ( )cos , sinQ a bφ φ are two points on the ellipse 2 2

2 2 1x y

a b+ = , where

2θ φ π+ ≠ , and if the line PQ touches the ellipse 2 2

2 2

2x y x

aa b+ = , show that sec sec 1θ φ+ = .

Q16

If the normal to the parabola 2 4y ax= at the points ( )2 , 2a aλ λ and ( )2 , 2a aµ µ intersect on

the curve, then show that 2λµ = if 0λµ > .

Q17 A population of bacteria grows logistically. Suppose the initial population is 3 mg of bacteria,

the carrying capacity is 100 mg, and the growth parameter is 0.2 hour 1− . (a) Find the differential equation satisfied by the population. (b) Find the population at any time. (c) When will be the population reach 90 mg?

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Q18

Note: Ignore the part about the phase diagram. Q19

Q20

H2 Further Mathematics Topical Questions - … Further Mathematics Topical Questions Compiled by Wee...

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