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Further Mathematics

A Level

It is given that f(x)=(x^2 +9x)/((x-1)(x^2 +9)). (i) Express f(x) in partial fractions. (ii) Hence find the integral of f(x) with respect to x.

(i) Let f(x) = A/(x-1) + B/(x²+9). Multiplying through by (x-1)(x²+9) we get x²+9x = A(x²+9) + B(x-1). By substituting x=1 in to eliminate B, we find that A=1 ,...

Answered by Amy C. • Further Mathematics tutor

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Find the square roots of 2 + isqrt(5)

Since we’re finding the square roots of 2 + isqrt(5) then (x+iy)^2 = 2 + isqrt(5)Thereforex^2 + 2ixy - y^2 = 2 + isqrt(5)Take real and imaginary parts it followsx^2 - y^2 = 2 and 2ixy = isqrt(5)solving th...

Answered by Samuel L. • Further Mathematics tutor

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How to multiply and divide by complex numbers

Multiplying and dividing by complex numbers is very similar to how you have learned how to multiply and divide surds (numbers with a rational and irrational part) in GCSE and early A-Level. Take two compl...

Answered by • Further Mathematics tutor

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A particle is projected from the top of a cliff, 20m above the sea level at an angle of 30 degrees above the horizontal at 20m/s. At what vertical speed does it hit the water?

Using SUVAT equations:s = -20mu = 20sin(30) = 10m/sv = ?a = -9.8m/s^2t = ?v^2 = u^2 + 2asv = sqrt(100 + 40x9.8)= 22.2m/s

Answered by Adam R. • Further Mathematics tutor

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A child weighing 50kg is pushed down a 2m long slide (u=0.1), angled at 45 degrees from the horizontal, at 5m/s. At what speed does the child reach the bottom of the slide?

Change in GPE=Change in KE + ResistanceResistance = ForcexDistnaceForce=Friction= R u = masscos45g2 * 0.1Change in KE = 0.5m*(v²-25)Change in GPE = mg2Sin 45Can cance...

Answered by Matthew W. • Further Mathematics tutor

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