![]() How do we solve first order differential equations? If the mean value of a function f(x) between a,b is M, what is the mean value of kf(x), f(x) + k and -f(x) ? How do we integrate fractions which can't be made into ln ? Get it into the form of the formulas and apply them. How do we integrate inverse trig functions? Use implicit differentiation after removing the arc, OR use chain rule alongside formula in the book How do we differentiate inverse trig functions (2 methods)? How do you work out the mean value of a function between ? How can we find the series expansion of compound functions? (Like e^sinx)Ĭo-ordinate written (r,θ) where r is its distance from the pole (0,0) and θ is the angle made with the initial line (usually + x axis)įor a curve with equation r = a(p+qcosθ) where p≥q, what are the 3 scenarios for a graph? How can we show the series expansion of any function using the maclaurin series?ĭifferentiate the function and plug in the correct values into the formula. What will happen if a method of differences is applied to f(r) - f(r+2) ?Īll will cancel except 2 terms at the start and 2 at the end Expand the sum and you should be able to cancel all expect the first and last term Get it in a form where you have the f(r) - f(r+1). How can we use the method of differences to find the sum of a series? Keep multiplying the exponential form of the vertex by 2π/(no. If given one complex vertex of a shape, how can you find the rest? ![]() They form each vertex of a regular n-gon with centre (0,0). When you find the nth roots of a complex number what is special about the roots? If n=4, sub in k=0,1,2,3 to find all your solutions (etc) Rewrite a + bi into the mod-argument form. How do we solve an equation z^n = a + bi ? Use any trig identities needed, then C = real parts, S = im parts Use reverse binomial expansion to find an exact value. With series C (cos based) and S (sin based), work out C+iS. When given two series (one involving cos, the other sin) how can you show what a specific series is equal to? Replace other e's with trigįor any sum of a complex series, what do the real and imaginary parts equal? You should now have a which you can replace with trig. The fraction will be over something including e^iθ, so times the num. How do we work out the sum of a complex series? Rewrite the 'z' side using the identities and replace with 2cos/2isin. ![]() ![]() Use the or identity and raise it to the relevant power. How do you make (cosθ)^n or (sinθ)^n into the sum of non-exponential cos/sin (i.e. Use trig identities to finish the question Equate real parts for cos or imaginary parts for sin. How do you use De Moivre's to show that sin(nθ) or cos(nθ) = some expansion involving powers of sinθ or cosθĮxpand (cosθ+isinθ)^n using both the binomial expansion and De Moivre's. (r/g)e^i(θ-x) (divide modulus, minus argument) Rge^i(θ+x) (multiply modulus, add argument) What is the exponential form of a complex number? Core Pure Year 2 A-Level Further Maths- Edexcel Question ![]()
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