EDEXCEL A LVL MATHS - Partial Fractions

if there is a repeated factor, (e.g the one in the image), how do u write out the partial fractions?

do the one from image

• have to do the squared term twice (one where it is squared, and 1 where it is single)

when doing the comparing coefficients method, do u have to compare all the coefficients, or just some or just 1

just 1 is needed

for partial fractions with a squared denominator, how do u find out the terms after doing substitution (the 2 methods which u could use)

• either do substitution again, but with a value which is not in the brackets e.g 0, but for all terms

• or do it by comparing coefficients

—> prob easier / quicker to compare coefficients

when is an algebraic fraction improper?

when the order of the numerator is greater than or equal to the order of the denominator

when dealing with improper fractions, how can u solve them with the remainder and which way should u do for fullproof method

• algebraic long division, and then partial fractions

• just going straight to partial fractions, but a longer partial fractions question

—> algebraic long division method

for comparing coefficients, which should u always compare and which should u try to avoid comparing because it can get complicated

• compare the highest power, and / or the lowest power (I mean the constant, without a variable, e.g 5, not 5x)

• stay away from in betweens e.g 2x

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mark scheme

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