Quick questions on Partial fractions: distinct and repeated linear factors - OCR A-Level Maths A

5short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What are repeated factors?

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A repeated factor

(x - a)^2

needs both

\dfrac{A}{x - a}

and

\dfrac{B}{(x - a)^2}

in the decomposition. Substituting

x = a

gives the

B

term directly; the remaining constant comes from a second substitution or by comparing coefficients.

What are improper fractions?

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If the numerator's degree is at least the denominator's, the fraction is improper: divide first to get a polynomial plus a proper fraction, then split the proper part.

What is sign slips clearing the denominator?

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Expand

A(x - b)

and

B(x - a)

carefully and substitute the values that zero a factor to isolate each constant.

What is q1?

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Express

\dfrac{7}{(x - 2)(x + 5)}

in partial fractions. [3 marks]

What is q2?

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Integrate

\displaystyle\int\dfrac{1}{x - 2} + \dfrac{2}{x + 1}\,dx

. [2 marks]

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