Neco 2020 Further Mathematics Question 4

Practice essay / theory question 4 from the 2020 Neco Further Mathematics examination. This question covers Partial Fractions .

Neco 2020 Further Mathematics Essay / Theory

Topic: Partial Fractions

Question 4 NECO • 2020 • FURTHER_MATHEMATICS • essay

Consider the rational expression \(\dfrac{2x+k}{x^{2}+5x+6}\). The denominator can be factorised as \((x+2)(x+3)\).

Question Parts

( a )

Find the integer value of \(k\) for which the partial‑fraction decomposition \(\dfrac{2x+k}{(x+2)(x+3)}=\dfrac{A}{x+2}+\dfrac{B}{x+3}\) yields integer constants \(A\) and \(B\).

( b )

For the value \(k=4\) found in part (a), determine the constants \(A\) and \(B\).

( c )

Verify the decomposition by recombining the fractions for \(k=4\).

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About This Question

This is Neco 2020 Further Mathematics Question 4. It is one of the essay questions from the 2020 Neco Further Mathematics examination.

The question covers Partial Fractions .

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