Edexcel A-Level Mathematics A2 P4.2.1 Decompose Rational Functions Into Partial Fractions Questions

Practise Edexcel IAL P4.2.1 partial fractions: factor denominators, clear them to find constants, and present simplified decompositions.

Exam points

Choose the correct partial-fraction form after factoring the denominator
Clear denominators and solve the constants by substitution or coefficient comparison
State the simplified decomposition, including division first for improper forms

[Maximum number: 3]

Figure 2

Figure 2 shows a sketch of the curve defined by the parametric equations

x=t^{2}+2 t \quad y=\frac{2}{t(3-t)} \quad a \leqslant t \leqslant b

where a and b are constants.
The ends of the curve lie on the line with equation y=1

Write $\frac{t+1}{t(3-t)}$ in partial fractions.

(ii)

$\frac{t+1}{t(3-t)}=\frac{A}{t}+\frac{B}{3-t}$ $\Rightarrow t+1=A(3-t)+B t$

E.g. $t=0 \Rightarrow 1=3 A \Rightarrow A=\frac{1}{3} ; t=3 \Rightarrow 4=3 B \Rightarrow B=\frac{4}{3}$ $\frac{t+1}{t(3-t)}=\frac{1}{3 t}+\frac{4}{3(3-t)}$

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Edexcel A-Level Mathematics A2 P4.2.1 Decompose Rational Functions Into Partial Fractions Questions question 1