| Exam Board | WJEC |
|---|---|
| Module | Unit 3 (Unit 3) |
| Year | 2019 |
| Session | June |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Partial Fractions |
| Type | Repeated linear factor with distinct linear factor – decompose and integrate |
| Difficulty | Moderate -0.3 This is a standard partial fractions question with a repeated linear factor, requiring routine application of the cover-up method and standard integration of partial fractions. The decomposition is straightforward (form A/(x-1) + B/(x+2) + C/(x+2)²), and the integration involves only logarithms and a power rule, making it slightly easier than average but still requiring competent technique. |
| Spec | 1.02y Partial fractions: decompose rational functions1.08j Integration using partial fractions |
| Answer | Marks |
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| 1 | 0 |
| 1 | 1 |
| 1 | 2 |
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| 1 | 4 |
| 1 | 5 |
Question 1:
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1 | 5a) Express $\frac { 9 } { ( x - 1 ) ( x + 2 ) ^ { 2 } }$ in terms of partial fractions.
b) Find $\int \frac { 9 } { ( x - 1 ) ( x + 2 ) ^ { 2 } } \mathrm {~d} x$.
\hfill \mbox{\textit{WJEC Unit 3 2019 Q1}}