SPS SPS FM Pure 2021 June — Question 5 8 marks

Exam BoardSPS
ModuleSPS FM Pure (SPS FM Pure)
Year2021
SessionJune
Marks8
TopicIntegration by Parts

5
2
4 \end{array} \right) + \mu \left( \begin{array} { c } 3
1
- 2 \end{array} \right) \end{aligned}$$ \(P\) is the point of intersection of \(l _ { 1 }\) and \(l _ { 2 }\).
  1. Find the position vector of \(P\).
  2. Find, correct to 1 decimal place, the acute angle between \(l _ { 1 }\) and \(l _ { 2 }\).
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    4. Solve the quadratic equation \(x ^ { 2 } - 4 x - 1 - 12 i = 0\) writing your solutions in the form \(a + b i\).
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    5. \(\int _ { 1 } ^ { 2 } x ^ { 3 } \ln ( 2 x ) \mathrm { d } x\) can be written in the form \(p \ln 2 + q\), where \(p\) and \(q\) are rational numbers. Find \(p\) and \(q\).