CAIE P3 2020 Specimen — Question 4

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2020
SessionSpecimen
TopicParametric equations

4 Th \(\mathbf { p }\) rametric eq tion \(\mathbf { 6 }\) a cn \(\mathbf { E }\) are $$x = \mathrm { e } ^ { 2 t - 3 } , \quad y = 4 \ln t$$ wh re \(t > 0\) Wh \(\mathrm { n } t = a\) th \(\mathbf { g }\) ad en 6 th cn ⊕ is 2
  1. Sba that \(a\) satisfies th eq tin \(a = \frac { 1 } { 2 } ( 3 \quad \mathrm { n } a )\).
  2. Verifyb \(y c\) alch atin \(\mathbf { h }\) tth s eq tim sarb \(\mathbf { b }\) tween \(\mathbf { l } \mathbf { d }\)
  3. Use th iterati fo mlu a \(a _ { n + 1 } = \frac { 1 } { 2 } \left( 3 - \ln a _ { n } \right)\) to calch ate \(a\) correct to 2 d cimal p aces, sh ig th resh to each teratin od cimal \(p\) aces.