Access this ZIMSEC A-Level Pure Mathematics 2018 study guide for revision, practice, and exam preparation in Zimbabwe.
A free account is needed to download. Sign in or create one
This is the ZIMSEC A-Level Pure Mathematics study guide for Paper 2 from 2018. It is a free study guide for revision. The paper code is 6042/2.
(1)
ZIMSEC Specimen 2018
6042/2
Pure Nathematics 2
Suggested Marking Guide.
Prepared by Tarakino Nyashy Pi (Trockers) 0772978155 10717267175 SECTIONA
(1) $y=e^{x} \sin x$
\[
\begin{aligned}
\frac{d y}{d x} | =e^{x}(\operatorname{Cos} x)+\operatorname{Sin} x\left(e^{x}\right) | =e^{x}(\operatorname{Cos} x+\operatorname{Sin} x)
\frac{d^{2} y}{d x^{2}} | =e^{x}(-\operatorname{Sin} x+\operatorname{Cos} x)+(\operatorname{Cos} x+\operatorname{Sin} x) e^{x} | =-e^{x} \operatorname{Sin} x+e^{x} \operatorname{Cos} x+e^{x} \operatorname{Cos} x+e^{x} \operatorname{Sin} 4 | =2 e^{x} \operatorname{Cos} x
\end{aligned}
\]
showing that $\frac{d^{2} y}{d x^{2}}=2\left(\frac{d y}{d x}-y\right)$
$\frac{\text { Now }}{d^{2}}$
\[
\begin{array}{l}
\frac{d^{2}}{d x^{2}}=e^{x}(\sin x)
\begin{aligned}
\frac{d^{2} y}{d x^{2}} | =2 e^{x} \cos x+2 e^{x} \sin x-2 e^{x} \sin x | =2 e^{x}(\cos x+\sin x)-2 e^{x} \sin x | =2\left[e^{x}(\cos x+\sin x)-e^{x} \sin x\right] | =2\left(\frac{d y}{d x}-y\right)(\operatorname{shon} x)
\end{aligned}
\end{array}
\]
Scanned by CamScanner