ZIMSEC Secondary Mathematics Paper 1 June 2011 Marking Scheme

About this marking scheme

This is the ZIMSEC Mathematics marking scheme for Paper 1 from June 2011. It shows how marks are awarded, so you can mark your own answers.

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Text from the first page

JUNE ZOIV? 1) $\left|3^{-32}-54\right|<27$
\[
\begin{aligned}
-27  |  <3^{-34}-54
27  |  3^{-33}
\end{aligned}<7
\]
critical values.
\[
\begin{array}{l}
\left(3^{-3 x}-54\right)^{2}=27^{2}
\left(3^{-3 x}\right)^{2}-54 \cdot 3^{-3 x} \cdot 2+2916=729 .
\left(3^{-3 x}\right)^{2}-108\left(3^{-3 x}\right)+2197=0 .
\end{array}
\]
lef $y=3^{-3 x}$
\[
\begin{aligned}
y^{2}-108 y+2187  |  =0
(y-54)^{2}  |  =-2187+2196
(y-54)^{2}  |  =729
y-54  |  = \pm 27
y  |  =54 \pm 27   |  =27 \text { or s1. }
\end{aligned}
\]
\[
\begin{aligned}
3^{-3 x}  |  =2 / 7
3^{-3 x}  |  =3^{3}
-3 x  |  =3
x  |  =-1
\end{aligned}
\]
\[
\begin{aligned}
3^{-3 x}  |  =81
3^{-3 x}  |  =3^{4}
-3 x  |  =4
x  |  =-\frac{4}{3}
\end{aligned}
\]
\[
\therefore-4 / 3<x<-1
\]