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PSLE Foundation Mathematics

<ol class="abc-list"><li><div class="list-item-paragraph">State a sequence of transformations that will transform the circle with equation \({{x}^{2}}+{{y}^{2}}=1\). State a sequence of transformations that will transform the circle with equation \(\frac{{{\left( x-2 \right)}^{2}}}{9}+{{y}^{2}}=1\).<span class="inline-marks">[2]</span></div></li><li><div class="list-item-paragraph">A curve \(C\) with cartesian equation \(y=\frac{x}{\sqrt{5-{{x}^{2}}}}\) is shown below. \(R\) is the finite region enclosed by \(C\), the \(x\)-axis and the line \(x=1\).</div><div class="content-block list-item-image" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/converted/1759918646437-xhkm9yl7e6.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvY29udmVydGVkLzE3NTk5MTg2NDY0MzcteGhrbTl5bDdlNi5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkzODU0NzQ2LCJleHAiOjE3OTM4NTUwNDZ9.uUWK40BZWWQ4Q_ypBAn-vhTwsVYEszlTlgfYsR8L8TQ" alt="List item image" class="aligncenter custom-width" style="max-width: min(400px, 100%); height: auto;" /></div><ol class="i-list"><li><div class="list-item-paragraph">Find the exact area of \(R\).<span class="inline-marks">[3]</span></div></li><li><div class="list-item-paragraph">Find the exact volume of the solid formed when&nbsp;\(R\) is rotated through \(2\pi \) radians about the \(y\)-axis.<span class="inline-marks">[6]</span></div></li></ol></li></ol>

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