Core 3 OCR Past Papers - The Grange School Blogs
Core 3 OCR Past Papers - The Grange School Blogs
Core 3 OCR Past Papers - The Grange School Blogs
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Jan 2007<br />
6<br />
3<br />
<strong>The</strong> diagram shows the curve with equation y =<br />
and the lines x = 0, x = 2andy = 0.<br />
1<br />
√ 3x + 2<br />
. <strong>The</strong> shaded region is bounded by the curve<br />
(i) Find the exact area of the shaded region. [4]<br />
(ii) <strong>The</strong> shaded region is rotated completely about the x-axis. Find the exact volume of the solid<br />
formed, simplifying your answer. [5]<br />
7 <strong>The</strong> curve y = ln x is transformed to the curve y = ln( 1 x − a) bymeansofatranslationfollowedbya<br />
2<br />
stretch. It is given that a is a positive constant.<br />
(i) Give full details of the translation and stretch involved. [2]<br />
(ii) Sketch the graph of y = ln( 1 x − a). [2]<br />
2<br />
(iii) Sketch, on another diagram, the graph of y = ∣ ∣ ln(1 2 x − a)∣ ∣ . [2]<br />
(iv) State, in terms of a, thesetofvaluesofx for which ∣ ln(1 2 x − a)∣ ∣ =−ln(1 x − a). [2]<br />
2<br />
[Questions 8 and 9 are printed overleaf.]<br />
© <strong>OCR</strong> 2007 4723/01 Jan07 [Turn over