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 2006<br />
1 Show that <br />
2<br />
8<br />
2<br />
3<br />
dx = ln 64. [4]<br />
x<br />
2 Solve, for 0 ◦ < θ < 360 ◦ , the equation sec 2 θ = 4tanθ − 2. [5]<br />
3 (a) Differentiate x 2 (x + 1) 6 with respect to x. [3]<br />
(b) Find the gradient of the curve y = x2 + 3<br />
x 2 at the point where x = 1. [3]<br />
− 3<br />
4<br />
<strong>The</strong> function f is defined by f(x) =2 − √ x for x ≥ 0. <strong>The</strong> graph of y = f(x) is shown above.<br />
(i) State the range of f. [1]<br />
(ii) Find the value of ff(4). [2]<br />
(iii) Given that the equation |f(x)| = k has two distinct roots, determine the possible values of the<br />
constant k. [2]<br />
5<br />
<strong>The</strong> diagram shows the curves y =(1 − 2x) 5 and y = e 2x−1 − 1. <strong>The</strong>curvesmeetatthepoint( 1 2 ,0).<br />
Find the exact area of the region (shaded in the diagram) bounded by the y-axis and by part of each<br />
curve. [8]<br />
4723/Jan06
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