MEI C2 Study Resources Core2 Further Differentiation And by Catherine Berry

By Catherine Berry

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X2 y x Find the area enclosed between the graph and the x-axis.

3] (ii) Find the value of x for which A has a stationary point, and show that this is a minimum point. [4] (iii) Find the dimensions of the tank for which A is as small as possible, and the corresponding value of A. [2] © MEI, 18/08/08 1/2 MEI C2 Further calculus assessment 8. The diagram shows part of the graph of y = 5 − x 2 − 4 . x2 y x Find the area enclosed between the graph and the x-axis.

MEI C2 Further calculus Section 2 MC tests 5) 1 ∫ (2 x − 1) 3 0 x dx = (b) − 32 (a) 103 (c) 0 (d) 3 28 (e) I don’t know 6) A curve has gradient function dy 3 and passes through the point (3, 2). = dx x 2 The equation of the curve is 3 +1 x 3 3 (c) y = + 2x 2 (e) I don’t know 3 x 5 3 (d) y = − 2 2x (a) y = (b) y = 3 − 7) A curve has gradient function dy 1 and passes through the point (4, 3). = dx x The equation of the curve is (a) y = 1 2 (b) y = 2 x − 1 x +2 (c) y = 2 x − 5 (e) I don’t know (d) y = 8) The area under the graph y = 1 − (a) 118 (c) 1 1 2 x +1 1 between x = -2 and x = -1 is x3 (b) 13 8 (d) 5 4 (e) I don’t know 9) The area enclosed by the graph y = x , the x-axis and the line x = 4 is (a) 43 (c) 16 (b) 12 (d) 16 3 (e) I don’t know © MEI, 18/08/08 2/3 MEI C2 Further calculus Section 2 MC tests 10) The area enclosed by the graph y = 1 , the coordinate axes, the line x = 2 and the x2 line y = 4 is (a) 1 4 (c) 72 (e) I don’t know (b) 3 2 (d) 5 2 © MEI, 18/08/08 3/3 MEI Core 2 Further differentiation and integration Chapter assessment 1.

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