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C2 differentiation and integration questions

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Edexcel GCE Core Mathematics C2 Advanced Subsidiary Differentiation and Integration Materials required for examination Mathematical Formulae (Pink or Green) Items included with question papers Nil Advice to Candidates You must ensure that your answers to parts of questions are clearly labelled. You must show sufficient working to make your methods clear to the Examiner. Answers without working may not gain full credit. 1. Find the coordinates of the stationary point on the curve with equation y = 2x2 – 12x. (4) f(x) = x3 + 3x2 + 5. 2. Find (a) f ″(x), (3) 2 ⌠ (b)  f ( x ) dx . ⌡1 (4) 2 3. 8 1 ⌡1 √ x Evaluate ⌠ dx, giving your answer in the form a + b√2, where a and b are integers. (4) 4. Use calculus to find the value of 4 ⌠  (2 x + 3 √ x) dx . ⌡1 (5) 3 5. Figure 1 y y = 2x + – 5 P Q R O x Figure 1 shows part of a curve C with equation y = 2x + 8 – 5, x > 0. x2 The points P and Q lie on C and have x-coordinates 1 and 4 respectively. The region R, shaded in Figure 1, is bounded by C and the straight line joining P and Q. (a) Find the exact area of R. (8) (b) Use calculus to show that y is increasing for x > 2. (4) 4 6. The curve C has equation y = 2x3 – 5x2 – 4x + 2. (a) Find dy . dx (2) (b) Using the result from part (a), find the coordinates of the turning points of C. (4) (c) Find d2 y . dx 2 (2) (d) Hence, or otherwise, determine the nature of the turning points of C. (2) 2 7. 4 ⌠  U ...
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