Topic Past Papers – Integration

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Presentation transcript:

Topic Past Papers – Integration Advanced Higher Topic Past Papers – Integration Unit 1 Outcome 3 2002 A6. Use the substitution x + 2 = 2 tan θ to obtain 5 marks 2003 A5. Use the substitution to evaluate 3 marks 2004 9. Use the substitution x = ( u – 1 )2 to obtain 5 marks 11. A solid is formed by rotating the curve y = e-2x between x = 0 and x = 1 through 360o about the x-axis. Calculate the volume of the solid that is formed. 5 marks 2005 5. Use the substitution u = 1 + x to evaluate 5 marks 2006 6. Find 3 marks 2007 10. Use the substitution u = 1 + x2 to obtain A solid is formed by rotating the curve between x = 0 and x = 1 through 360o about the x-axis. Write down the volume of this solid. 5 marks 1 mark 2008 10. A body moves along a straight line with velocity v = t3 – 12t2 +32t and time t. (a) Obtain the value of its acceleration when t = 0. (b) At time t = 0, the body is at the origin O. Obtain a formula for the displacement of the body at time t. Show that the body returns to O, and obtain the time, T, when this happens. 1 mark 2 marks 2 marks Lanark Grammar Mathematics Department Mrs Leck

Topic Past Papers – Integration Advanced Higher Topic Past Papers – Integration Unit 1 Outcome 3 2009 5. Show that 4 marks 7. Use the substitution x = 2sinθ to obtain the exact value of (Note that cos2A = 1 – 2sin2A.) 6 marks 2010 15. A new board game has been invented and the symmetrical design on the board is made from four identical “petal” shapes. One of these petals is the region enclosed between the curves y = x2 and y2 = 8x as shown shaded in diagram 1 below. Calculate the area of the complete design, as shown in diagram 2. 5 marks The counter used in the game is formed by rotating the shaded area shown in diagram 1 above, through 360o about the y-axis. Find the volume of plastic required to make one counter. 1 mark 2011 11. Obtain the exact value of 3 marks 2012 6 marks 2013 3 marks 4 marks Lanark Grammar Mathematics Department Mrs Leck

Topic Past Papers – Integration Advanced Higher Topic Past Papers – Integration Unit 1 Outcome 3 2014 5 marks 6 marks Lanark Grammar Mathematics Department Mrs Leck

Topic Past Papers – Integration Advanced Higher Topic Past Papers – Integration Unit 1 Outcome 3 ANSWERS 2002 A6. 2003 2004 9. (5) 11. (5) 2005 2006 (3) 2007 (5) (1) 2008 10.a) Acc = 10 b) c) t = 8 (1) (2) (2) 2009 5. Proof 7. (6) 2010 15. 2011 2012 2013 2014 Lanark Grammar Mathematics Department Mrs Leck