2 > 2x. x2 (7) [P4 June 2004 Qn 4] 36. (a) Sketch the graph of = 2a, given that > 0. y x a – (2) (b) Solve 2a > 2x + where > 0. x a, a – (3) [FP1/P4 January 2005 Qn 1] 43. (a) On the same diagram, sketch the graphs of = 4 and = 2x 1 , showing the y x2 y – – coordinates of the points where the graphs meet the axes. (4) (b) Solve 4 = 2x 1 , giving your answers in surd form where appropriate. x2 – – (5) (c) Hence, or otherwise, find the set of values of for which of 4 > 2x 1 . x x2 – – (3) [FP1/P4 June 2005 Qn 6] 48. Find the set of values of for which x > 2x. (6) [FP1/P4 January 2006 Qn 2] 58. (a) Use algebra to find the exact solutions of the equation 2x2 + 6 = 6 3x. x – – (6) (b) On the same diagram, sketch the with equation = 2x2 + 6 and the line with y x – equation = 6 3x. y – (3) (c) Find the set of values of for which x 2x2 + 6 > 6 3x. x – – (3) [FP1 June 2006 Qn 7]
x2 2 > 2x. (7) [P4 June 2004 Qn 4] 36. (a) Sketch the graph of y = x – 2a, given that a > 0. (2) (b) Solve x – 2a > 2x + a, where a > 0. (3) [FP1/P4 January 2005 Qn 1] 43. (a) On the same diagram, sketch the graphs of y = x2 – 4 and y = 2x – 1 , showing the coordinates of the points where the graphs meet the axes. (4) (b) Solve x2 – 4 = 2x – 1 , giving your answers in surd form where appropriate. (5) (c) Hence, or otherwise, find the set of values of x for which of x2 – 4 > 2x – 1 . (3) [FP1/P4 June 2005 Qn 6] 48. Find the set of values of x for which > 2x. (6) [FP1/P4 January 2006 Qn 2] 58. (a) Use algebra to find the exact solutions of the equation 2x2 + x – 6 = 6 – 3x. (6) (b) On the same diagram, sketch the with equation y = 2x2 + x – 6 and the line with equation y = 6 – 3x. (3) (c) Find the set of values of x for which 2x2 + x – 6 > 6 – 3x. (3) [FP1 June 2006 Qn 7]
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