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C3 : EXPONENTIALS AND LOGARITHMS Score: 1) Percentage: Grade: Effort: The function f is given by f: x ↦ ln (3x 6), x ℝ, x > 2. (a) Find f1(x). (3) ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………….. (b) Write down the domain of f1 and the range of f1. (2) ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………….. (c) Find, to 3 significant figures, the value of x for which f(x) = 3. (2) ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… [Edexcel P2 June 04 Qu 8] Produced for GlosMaths by S Milthorp & S Lomax 2) figure 1 y O A x B Figure 1 shows a sketch of the curve with equation y = f(x) where the function f is given by f : x ex2 1 , x . The curve meets the x-axis at the point A and the y-axis at point B. a) Write down the coordinates of A and B (2) ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………….. b) Find, in the form f 1 ( x) : x ....... , the inverse function of f and state its domain. (5) ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………….. ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… [Edexcel P2 Mock Paper Qu 8] Produced for GlosMaths by S Milthorp & S Lomax 3) Find, giving your answers to two decimal places, the values of w and y for which a) e w 4 (2) ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………….. b) ln( y 1) ln y 0.85 (2) ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………….. ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………….. [Edexcel P2 Mock Paper Qu 7] Overall, for this assessment I think my success level is: Produced for GlosMaths by S Milthorp & S Lomax Low O High O O O Did your score match your estimated ‘success level’ ? Skill I I I I I Qu know y=ln x is the inverse function of y=ex know the properties of the function ln x and its graph know the properties of the function ex and its graph can solve equations involving y=lnx can solve equations involving y= ex Yippee!! - I got all the questions correct. I made mistakes and need to practise this topic more. Top 3 topics I need to study further are: ☺ ☺ ☺ Produced for GlosMaths by S Milthorp & S Lomax