1. The function f is given by: Given that: where A, B and C are constants, (i) find the values of B and C, (ii) show that A = 0. (Marks available: 4 marks) Answer Answer outline and marking scheme for question: 1 Give yourself marks for mentioning any of the points below: (max 3 marks) (max 1 mark) (Marks available: 4) 2. The function f is defined for the domain by: a) Deduce that f is a decreasing function for all. (Marks available: 2) Answer Answer outline and marking scheme for question: 2 a) The function f(x) is decreasing if f '(x) is negative. Therefore we need to show that f '(x) is less than zero, shown below: rearranging this and changing back to square roots gives: rearranging further gives: which is always true for all. (2 marks) (Marks available: 2) 3. A function is given by: find the value of the constants A and B. (Marks available: 3) Answer Answer outline and marking scheme for question: 3 Give yourself marks for mentioning any of the points below: Adding the two fractions on the right hand side gives: As the denominators are now the same the numerators must match as well. Therefore: Selecting x = -1, will eliminate the constant B. This gives: -2 -1 = A (-3 + 2 ) -3 = -A A = 3 Selecting x = 2/3 to this will eliminate the constant A. This gives: -2/3 x 2 -1 = B (-2/3 +1) -4/3 -1 = B (1/3) -7/3 = 1/3 B -7 = B B = -7 Therefore: (Marks available: 3)