1. A graph has equation y = cos2x, where x is a real number. a) Draw a sketch of that part of the graph for which b) On your sketch show two of the lines of symmetry which the complete graph possesses. (Marks available: 4) Answer Answer outline and marking scheme for question: 1 Give yourself marks for mentioning any of the points below: a) The graph would look like: Note 1: it must be a sine-wave shape - not W shape. (the curve is only shown in the domain) Note 2: Stationary Points at (0.1). (π/2.-1) . etc (degrees not allowed here) (2 marks) b) Lines of symmetry are: x = 0 or π/2 or π etc (you will get a mark for each correct line of symmetry, up to 2 marks). (2 marks) (Marks available: 4) 2. The function f is defined on the domain x > -1 by a) Write down the equations of the asymptotes to the curve y = f(x). b) Give the range of the function f. c) Give the domain and range of the inverse function f -1. d) Find an expression for f -1(x). (Marks available: 7) Answer Answer outline and marking scheme for question: 2 Give yourself marks for mentioning any of the points below: a) Asymptotes are defined by the lines x = -1, y = 2 (2 marks) b) The range of f is y > 2 (1 mark) c) The domain of f -1 is x > 2 The range of f -1 is x > -1 (1 mark) d) Changing subject of y = f(x) (3 marks) (Marks available: 7) 3. The functions f and g are defined for all real numbers by: a) (i) State whether f is an odd function, an even function or neither. (ii) State whether g is an odd function, an even function or neither. b) Given that f and g are periodic functions, write down the periods of f and of g. c) Solve, for -π < x ≤ π the equations (Marks available: 10) Answer Answer outline and marking scheme for question: 3 Give yourself marks for mentioning any of the points below: a) f is odd g is even (2 marks) b) Period of f is π Period of g is 1/2 π (2 marks) c) (i) Solving f (x) =1/2, gives: (ii) Solving g (x) =1/2, gives the same results as above, but with ±. (6 marks) (Marks available: 10)