AQA AS FURTHER MATHEMATICS Paper 1 7366/1|QUESTION & MARKING SCHEME MERGED| GRADED A+|

Answer all questions in the spaces provided. 1 Which expression below is equivalent to tanh x ? Circle your answer. [1 mark] sinh x cosh x sinh x cosh x cosh x sinh x sinh x + cosh x 2 The two vectors a and b are such that a.b = 0 State the angle between the vectors a and b Circle your answer. [1 mark] 0° 45° 90° 180° 3 Do not write outside the box (03) G/Jun23/7366/1 Turn over 8 3 The matrices A and B are given by A = [ 3 1 ] 0 5 B = [ 0 4] 7 1 Calculate AB Circle your answer. [1 mark] [ 3 5 ] 7 6 [ 0 20 ] 21 12 [ 0 4 ] 0 5 [ 7 13] 35 5 4 The roots of the equation 5x3 + 2x2 – 3x + p = 0 are α, β and γ Given that p is a constant, state the value of αβ + βγ + γα Circle your answer. [1 mark] – 3 5 – 2 5 2 5 3 5 4 Do not write outside the box (04) G/Jun23/7366/1 5 The function f is defined by f (x) = 3x2 1 ≤ x ≤ 5 5 (a) Find the mean value of f [2 marks] ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ 5 (b) The function g is defined by g (x) = f (x) + c 1 ≤ x ≤ 5 The mean value of g is 40 Calculate the value of the constant c [2 marks] ______________________________________________________________