Question 2. [13 marks] Let The of (x) is shown below. There is a minimum point at R and a maximum point at S. The f curve intersects the at the points (a, 0) (1, 0) (2, 0) and (b, 0). x-axis a. Find the exact value of i. a ii. b [2 marks] The regions between the curve and the are shaded for as shown. x-axis b. i. Write down an expression which represents the total area of the shaded regions. ii. Calculate this area, giving your answer to 1 decimal place. [2 + 1 = 3 marks] c. The of R is y-coordinate –0.24. i. Write down the coordinates of S giving your answer correct to 2 decimal places. ii. Hence or otherwise, find the range of values of for which the equation k (x 2) sin (x 1) = has four distinct solutions, – – k giving your answer correct to 2 decimal places [1 + 2 = 3 marks] d. i. Find the equation of the normal to (x) at = 1 f x
Question 2. [13 marks] Let The of f (x) is shown below. There is a minimum point at R and a maximum point at S. The curve intersects the x-axis at the points (a, 0) (1, 0) (2, 0) and (b, 0). a. Find the exact value of i. a ii. b [2 marks] The regions between the curve and the x-axis are shaded for as shown. b. i. Write down an expression which represents the total area of the shaded regions. ii. Calculate this area, giving your answer to 1 decimal place. [2 + 1 = 3 marks] c. The y-coordinate of R is –0.24. i. Write down the coordinates of S giving your answer correct to 2 decimal places. ii. Hence or otherwise, find the range of values of k for which the equation (x – 2) sin (x – 1) = k has four distinct solutions, giving your answer correct to 2 decimal places [1 + 2 = 3 marks] d. i. Find the equation of the normal to f (x) at x = 1
MM-AT4.1-2018-TEST-Part-B.docx