ii. On the axes the graph of is shown. Draw the graph of the normal at = 1. Label the points of x intersection of the normal and with their coordinates correct to 1 decimal place. f(x) iii. Calculate the total area bounded by the graph of and the normal at = 1, giving your answer f(x) x correct to 1 decimal place. [1 + 2 + 2 = 5 marks] Question 3. [7 An architect is designing a new clubhouse for a Surf Life Saving Club (SLSC). The roof is to be designed to look like a smooth wave. A diagram of the side profile of the clubhouse is shown below with some key measurements and points noted. Relative to the point the point has coordinates (0, 12.6), the O, P point is a local maximum, the point is a local minimum. From the point there is to be a sloping wall for easier Q R S storage. The architect’s design for the roof is to use a function metres measures f, f(x) the height of the roof above the ground and metres measures the horizontal distance from with equation x O a. What is the average height, of the roof from = 0 to = 6? in metres, x x
ii. On the axes the graph of is shown. Draw the graph of the normal at x = 1. Label the points of intersection of the normal and f(x) with their coordinates correct to 1 decimal place. iii. Calculate the total area bounded by the graph of f(x) and the normal at x = 1, giving your answer correct to 1 decimal place. [1 + 2 + 2 = 5 marks] Question 3. [7 An architect is designing a new clubhouse for a Surf Life Saving Club (SLSC). The roof is to be designed to look like a smooth wave. A diagram of the side profile of the clubhouse is shown below with some key measurements and points noted. Relative to the point O, the point P has coordinates (0, 12.6), the point Q is a local maximum, the point R is a local minimum. From the point S there is to be a sloping wall for easier storage. The architect’s design for the roof is to use a function f, f(x) metres measures the height of the roof above the ground and x metres measures the horizontal distance from O with equation a. What is the average height, in metres, of the roof from x = 0 to x = 6?
MM-AT4.1-2018-TEST-Part-B.docx