[3+3 = 6 marks] QUESTION 1 a. A bridge is built across a river, as shown below. The bridge can be modelled by the equation y = ax +bx+c, where y is the vertical distance (in metres) from the surface of the water and x is the horizontal distance (in metres) from the point O. BRIDGE RIVER P If the distance between points O and P is 200 metres, and the highest point on the bridge is 40 m above the surface of the water, find the values of a, b and c. b. In the figure given below y = 1 - a(x-3)2 intersects the x-axis at A and B. Point C is the vertex of the curve and a is a positive constant. Find the coordinates of A and B in terms of a . C BQUESTION 2 [3+3+2 = 8 marks] an open (a box without a lid) with a base length twice its width is to be made from 120m of metal. 2x a) Show that the height is given by the expression h = 20 X w / b) Express the volume, V, in terms of x only. (Give your answer in simplest form) c) Find the maximum volume and give the dimensions of the box for which this maximum occurs . QUESTION 3 [2 + 2 + 3 + 2 +3+ 1 = 13 marks] Jim runs every day and is on the local high school's cross-country team. This summer Jim has been training a lot, and the graph below shows the distance (d, in miles) from home based on the number of minutes (m) Jim ran on one of his training runs:6. Writing: Earlier, the three functions were described as linear. Explain why each of the three pieces of the function are linear (ie what makes each piece linear and not exponential, for example). QUESTION 4 [3+ 3 + 3 = 9 marks] The distance of a group of hikers, d km, from their starting point t hours after setting off on a hike can be modelled by d(t) = at?(b-t) . The hikers are 3 km from the start after 2 hours and return to the starting point after 5 hours. a) Find the values of a and b. b) Rewrite the rule for d(t) stating its domain and range. c) Sketch the graph of d(t) QUESTION 5 [2+3+3+1 = 9 marks] The prism shown in the diagram has a triangular cross section. The 'ends' of the prism shown are right angled triangles with the right angles at C and Z. AX = CZ = BY =y cm , AC = XZ =3x cm and CB = ZY = 4x cm. The volume of the prism is 1500 cm2 a. Express y in terms of x.b. Show that total surface area S cm2 is given by S = 12x2 + 3000 c. Draw a graph of S against x over the largest possible domain, showing all relevant points. d. Find the value of x that will give the maximum surface area. e. Find the maximum surface area. END OF ASSIGNMENT