Mathematics Higher Level Robert Joinson

©Sumbooks2002Higher Level29. Graphs 281. a) Complete the table of values of y = 2x + -- for the values of x from 0.5 to 6.xx 0.5 1.0 1.5 2.0 2.5 3 4 6 7y=2x8+ --xb) Using a scale of 2cm to represent 1 unit on the x axis and 1cm to represent 1 unit on the y8axis plot the graph of y = 2x + -- .xxc) Using the same axes draw the lines representing y = 14 and y = 12 – -- .2d) By considering the points of intersection of two graphs write down the approximate8solutions to the equation 2x + -- – 14 = 0.x8xe) Show that the intersection of the graphs y = 2x + -- and y = 12 – -- gives a solution tox2the equation 5x 2 – 24x + 16 = 0. What are the approximate solutions to this equation?8f) What is the gradient of the curve y = 2x + -- when x = 4?x2. a) Complete the table of values of y = 4+3x – x 2 for values of x from –4 to +4.b) Draw the graph of y = 4 + 3x – x 2 using a scale of 2cm to represent 1 unit on the x axisand 2cm to represent 4 units on the y axis.c) On the same axes draw the line y = 3 and write down the approximate co-ordinates of thepoint of intersection of the two graphs.d) Show that the x co-ordinates at this point are an approximate solution to the equation3x – x 2 + 1 = 0.e) What is the solution to the equation 4+ 3x – x 2 = 0?f) By drawing a straight line, find an approximate solution to the equation 8+ 3x – x 2 = 0.3x + 53. Draw the graphs of y = ( x + 3) ( 3–2x)and y = -------------- for values of x from –4 to +22using a scale of 2cm to 1 unit on the x axis and 1 cm to 2 unit on the y axis. From your graphestimate the solutions to the equations;a) 13 – 9x – 4x 2 = 0 andb)x = –4 –3 –2 –1 0 1 2 3 4 5y = 4+3x – x 23– 3x – 2x 2 = 0