GCE Mathematics 2022 Theory — Question 6

Model answer

This question requires reading specific values directly off the printed graph in the exam paper (the scale, and the coordinates of key points such as the y-intercept, x-intercepts, and points P and Q). General method: (a) State the scale exactly as printed on each axis of the given graph (e.g. 2cm to 1 unit on the x-axis, 2cm to 10 units on the y-axis). (b) The value of r is the y-intercept (where x=0). The values of m and n are found by substituting the coordinates of two other points read from the curve into y=mx^2+nx+r and solving the resulting simultaneous equations. (c) Gradient of line PQ = (change in y between P and Q) / (change in x between P and Q), using the coordinates of P and Q read from the graph. (d) The range of values of x for which y>0 is read directly from the graph as the interval(s) where the curve lies above the x-axis.