Paper 2 · Variation
Two variables R and V are connected by the equation R = kV + c, where k and c are constants. (a) Write down the type of variation between R and V. [1] (b) If the graph of R = kV + c is drawn with R on the vertical axis, write down, in terms of k and/or c the coordinates of the point where the graph crosses (i) the vertical axis, [2] (ii) the horizontal axis. [2] (c) Make V the subject of the equation R = kV + c. [2] (d) Given that R = 14 when V = 6 and that R = 8 when V = 2, (i) form a pair of simultaneous equations in k and c, [1] (ii) hence find the numerical value of k and the numerical value of c. [3]
Model answer
(a) partial variation; (b)(i) (0, c) (ii) (-c/k, 0); (c) V = (R - c)/k; (d)(i) 6k + c = 14 and 2k + c = 8 (ii) k = 3/2, c = 5
Also accepted: partial variation; (0; c); (-c/k; 0); V = (R - c)/k; k = 1.5, c = 5, partly constant and partly varying; (0, c); (-c/k, 0); V = (R-c)/k; k = 1,5 and c = 5, k = 3/2, c = 5, k = 1.5, c = 5, k=3/2,c=5
ZIMSEC Mathematics 4028/2, June 2010, Q4, via the Topical Collection