Topical Revision Paper 11 Unit 11 Application s of straight line graphs

Topical Revision Paper 11 Term 3 Unit 11: Applications of straight line graphs Question 1: It is given that x and y are connected by xy ab where a and b are constants. Experimental values of x and y were obtained and the straight line graph of lg against yx was plotted. The diagram shows the points (0, 0.7) and (12, 2.5). Estimate, to 2 significant figures, the value of a and of b. [5] Solution: 0.7 0.15 lg lg lg lg 0.7 10 5.0 (2 s.f.) 2.5 0.7lg 12 0 10 1.4 (2 s.f.) y a x b a a b b       Question 2: The diagram shows the straight line graph of xy against 2x passing through the points A(0, 6) and B(8, 4). Express y in terms of x. [3] lg y x

Solution: xy – intercept is 6 gradient 6 4 1 0 8 4   Equation of straight line is of the form “ Y = mX + c “ i.e. 2xy mx c 21 64xy x  Hence 21 6 24 or44 xyx xx    Question 3: The variables x and y are related by the equation 5px qy  where p and q are constants. Given that the graph of 5px qy  passes through  0.5,1 and  2,125 , and 0x , (i) show that p = 2 and q = –1. [3] (ii) Using the values p and q in (i), express 5px qy  in a linear form and hence, sketch the linear graph for the equation, indicating your axes and intercepts clearly. [3] O B (8, 4) A (0, 6) xy O B (8, 4) A (0, 6) xy

Solution: () 5 px q i y  At  0.5,1 , 1 2 1 0 2 15 55 1 0.............( 1)2 1 2 pq pq p q eqn qp       At  2,125 , 2 32 125 5 55 2 3..........( 2) pq pq p q eqn        123 2 3 32 2 1 212 pp p p q         (ii) 5px qy  21 5 5 21 xy log y x   Alternatively use  ln 2ln 5 ln 5yx 5log y

x Question 4: Given that x and y are related by 3 4 xex y  and are represented by a straight line shown in the diagram below. The straight line cuts the vertical and horizontal axes at P and Q respectively. (i) Find the gradient of the line. [2] (ii) Find the value of  which is the acute angle in degree made by the straight line and the horizontal positive x-axis. [2] (iii) Find the coordinates of P and Q. [2] Solution: (i) Q P

3 4 43 43 x x x ex y e y x y e y x y    (ii) tan 4 76.0 (1d.p)     (iii) 4(0, 3) and ( ,0)3 PQ  Question 5: Two variables x and y are known to be related by the equation y ax b x 1 . (i) Show that a straight line graph can be obtained by plotting the graph of xy + x against x2. (ii) Hence, state its gradient and y-intercept. Solution: (i) y ax b x 1 xy = ax2 + b – x xy + x = ax2 + b Y = mX + c Thus, a straight line graph can be obtained by plotting the graph of xy + x against x2. (ii) The gradient of the straight line graph is a and its y-intercept is b.