Topical Revision Paper 3 Unit 3 Equations and Inequalities Students

Topical Revision Paper 3 Term 1 Unit 3: Equations and Inequalities Question 1: (a) Solve the equation 2 3 2xx . [4] (b) Find the range of values of x for which 2 6xx . Hence, find the range of values of x that satisfy    22 3 6 0x x x    . [6] Answer: (a) x = 3 or 1x (b) 32 x   ; 33 2x   or 2x Question 2: Find the possible values of k for which the line 1 kxy is a tangent to the curve 32 xy . Hence ,state the range of values of k for which the line will not meet the curve. [6] Answer : 44 k   Question 3: Solve the equation 2 1 12 7(2 ) 36xx , leaving your answers in two decimal places. [4] Answer : 3.17y Question 4: Find the range of values of k for which the graph of 22 13 2 2 2y x kx k k      intersects the x -axis at two distinct points. [3] Answer : 4 or 2kk   Question 5: B O y x A

The diagram above shows part of the graph of 1 33yx with A and B as the x and y intercepts respectively. (i) State the coordinates of A and B. [2] (ii) For each of the cases below, determine the number of intersections of the line y mx c with 1 33yx , justifying your answer. (a) 1 3m and 0c , [2] (b) 1 4m and 3c . [2] Answer: (i) ( 9,0) and (0,3)AB (ii) cmxy  is parallel and below 1 3 for all 3y x x . Hence will not intersect at any point or zero intersection cmxy  will intersect 1 33yx at (0,3) and also intersect 1 3 for 93y x x   (iii) Hence, two intersections