MATHS REVISION FOR PLUS 2 , JEE - IIT , CAMBRIDGE A-LEVEL , IB

MATHS REVISION FOR PLUS 2, JEE-IIT BY IGNATIUS GEORGEFOLLOWING QUESTIONS WILL BE DISCUSSED IN MY NEXT WIZIQ CLASS SCHEDULED ON SATURDAY , 26 th JUNE AT 5 PMGOOD FOR OBTAINING BETTER GRADES IN PLUS-2 , A- LEVEL , IB , JEE & IIT EXAMINATIONS ASSIGNMENT 1[1]Solve the inequality [2] The polynomial 2x3 – x2 + ax - 6 where a is a constant, is denotedby p(x) . It is given that (x + 2) is a factor of p(x)(i) Find the value of a (ii) when a has this value , factorise p(x) completely[3] The variables x and y satisfy the equation y = A (b-x) where a and b are real constants.The graph of In y against x is a straight line passing through (0 , 1.3 ) and (1.6 , 0.9 ) as shown in the diagramFind the values of A and b, correct to two decimal places.[4] (i) Show that the equation sin ( x + 30 ) = 2 cos ( x + 60 )can be written in the form(ii) Hence solve the equation sin ( x + 30 ) = 2 cos ( x + 60 )For[5] Show that[6] Find the exact coordinates of the point on the curve at which [7] (i) By sketching a suitable pair of graphs, show that the equation cos x = 2 - 2x , where x is in radians , has only one root for (ii) verify by calculation that this root lies between 0.5 and 1(iii) Show that , if a sequence of values given by the iterative formulaXn+1 = 1 – ½ cos xn converges , then it converge to the root of the equation in part (i)(iv) Use the iterative formula , with initial value x1 = 0.6 , to determine this root correct to two decimal places. Give the result of each etaration to four decmal places.[8] (a) Prove the identity sec 2 x + secx tanx = (b) Hence prove that© (i) By differentiating , show thatIf y = sec x , then= sec x tan x (ii) using the result obtained in part (a) and (b) , find the exact value of dx