Higher Supported Study May 2015 Session 2 Paper 2

Question 1 A curve has equation (a) Express in the form where k > 0 and (b) Hence find, in the interval , the x – coordinate of the point on the curve where the gradient is 1. 06 December 2018

Question 2 F is the point (8, 4, 6). P divides AE in The diagram shows a cuboid OABC, DEFG F is the point (8, 4, 6). P divides AE in the ratio 2:1 Q is the midpoint of CG (a) State the coordinates of P and Q   (b) Write down the components of PQ and PA (c) Find the size of angle QPA     06 December 2018

Question 3 The curve is such that The curve passes through the point (-1,9). Express y in terms of x 06 December 2018

Question 4 The curve with equation , where x > 1 cuts the x-axis at the point (a,0). Find the value of a or 06 December 2018

Question 5 Find the coordinates of the turning points of the curve with equation and determine their nature. When x = -1 When x = 3 and x -2 -1 3 4 _ + + slope Max TP at (-1,17) Min TP at (3,-15) 06 December 2018

Question 6 The diagram shows the graph of a cubic Function and its derived function (a) Given that is of the form (i) write down the values of a and b (ii) find the value of k (b) Find the equation of the graph of the cubic function 06 December 2018

Question 7 Find the value of 06 December 2018

Question 8 Functions f , g and h are defined on suitable domains by (a) Find expressions for (b) Hence solve 06 December 2018

Question 9

Solve algebraically the equation Question 10 Solve algebraically the equation

Question 11a Kite ABCD has two of its vertices at A(3,8) and B(7,14) as shown. Given that the equation of the longer diagonal BD is , find the equation of the short diagonal AC A(3,8) B(7,14) C D E O x y

Question 11b (b) Find the coordinates of E, the point of intersection of the two diagonals.

Question 11c (c) Hence establish the coordinates of C. A(3,8) E (5,6)

Question 12 For what values of x is the function increasing?