Quarter 2 AICE math Problem Set Show complete work to earn full credit. This will be graded like an AICE exam. 1)Given that the coefficient of x2 in the expansion of (a + 2x ) is 30, find the value of the constant a. 2) Prove that tan20 - sin20 = (sin20)(tan20) 3) By, converting to an equation using only tangent, Solve the equation sin(2x) + 3cos(2x) = 0 on OSx5360 4) The coordinates of the points A and B are (-1,-2) and (7,4) respectively. a) Find the equation of the circle C, for which AB is a diameter. b) Find the equation of the tangent line to circle C at point B.5) The 1st, 2nd and 3"d terms of a geometric series are 8k, 10 and z k respectively. 8 ) a) Given that k is positive, solve for k. A curve has equation y = 2x2 - 6x + 5. (i) Find the set of values of x for which y > 13. b) Hence, find the exact values of r and a and the sum to infinity. (ii) Find the value of the constant k for which the line y = 2x + k is a tangent to the curve. 6) A curve y is such that its derivative is ax = 2(3x + 4)2 - 6x - 8 i) Find dry 9 ) ii) Verify that the curve y has a stationary point at x = -1 and determine its nature. 10 cm O