1. Solve the following system of equations. logx+1 y = 2 logy+1 x = 1 4 2. Let a be the angle between the unit vectors a and b, where 0 ? a ? T. (a) Express |a-band a +b |in terms of a. (b) Hence determine the value of cos a for which | a + b | = 3 | a -b |. 3. Given that 4 In 2 - 3ln 4 = - In k, find the value of k. (Total 5 marks) 4. Solve the equation log3(x + 17) - 2 = log3 2x. 5. Solve the equation 2x+2 - 10 x 2x +4 = 0, x E R. (Total 6 marks) (3) (Total 5 marks) (2) (Total 5 marks) (Total 6 marks) IB Questionbank Mathematics Higher Level 3rd edition 1