SM015 REVISION Prepared by: Nurul Amani “YOUR FUTURE IS CREATED BY WHAT YOU DO TODAY” TOPIC: 1,2 AND 5 SET 1 1. Express 2 3 2 3 + - in the form of a b c + . 2. Given ( )( ) x yi i i + - = - 2 3 , find real numbers of x and y. 3. Solve: (a) 2ln ln 12 7 1 x x e e = - (b) ( ) 6 3 9 log 3 log 3 log 3 x x + = 4. Solve the following inequalities: (a) 2 4 x x < + (b) 1 1 2 1 x x - > + 5. The functions f and g are defined by f x x ( ) ln(3 1) = - (a) Determine the inverse function of f. Hence, state the domain and range of 1 f - . (b) Sketch the graphs of f and 1 f - on the same axes.
SM015 REVISION Prepared by: Nurul Amani SET 2 1. Given that z i = - 2 , express 1 z z - in polar form. 2. Solve ( )1 25 1 26 5 x x- + = 3. Solve the following equation x x x + - + = + 6 3 2 5 4. Consider functions of 2 , 12 2 xxxf and ln xxxg 0 , 1 . (a) Find xf 1 and xg 1 , and state the domain and range for each of the inverse function. (b) Obtain xfg . Hence, evaluate fg 2 . 5. Find the solution set of the following inequalities: (a) x x - > + 1 2 1 (b) x x - ³ + 1 2 5
SM015 REVISION Prepared by: Nurul Amani SET 3 1. Given 1 z i = +3 2 and 2 z i = - 2 5 , find 1 1 2 2 z z z z - . 2. Solve the equation. (a) ( ) ( ) 2 2 2 log 3 2 1 log 2 x x x + + = + + (b) 2ln ln 6 ln3 x x = - + ( ) 3. Given the function ( ) 2 1 x g x e - = . (a) By using algebraic method, show that xg is one-to-one function. (b) Hence, find xg 1 . 4. Given ( ) ln(3 6) and ( ) 2 3 x e p x x q x , show that p x q x ( ) and ( ) are inverse of each other. 5. Solve 2 - - £ 3 2 x x . Give your answer in interval form.
SM015 REVISION Prepared by: Nurul Amani SET 4 1. Given 2 1 , 0. 5 x f x x (a) Determine 1 f x . Hence, if 1 2 3 1 1 , 5 x f g x e show that 3 1 . x g x e (b) Evaluate g f 2 correct to three decimal places. (c) Assume that the domain for g x x is 0 , determine 1 g x and state its domain and range. 2. Solve the equation 5 4 log 5 log 5 log 64 x x . 3. Given that 1 z i 2 3 and 2 z i 3 2 are two complex numbers. Find 1 2 z z . Hence, determine the modulus of 1 2 z z . 4. Determine the value of x for 3 3 10 3 x x x x . Express your answer in the interval form. 5. Function f and g are defined as: f x x 3 2 1 x g x e (a) Determine whether xf is a one-to-one function. (b) Find xg 1 and 2 1 fg (c) State the range of xf and xg