AAMS1623 CALCULUS AND ALGEBRA 3 Question 1 a) b) d) Given three points, P(5,7), Q(l,1) and R(2,3). If M is the midpoint of PQ, determine the (i) coordinates of M, (3 marks) (ii) equation of the straight line that passes through point M and perpendicular to the line joining Q and R. (4 marks) Find the equation that is parallel to x + y : 5 and passes through the point (3 ,4). (5 marks) Find a Cartesian equation given by the following parametric equations. x = 41' y = 2:2 l (6 marks) Find the centre and the radius of the circle given below. Correct your nal answer to 4 decimal places. x2+y2+8x2y=l3 (7 marks) [Total: 25 marks] Question 2 a) Find the domain and range for each of the following functions. (0 f (x) : m (2 marks) (ii) g(x) : ln(x + 2) (2 marks) (iii) h(x) :% (2 marks) b) Given the function f(x) = x2 2x1 , find x when the image is 2. Hence, determine whether f (x) is one-to-one. Justify your answer. (5 marks) AAM81623 CALCULUS AND ALGEBRA 4 Question 2 (Continued! 0) Given that f(x) 2 2x2, g(x) : 3x1, and h(x) : %,x i 1. Find 3C 0) (f 0906); (3 markS) (ii) g_1(x 1) , (3 marks) (iii) (h o g o g)(0) , (4 marks) (iv) (g o h\" )(x) . (4 marks) [Total: 25 marks] AAMSIZS CALCULUS AND ALGEBRA 5 Question 4 a) b) d) Solve the simultaneous equations. Correct your nal answer to 3 decimal places. 2x + y = 1 x2 + y2 = 3 (6 marks) Solve the inequality given below. 2xl > 4 (4 marks) x+l 3 0 1 0 4 5 _ LetA: 0 2 ,B: 0 1 andC=[1 l].l:1d 0 l 0 l (i) ART, (3 marks) (ii) C ". (3 marks) Solve the following system of linear equations using inverse matrix method. x+5y+3_ = 5x+y:= x+2y+2- = (9 marks) [Total: 25 marks]