Scribd
Upload
39 views5 pages

Set 2

22423r32wtfq232

Uploaded by

Chan Yong Sheng
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF or read online on Scribd
39 views5 pages

Set 2

22423r32wtfq232

Uploaded by

Chan Yong Sheng
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF or read online on Scribd
You are on page 1/ 5
Answer all questions in this section, 1 Functions m and n are defined by m : x» x +2,x € Rand nx x?-4,"€ p a (a) Find mn(x) + nm(a). hn (b) Hence, solve the equation mn(x) + nm(x) = =4, (3 marks] 2 A convergent sequence is defined by u, = 1+ 4u, and u, = . ety (®) Write down each of the terms uy u,and u nthe form (1), and show that an explicit formula for u,is given by u, 31 5 ()} {5 marks] (b) Determine the limit of u, as r tends to infinity, (2 marks] 3 Solve the following system of linear equations using Gaussian elimination. ~3x + 2y- 62 =6 Sx + Ty -52=6 x+4y-27=8 [6 marks] 4 The complex numbers z and w are given by z= -I +i and w = ; (a) Find w in the form x + yi, when x, y © R. State the real and imaginary parts of w. (4 marks] (b) Express w in polar form. [3 marks} (©) Using de Moivre’s theorem, determine the cube roots of w. Give your answer in Cartesian form, [5 marks] 5 A circle has equation x?+ y?+ 2x ~ By = 152. (a) Find the radius and the coordinates of the centre. [4 marks (b) The point X lies on the circle and has coordinates (a, 16) where a > 0, (i) Determine the value of a. (3 marks} (ii) Find the coordinates of the point ¥ at the opposite end of the diameter from X. (2 marks} 6 Find the angle between the straight lines L : -31 + J + 4k and L’ : 31—k. [4 marks} 8 MODEL PAPER SET2 Answer any one question in this section. 7 Express 12 cos @ — 5 sin @ in the form r cos (6 + a where r > 0 and 0R, 43 | 43 7 - 4218 [-4R, +R, R, 4B | 43 -4 26 | 24, ses =o ces eno 4 ses 0 10 : manne (0 6 fi rewsten as (9 9 SUGGESTED ANSWERS 53 5 (@) (+ 1P- 14-47 — (+ IP +0- are bd +P +0-4) « Radius = 13 and centre (-1 a (©) (@ Substitute x= a and, @+ 16+ 2a-8(16) 21+ 22-1) 4-7 424-24: i (a+6\(a-4 tt a 4 = a=~6 (rejected) ora=4 . ii) The centre (-1, 4) i the midpoint of a sien X(4, 16) and Y(k, m). 441 16 + m' 1,4) +. Real part of w= 0, imaginary part of w= @) 1400.1) 6 Leta=-3i+j+4kandb=3i-k NCP HT + # = 126 Ca TF = VI0 \. lall bl cos @ a-b cos 8: lallbr (3)3) + QO) + 4D) 26 VI0 =0,8062 43.7° | Section B 7 Let 12.cos 6-5 sin @ = rcos (6+ a) cos 8 cos or—rsin @ sin a 6 Forn=1,2= = sin( E422 nom Bit Squaring each of (1) and @) and adding, P cos? ort r sin? a= 127+ 5? P (cos? a+ sin? @) = 169 P= 169 r= 13 (since r> 0) 54 SUGGESTED ANSWERS Hence, 12 cos 6-Suinge 13 cos (8 + 0.395) (a) Maximum value occurs when cos (6 + 0.395) = 1 => Max value = 13. Minimum value occurs when cos (6 + 0.395) =—1 = Min value =-13. (b) 12cos 6-5 sin 13 cos (8 + 0.395) cos (8 + 0.395) =0 0<6<2n 0.395 < 0 <2 + 0.395 040395 =% or @=1.176 014.317 (©) -5=12cos @-5Ssin@ 3cos (8 + 0.395) £05 (0 + 0.395) = = 0<0<2 5 5 ay <9 <2 8 + 0.395 = 1.966 oF 4.318 O=1.571 013.923 From the graph, the range satisfying -5 < I2cos 0 Ssin 8

You might also like