Maths_Sample_Test_Paper

Mathematics Examination

Section A

Answer all questions within this question booklet. No

supplementary booklet will be provided. You are allowed to use both sides of the paper. Show full details of your solutions.

Name (Block Letters)

Question 1(c) Find absolute the maximum and minimum of the function f(x) = x 4 over

the interval [-2, 1]. (6 marks)

Question 2 (c) Evaluate ])[(sin ln 22u du

. (5 marks)

marks)

(12 . 1u u

sin that given derivative

using without x x

sin x)-x (x sin Find (b) 1 Question im im 0

u 230

x =++→→l l )7( . derivative using without 8

x 2

Find (a) 1 Question 32

- x im marks ++→l )10(.ln Find (b) 2 Question 3

marks dx x x

∫

)10(.11tan tan Find (a) 2 Question 2

11marks x x dx d that given dx x x +=??∫

Mathematics Examination

Section B

Answer all questions within this question booklet. No

supplementary booklet will be provided. You are allowed to use both sides of the paper.

Name (Block Letters)

Question 3

(a) Given the matrix []423=A , determine A A B T = and T AA C =. Find the

determinants and inverses of B and C .

(13 marks)

(b) If EF D =, find d 45 (i.e., the element in the fourth row and fifth column of matrix)

given,

????????

??????????=565421863565421863E and ??????????=565427863565429853F (5 marks)

k j b z y += is a unit vector that is perpendicular to a.

(7 marks)

Question 4

(a) In the triangle below, the lengths of OA and OB are L A and L B respectively. (i)

Determine an expression for the length h and an expression for the area of the triangle in terms of θ, L A and L B only. (ii) Hence, determine the area given k j i ++=OA and j i 2?=OB .

(10 marks)

(b) Determine the modulus and argument of the complex number, i

i i z 318

)3(22++

?+=

, where i 2= -1. (7 marks)

(c)

Solve for the complex numbers z 1 and z 2 given,

z i z i

z z i 24)1(41)1(2121+=?++=++ (Note : i 2=-1)

(8 marks)