Semester 1 STPM 2021

Name : ………………………………………. Class : …………………………..

I.C Number : …………………………………
MATHEMATICS (T)
954/1, FEBRUARY 2021

KOLEJ TINGKATAN ENAM SHAH ALAM
JALAN TIMUN 24/1

SHAH ALAM SELANGOR DARUL EHSAN

SEMESTER 1 TRIAL EXAMINATION STPM 2021

MATHEMATICS (T)

PAPER 1
DURATION: 1 HOUR 30 MINUTES

Instruction to candidates:

DO NOT OPEN THIS QUESTION PAPER UNTIL YOU ARE TOLD TO DO SO.

Answer all questions in Section A.

Answer one question only in Section B. You may answer
all questions but, only the first answer will be marked.

Write the answers on your examination test pad. Begin
each answer on a new page. All workings should be shown.

Non-exact numerical answers may be given correct to
three significant figures, or one decimal place in the case of
angles in degrees, unless a different level of accuracy is
specified in the question, Scientific calculators may be used.
Programmable and graphic display calculators are
prohibited.

Prepared by: Checked by: Validated by:
…………………………… …………………………… …………………………..
Baizura Mohamed Idris
Chin Li Mei Maziah Muhammad Zain
Head of Mathematics T Unit Science & Mathematics Head

1

SECTION A (45 MARKS) [3 marks]
[3 marks]
Answer all questions.

1. The functions f and g are defined as follows

f : x → √9 − 2 , −3 ≤ ≤ 3
g : x → 2 + 5 , ∈ R

a) Express the composite function g ᴑ f in the same form.
b) State if f ᴑ g is defined, giving your reason.

2. Expand √11−+ in ascending powers of x up to and including the term in 2 where | |< 1.

1 663 [7 marks]
By assuming x = 10 , show that √11 = 200 .

3. Find all matrices A such that A = ( ) and A (I – A) = 0 , where I is the 2 x 2 identity
matrix and 0 is the 2 x 2 zero matrix. [7 marks]

4. Solve the following equations. [5 marks]

a) zz* − 5iz = 10 – 20i
b) ( − 1)3 = 8 3

5. Given an equation 9 2 − 72 − 16 2 − 32 = 16. [3 marks]
[3 marks]
a) Show that the equation represents a hyperbola. [2 marks]
b) Determine the coordinates of the centre, vertices and foci of the hyperbola. [2 marks]
c) Find the asymptotes.
d) Sketch the hyperbola.

2

6. Using vector algebra, find the area of the triangle whose vertices are A(2 , 1 , 3) ,

B(-1 , 5 , 4) and C(-2 , -2 , 1). [5 marks]

SECTION B (15 MARKS)

Answer any one question in this section.

1 12
7. a) Matrix A is given by A = ( 0 2 2) . Find −1 using elementary row operations.

−1 1 3

[5 marks]

b) A factory produces three types of dried fruits, namely prunes, olives and raisins. The

profit from 1 kg of prunes, 1 kg of olives, and 2 kg of raisins is RM 9. The profit from

1 kg of olives and 1 kg of raisins is RM 3. The profit from 1 kg of olives and 3 kg of

raisins is equal to the profit from 1 kg of prunes. If x , y and z represents the profit from

1 kg of prunes, 1 kg of olives and 1 kg of raisins, write a matrix equation to represent the

above information. Hence, determine the profit from 1 kg of prunes, 1 kg of olives and

1 kg of raisins. [10 marks]

8. The line 1 passes through the point R(1, 3 , -5) in the direction of − + . The line 2
passes through the point S(-1 , 5 , -7) in the direction of + + .

a) State the equations for 1 and 2 in vector form. [2 marks]

b) Show that S lies on 1 . [3 marks]

c) Calculate the angle between the lines 1 and 2 . [2 marks]

d) Show that = − is perpendicular to both 1 and 2 . [3 marks]

e) Find the equation, in Cartesian form, for the plane containing 1 and the point T(5 , -2 , 3)

. [5 marks]

3