7/30/2019 Ujian Pengesanan Profesiansi 1 Math M 2012

1/4

950 STPM

UNIT PENILAIAN & PEPERIKSAAN

SMK DATO JAAFAR, JOHOR BAHRU

UJIAN PENGESANAN PROFISIENSI 1

SIJIL TINGGI PERSEKOLAHAN MALAYSIA

_____________________________________________________________________________________

MATHEMATICS M

(One and a half hours)

_____________________________________________________________________________________

Instruction to candidates:

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

Answerall questions in Section A and any one question in Section B. Answers may be written in either

English or Bahasa Malaysia.

All necessary working should be shown clearly.

Scientific calculators may be used. Programmable and graphic display calculators are prohibited. A list of

mathematical formulae is provided on page 3 of this question paper.

_____________________________________________________________________________________

This question paper consists of4printed pages.

Prepared by:

......

(MASYATI KARIM)

Checked by:

......................................

(TAN SIEW NEE)

Verified by:

...................................

7/30/2019 Ujian Pengesanan Profesiansi 1 Math M 2012

2/4

CONFIDENTIAL*/SULIT*

STPM 950

Section A [45 marks]

Answerall questions in this section.

1 (a) If , expressx in terms ofa.

[6 marks]

(b) Find the value of . [3 marks]

2 Given that . Show that and

determine the values ofA and

B.

[3 marks]

Hence, evaluate correct to 3 decimal

places.

[3 marks]

3 For the geometric series , obtain smallest

value of n if the difference between the

sum of the first term and the sum of the

first n term is less than . [6 marks]

4 (a) The functionfis denoted by

where . Find the value ofa

if exist.

[4 marks]

(b) If , show that .

[4

marks]

5 Given and .

(a) Find AB.

[3 marks]

(b) Hence, determine . [4marks]

6 It is given that .

(a) Calculate and . Hence, write

down a factor of . [3 marks]

(b) Find m and n such that .

[3 marks]

(c) Solve the equation . [3 marks]

950/2

* This question paper is CONFIDENTIAL until the examination is over. CONFIDENTIAL*

* Kertas soalan ini SULIT sehingga peperiksaan kertas soalan ini tamat . SULIT*

( )axax

aaa 2log2log3log 2 =

27log3

1e

e

( ) ( ) 4314311358

22

2

++

+

+

+x

CBx

x

A

xx

xx 0=C

( ) ( )

dx

xx

xx

+

+01

2

2

431

1358

...2

336 +++

4+n64

45

( )

7/30/2019 Ujian Pengesanan Profesiansi 1 Math M 2012

3/4

CONFIDENTIAL*/SULIT*

Section B [15 marks]

Answer any one question in this section.

7 (a) If , and , where I is the

identity matrix,

determine the values of a, b

and c. Hence find .

[8 marks]

(b) Two groups of workers have their drinks at a stall. Given the following information for group A

andB.

GroupNumber of a cup / glass

Total costTea Coffee Fruit juice

A 5 2 3 11.80

B 3 1 2 7.10

The cost of a cup of tea and three glasses of fruit juice is the same as the cost of four cups of

coffee. If the costs of a cup of tea, a cup of coffee and a glass of fruit juice are RMx, RMy and

RMzrespectively, obtain a matrix equation to represent the above information. Hence, determine

the cost of each drink. [7

marks]

8 (a) If , show that .

[4 marks]

(b) Find .

[3 marks]

(c) If f is defined as . Find its

domain and range. Hence, sketch

the graph off.

[3 marks]

(d) Find the inverse function and

solve the equation .

[5 marks]

END OF EXAMINATION QUESTIONS

950/2

* This question paper is CONFIDENTIAL until the examination is over. CONFIDENTIAL*

* Kertas soalan ini SULIT sehingga peperiksaan kertas soalan ini tamat . SULIT*

=

213

341

325

P

=

c

b

a

Q

113

121

181IPQ 2=33

1P

x

e

xy

2

21+= 0242

2

22 =+

+ x

dx

dy

dx

yde x

dxe

xxx

2

2 1

( ) 32 += xyexf

1f( ) ( )xfxf 1=

3

7/30/2019 Ujian Pengesanan Profesiansi 1 Math M 2012

4/4

CONFIDENTIAL*/SULIT*

950/2

* This question paper is CONFIDENTIAL until the examination is over. CONFIDENTIAL*

* Kertas soalan ini SULIT sehingga peperiksaan kertas soalan ini tamat . SULIT*

4