QS015/1MahematixPaperlSemester ISession 2014/20152 hours

QSo15/1

Matematik

Keftas 1Semester I

Sesi 2014/20152 iam

KF.ME,NTE,RtANPENDIDIKANMATAYSIA

BAHAGIAN MATRIKULASIM4TRICU- TTON DIVBION

PEPERIKSMN SEMESTER PROGMM MATRIKULASIIT UTNCULAfiON PROGRAIUIME EXAMINATION

MATEMATIKKertas L

2 jam

JANGAN BUIG KERTAS SOALAN INISEHINGGA DIBERITAHU.N NOTOPEN IHISQUESI/ON PAPERUNNLYOU ARETOLD IODOSO.

Kertas soalan ini mengandungi 13 halaman bercetak.

This question papermrsfs of13 pnhfedp4ges.@ Bahagian Matrikulasi

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QSo15/1

INSTRUCTIONS TO CANDIDATE:

This question paper consists of 10 questions.

Answer all questions.

All answers must be written in the answer booklet provided. Use a new page for eachquestion.

The full marks for each question or section are shown in the bracket at the end of the question

or section.

All steps must be shown clearly.

Only non-programmable scientific calculators can be used.

Numerical answers may be given in the form of fi, e, swd, fractions or up to three significant

figures, where appropriate, unless stated otherwise in the question.

3

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QS01s/1

Quadratic equation ax' + bx + c = 0'.

*--ott[o'-+*2a

Arithmetie series:

T,=o+(n-a)d

LIST OF MATHEMATICAL FORMULAE

Geometric series:

s,=;Ba+@-a)dl

Tn = arn-l

s,=ff,r*rSum to infinity:

S-= 4 .rl

QS01il1

I Solve the equation 3' +3G-*) =12.

2 Soive the inequality + . -]-6-x x-l

16 marl

QSo15/1

6 (a) Given f(*)=2x+l and g(r) =x'+2x-1.

(i) Find (/ - g)(x).

(ii) Evaluate (3s -zf)(t).

[2 marksl

14 marksl

(b) Given .f (*) = E state the domain and range of /(r).Hence, on the same ixes, sketch the graph of /(x) and f-t(x).

16 marlal

7 lr;t z = a+bi be a nonzero complex number.

(a) show that ! = ft14 marks)

O) Show that if i = -2, then z is a complex number with only an imaginary part.13 marlal

(c) Find the value of a and b if z(2-i) =(i+1)(t+;).15 marksl

I

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QSo15/1

8 (a) Solve the following equation le*, +x_l tl= +.

16 marlu)

(b) Find the solution set for the inequality( x+2\ _2-l -t

QSo15/1

l0 (a) Determinewhether f(x)=* *O g(x)= T areinversefrurctionofeach other by computing their composite functions.

[5 marks)

(b) Given .{(x)=ln(l-3r).

(1) Determine the domain and range of f (x). Then sketch the graph off (x).

[6 marks]

(ii) Find /-r(x), if it exists. Hence, state the domain and range of f-t(x).[4 marks]

END OF QUESTION PAPER

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