Letter STUDENT NUMBER SPECIALIST MATHEMATICS. Written examination 2. Number of questions and mark allocations may vary from the information indicated.

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1 Victorin Certificte of uction SUPRVISOR TO ATTACH PROCSSING LABL HR Letter STUDNT NUMBR SPCIALIST MATHMATICS Section Written emintion Mony November Reing time:. pm to. pm ( minutes) Writing time:. pm to. pm ( hours) QUSTION AND ANSWR BOOK Number of questions Structure of book Number of questions to be nswere Number of mrks SAMPL A B Totl Stuents re permitte to bring into the emintion room: pens, pencils, highlighters, ersers, shrpeners, rulers, protrctor, set squres, is for curve sketching, one boun reference, one pprove technology (clcultor or softwre) n, if esire, one scientific clcultor. Clcultor memory DOS NOT nee to be clere. For pprove computer-bse CAS, full functionlity my be use. Stuents re NOT permitte to bring into the emintion room: blnk sheets of pper n/or correction flui/tpe. Number of questions n mrk lloctions my vry from the informtion inicte. Mterils supplie Question n nswer book of pges Formul sheet Answer sheet for multiple-choice questions Instructions Write your stuent number in the spce provie bove on this pge. Check tht your nme n stuent number s printe on your nswer sheet for multiple-choice questions re correct, n sign your nme in the spce provie to verify this. Unless otherwise inicte, the igrms in this book re not rwn to scle. All written responses must be in nglish. At the en of the emintion Plce the nswer sheet for multiple-choice questions insie the front cover of this book. You my keep the formul sheet. Stuents re NOT permitte to bring mobile phones n/or ny other unuthorise electronic evices into the emintion room. VICTORIAN CURRICULUM AND ASSSSMNT AUTHORITY

2 SPCMATH XAM SCTION A Multiple-choice questions Instructions for Section A Answer ll questions in pencil on the nswer sheet provie for multiple-choice questions. Choose the response tht is correct for the question. A correct nswer scores ; n incorrect nswer scores. Mrks will not be eucte for incorrect nswers. No mrks will be given if more thn one nswer is complete for ny question. Unless otherwise inicte, the igrms in this book re not rwn to scle. Tke the ccelertion ue to grvity to hve mgnitue g ms, where g. SCTION B Instructions for Section B Answer ll questions in the spces provie. Unless otherwise specifie, n ect nswer is require to question. In questions where more thn one mrk is vilble, pproprite working must be shown. Unless otherwise inicte, the igrms in this book re not rwn to scle. Tke the ccelertion ue to grvity to hve mgnitue g ms, where g. SAMPL Number of questions n mrk lloctions my vry from the informtion inicte.

3 Victorin Certificte of uction SPCIALIST MATHMATICS Written emintion FORMULA SHT Instructions This formul sheet is provie for your reference. A question n nswer book is provie with this formul sheet. Stuents re NOT permitte to bring mobile phones n/or ny other unuthorise electronic evices into the emintion room. VICTORIAN CURRICULUM AND ASSSSMNT AUTHORITY

4 SPCMATH XAM Specilist Mthemtics formuls Mensurtion re of trpezium curve surfce re of cyliner ( b) h π rh volume of cyliner volume of cone π r h π r h volume of pyrmi Ah volume of sphere re of tringle sine rule π r bcsin( A) b c sin( A) sin ( B) sin( C) cosine rule c b b cos (C ) Circulr functions cos () sin () tn () sec () cot () cosec () sin ( y) sin () cos (y) cos () sin (y) sin ( y) sin () cos (y) cos () sin (y) cos ( y) cos () cos (y) sin () sin (y) tn( ) tn ( y) tn( y) tn( )tn ( y) cos ( y) cos () cos (y) sin () sin (y) tn( ) tn ( y) tn( y) tn( )tn ( y) cos () cos () sin () cos () sin () tn( ) sin () sin () cos () tn( ) tn ( )

5 SPCMATH XAM Circulr functions continue Function sin or rcsin cos or rccos tn or rctn Domin [, ] [, ] R Rnge π π, [, ] π π, Algebr (comple numbers) z iy r( cos( θ) isin ( θ) ) r cis( θ ) z y r π < Arg(z) π z z r r cis (θ θ ) z z r cis θ r θ ( ) z n r n cis (nθ) (e Moivre s theorem) Probbility n sttistics for rnom vribles X n Y (X b) (X) b (X by ) (X ) b(y ) vr(x b) vr(x ) for inepenent rnom vribles X n Y vr(x by ) vr(x ) b vr(y ) pproimte confience intervl for μ z s z s, n n istribution of smple men X men vrince ( X ) µ vr ( X ) σ n TURN OVR

6 SPCMATH XAM Clculus n ( ) n n n n c, n n e e ( ) e e c ( log e() ) loge c ( sin( ) ) cos( ) sin( ) cos( ) c ( cos( ) ) sin ( ) cos( ) sin ( ) c ( tn( ) ) sec ( ) sin ( ( ) ) cos ( ( ) ) ( tn ( ) ) prouct rule quotient rule chin rule uler s metho ccelertion sec ( ) tn ( ) c sin c, > cos c, > tn c ( b n ) n ( ) ( b ) n c, n ( b) loge b c ( uv) u v v u v u u v u v v y y u u If y f( ), n y b, then n n h n y n y n h f ( n ) v v v v t t t rc length f ( ) or () t y () t t ( ) ( ) ( ) t Vectors in two n three imensions Mechnics r i yj zk r y z r i r y z r i j k t t t t r. r rr cos( θ ) yy zz momentum ND OF FORMULA SHT eqution of motion p mv R m

7 VC SPCIALIST MATHMATICS Written mintion ANSWR SHT STUDNT NAM: STUDNT NUMBR A INSTRUCTIONS: US PNCIL ONLY SIGN HR IF YOUR NAM AND NUMBR AR PRINTD CORRCTLY. F SIGNATUR: G J If your nme or number on this sheet is incorrect, notify the Supervisor. Use PNCIL for ALL entries. For ech question, she the bo which inictes your nswer. All nswers must be complete like THIS emple: Mrks will NOT be eucte for incorrect nswers. NO MARK will be given if more thn ON nswer is complete for ny question. If you mke mistke, RAS the incorrect nswer DO NOT cross it out. L R T W X SUPRVISOR US ONLY US PNCIL ONLY ON ANSWR PR LIN ON ANSWR PR LIN She the ABSNT bo if the stuent ws bsent from the emintion. ABSNT SUPRVISOR S INITIALS OFFIC US ONLY Plese DO NOT fol, ben or stple this form. NCS Person