Rufus Emare

NAME: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _Dat e: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ CLASS:SS2&3 SUBJECT:FURTHERMATHS SECTI ONA:OBJECTI VE Ti ckcor r ectanswer soutoft heopt i ons 1. Whenanel ementx1bel ongst oasetx, wewr i t ei tas( a)x∇X( b)x∇X ( c)xɆX( d)xEX 2. I fsetP=( 16)whatar et heel ement sofP( a)0, 1, 3, 4( b)0, 2, 39( c) 1, 2, 3, 4, 5, 6( d)2, 4, 5, 6 3. Det er mi net hecar di nal i t yoft heset sA=( a, b, e, f , g) ,B=( 1, 3, 6, 8) ( a) 5, 2( b)5, 4( c)3, 4( d)4, 6 4. I fauni v er sal setconsi st sofU=( 1, 3, 4, 5, 6, 7, 8)andN=( 3, 4, 6, 7)t henN’ wi l l be( a)( 26, 7, 8)( b)( 4, 5, 7, 8)( c)( 1, 5, 8)( d)( 1, 3, 4, 5, 6) 5. I fxQy=y x+y xt he4Q2wi l l be( a)16( b)8( c)9( d)6 6. I f5=( 0, 3, 6, 7, 9, 11)i . ex∆y=x+y xyf i nd9∆3 ( a)12ES( b)15ɆS( c)15Ɇs( d)10ES 7. a ac ab c a*( bØC)wi l l gi v e( a) ( b) ( c) ( d) bc b c ab a a2 a2 bc ( a) 2 ( b) ( c) ( d) 2 bc bc bc a 8. aØ( b* c) 9. x+y- I f * y= t hen3 * wi l l gi v ewhat ? ( a) ( b) ( c) ( d- 10. Whatn!t ot he3rd degr ee( a)n( n1) ( n+1) ( n+2) ( c)n( n1) ( n2) ( n3) ( d)n( n0) ( n1) ( n+2) ( b)n( n0) ( n1) ( n2) 11. 4P3i s_ _ _ _( a)12( b)24( c)32( d)52 12. Fi nd t he numberofdi f f er entper mut at i ons oft he l et t erwor d WAZOBI A ( a)2520( b)2150( c)2220( d)3250 13. 13 C2whati st heanswer ?( a)165( b)130( c)78( d)89 14. 8! Sol v e( a)48( b)56( c)66( d)80 5! 15. 9C6 whati st heanswer( a)84( b)96( c)112( d)64 16. 12cm 12cm Fi ndxi fPO2=Pm2+mo2 10cm ( a) 6. 633cm ( b)5. 432cm ( c)3. 234cm ( d)7. 342cm 17. Aci r cl ei sdef i nedas( a)Thepoi ntequi v al entf r om achor d( b)t he l ocusofpoi nt sequi di st antf r om af i xedpoi nt( c)t hedi st anceofa sect orf r om i t sor i gi n( d)t hepoi ntofasegmentt hr oughi t sor i gi n. 18. Ar adi usi sdef i nedas( a)t hedi st anceoft hemov i ngpoi ntf r om t he cent r e( b)t hedi st anceoft hest at i cpoi ntf r om t hecent r e( c)t he di st anceoft hel ocif r om t hear eaoft heci r cl e( d)t hedi st anceoft he or i gi nf r om t heper i met eroft heci r cl e. 19. Thescal arofa. b( a)a. bcosӨ( b)ábsi nӨ( c)absi nӨ( d)/ a/ / b/cosӨ 20. a=3i +3jb=i +2j t hena. bwi l l be( a)3( b)6( c)3( d)6 a=3i jb=5i +2j .usei nsol v i ngf r om 2122 21. / a/wi l l be( a)( a) 10( b) 9( c) 8( d)9 22. / b/wi l l be ( a) 25( b) 29( c) 30( d)25 23. x A x 10c 12c m 120c m m B C A02=AB2+BO2 A 24. O X 600 Fi ndAXB Y B ( a)60( b)900( c)300( d)1200 25. Usi ngt heci r cl ei nquest i on24f i ndBAX ( a)600( b)300( c)900( d)500 26. Usi ng Pascal ’ s t r i angl e expand and si mpl i f y- ( a) x+12xy +1+xy+8y ( b) x+6xy +12xy+8y- x+18xy+24xy+8y ( d)x+6xy +16xy+12y 3 ( 3x2y ) ( c) 4 27. Usi ngPascal ’ st r i angl eexpandandsi mpl i f y( x2y ) 2 3 4 3 3 4 ( a) x4+16x3y +24x3y +32x2y +x ( b) x4+8x2y +24x3y +32x2y +x ( c- x+8xy +24x+3xy+x ( d)x+8xy+24xy +32xy+x 28. Usi ngPascal ’ st r i angl eexpandandsi mpl i f y( 1. 01) ( a)1. 03030( b) 1. 0003( c)1. 1113( d-. Usi ngbi nomi alexpansi onf or mul aexpand( x+y ) ( a)x4 +4c1x y- c2xy + c3xy + c4y ( b)x + c1xy + c2xy + c3xy+ c4x ( c)x- +4c1xy + c3x4y + c4y ( d)x4+4c3x2y + c2x3y + c3x3y + c4y 2 30. Usi ngbi nomi alexpansi onf or mul aexpand( x+y ) ( a)x2 +2c1xy+ 2 2 3 c2y ( b)x2+2c1x2y+2c2y( c)x3+3c1x3y+3c2y( d)x2+2c1x3y+2c0y THEORY 1a. Theoper at i onont hesetRofr ealnumber si sdef i nedbyx* y=3x +2y 1; x, YERf i nd( i )4* 5( i i )3* 1 2. I fU=( m, a, j , o, r , i , t , y ) M =( r , i , t , a) H=( a, t , o, m) L=( r , i , o, t , s) Fi nd( a)( mnH)nL ( b)M n( HnL) 3. I nanexami nat i onf ort hef i naly earst udent sofaschool ,60of f er ed Hi st or y ,50 Economi csand 48 Li t er at ur e.30 of f er ed Hi st or yand Economi cs,16of f er edHi st or yandLi t er at ur e,22of f er edEconomi cs andLi t er at ur e.I f10candi dat esof f er edal l t het hr eesubj ect sf i nd; ai . Thenumbert hatof f er edHi st or yonl y i i . Thenumbert hatof f er edEconomi csonl y i i i . Thenumbert hatof f er edLi t er at ur eonl y b. How manycandi dat essatf ort heexami nat i on,assumi ngt hateach candi dat esatf oratl eastonesubj ect 8! a 4a. Ev al uat e; c6( i i ) 5! b. Fi nd t he number of per mut at i ons of t he l et t er of t he wor d mat hemat i cs ( ) 1 5 5a. Uset hebi nomi al t heor em t owr i t edownandsi mpl i f y 1-x 4 b. 4 Uset hebi nomi alt heor em t oev al uat e( 1. 004) cor r ectt of ourdeci mal pl aces 6a. Aci r cl eofr adi us26cm hasachor dofl engt h48cm, f i ndt hedi st ance oft hechor df r om t hecent r eoft heci r cl e. b. Achor di s24cm f r om t hecent r eofaci r cl eofr adi us40cm.f i ndt he l engt hoft hechor d. 7a. Fi ndt hescal arpr oductoft hef ol l owi ng i . 7i +3j 4kand4i 2j k i i . 3i 2j +kand2i 4j +5k b. Fi ndt hepr oj ect i onoft hev ect oraont hev ect orbi f i . a=2i +3j 7kandb=4i 2j +3k