Welcome! 1 FIRST CONVERSATIONS 3 NUMBERS. 2 SAYING HELLO a Read Conversation 1. Put the sentences in the correct order. c Choose the correct answer.

Size: px
Start display at page:

Download "Welcome! 1 FIRST CONVERSATIONS 3 NUMBERS. 2 SAYING HELLO a Read Conversation 1. Put the sentences in the correct order. c Choose the correct answer."

Transcription

1 Cmrig Univrsity Prss Cmrig English Empowr Elmntry Arin Doff, Crig Thin, Hrrt Puht, Jff Strnks n Ptr Lwis-Jons Exrpt Mor informtion Wlom! G Possssiv jtivs; qustion wors; /n; rgulr plurl forms V Numrs; th lpht; olours; lssroom ojts n instrutions 1 FIRST CONVERSATIONS Listn to fiv short onvrstions. Mth thm with piturs Listn gin. Who sys ths sntns? Mth thm with piturs. 1 Ni to mt you. 4 How o you spll tht? 2 How r you? 5 Cn w py, pls? 3 Wht s your nm n rss? 6 Is tht your fl t? 2 SAYING HELLO R Convrstion 1. Put th sntns in th orrt orr. Hllo. Ni to mt you. I m Pirr. Hllo, Pirr. Ni to mt you. Hllo. I m Tony, n this is my wif, Jonn. 1.2 Listn n hk your nswr. In pirs, sy hllo n sy your nm. In groups of four, sy hllo. Sy your nm n introu your prtnr. 1.3 R Convrstion 2 n omplt th sntns. Listn n hk your nswrs. 3 NUMBERS 1.4 Listn to Convrstion 3. Complt th ill. How muh o thy py? 2 offs 2 i rms TOTAL Thnk you 1.7 Listn n irl th numrs you hr. Thn sy ll th numrs Choos th orrt nswr. 25 = twnty n fi v / twnty-fiv 61 = sixty-on / on n sixty 110 = hunr tn / hunr n tn fin thnks how A Hi, Nik. 1 r you? B I m 2, thnks. An you? A I m OK, 3. Mt othr stunts. Hv onvrstion with two or thr popl in th lss. R th numrs lou. Thn sy th nxt thr numrs. 1, 2, 3, 4, 10, 20, 30, 15, 25, 35, 31, 33, 35, 50, 100, 150, 6 in this w srvi Cmrig Univrsity Prss

2 Cmrig Univrsity Prss Cmrig English Empowr Elmntry Arin Doff, Crig Thin, Hrrt Puht, Jff Strnks n Ptr Lwis-Jons Exrpt Mor informtion Wlom! Sy ths olours n spll th wors. f Writ two wors you know in English. Sy th wor n sk your prtnr to spll it. 1.5 Listn to Convrstion 4 n omplt th nm n rss. Mik K A King s Ro g Work in pirs. Stunt A, tll Stunt B: your fi rst n lst nm your rss. Stunt B, sk Stunt A to spll thir nm n rss. Writ th informtion own. Thn swp rols. How o you spll your...? 5 POSSESSIVE ADJECTIVES 4 THE ALPHABET 1.8 Listn to th lttrs of th lpht n sy thm. 1.6 R n listn to Convrstion 5. Unrlin th orrt nswr. A This is ni photo. This is my / your wif n his / hr rothr. B Oh ys. Is tht our / your fl t? A Ys, tht s our / thir fl t in Lonon. B Mm, it s vry ni. Complt th tl. our thir hr his I liv hr. Do you liv hr? This is my fl t. Is this your fl t? H livs hr. This is fl t. Sh livs hr. This is fl t. W liv hr. This is fl t. Pronunition Whih lttrs hv: Thy liv hr. This is fl t. 1 th sm long soun s s /iː/ 2 th sm long soun s y /ɪ/ 3 th sm short soun s gg // Tst prtnr. Stunt A, point to lttr. Stunt B, sy th lttr. Complt th sntns with wor from th tl in 5. 1 This is my rothr. nm is Gorg. 2 Jnny n Phil r ol frins n tht s ol r. 3 Tht s goo photo of you. An is tht ughtr? 4 In this photo, w r on holiy with frins Su n Bill. 5 I know tht girl in th photo. Wht s nm? 7 in this w srvi Cmrig Univrsity Prss

3 Cmrig Univrsity Prss Cmrig English Empowr Elmntry Arin Doff, Crig Thin, Hrrt Puht, Jff Strnks n Ptr Lwis-Jons Exrpt Mor informtion 6 CLASSROOM OBJECTS f g h j i Mth ojts 1 10 with j in th pitur. 1 1 notook 2 itionry 3 projtor 4 qustion 5 pn 2 6 upor 7 sk 8 whitor 9 n nswr 10 oursook 1.9 Pronunition Noti th strss sylll in th wors in 6. Listn, thn prtis sying th wors. Whn o w us n? Choos th orrt nswr. for,, i, o, u for othr lttrs Writ or n nxt to h wor. 3 f Look t how wors hng in th plurl. Complt th ruls. Singulr Plurl Rul pn pns Most wors in th plurl. y is Chng fi nl -y to n. glss glsss If wor ns in -s, -x, -sh or -h, w. 7 CLASSROOM INSTRUCTIONS 1.10 Listn n o wht th thr sys. Thn listn gin. Whih vrs o you hr h tim? opn los look t r turn to writ sk work ook ppl mr 1.11 Unrlin th orrt wors. Listn n hk. 4 glss 5 gg 6 y 1 Wht s / Who s this? An ppl or n orng? 2 Whn s / Whr s Tokyo? 3 How / Wht o you sy this wor? 4 Who s / Whn s th prsint? 5 Whn s / Wht s your English lsson? 7 i rm Is it ig? No. 8 ox Choos on of th wors from 6 or 6. Othr stunts sk qustions to guss th wor. Is it whit? No. Mth qustions 1 4 with nswrs. 1 Wht s migo in English? It s ot for rs n popl. 2 How o you spll night? P-pl. 3 Wht s frry? Frin. 4 How o you sy this wor? N-I-G-H-T. Writ qustion lik qustions 1 4 in 7. Thn sk othr stunts your qustion. 8 in this w srvi Cmrig Univrsity Prss

4 Cmrig Univrsity Prss Cmrig English Empowr Elmntry Arin Doff, Crig Thin, Hrrt Puht, Jff Strnks n Ptr Lwis-Jons Exrpt Mor informtion CAN DO OBJECTIVES Tlk out whr you r from Tlk out popl you know Ask for n giv informtion Writ n onlin profi l UNIT 1 Popl GETTING STARTED Look t th pitur n nswr th qustions. 1 Wht iffrnt ountris r th popl from? 2 Why r thy togthr? for sports gm for prty for musi onrt 3 How o thy fl? Hr r som is: or xit goo hppy s tir Whn o you mt popl from othr ountris? Hr r som mor is: on holiy on lngug ours nvr t work t prtis 9 in this w srvi Cmrig Univrsity Prss

5 Cmrig Univrsity Prss Cmrig English Empowr Elmntry Arin Doff, Crig Thin, Hrrt Puht, Jff Strnks n Ptr Lwis-Jons Exrpt Mor informtion 1A I m from Frn Lrn to tlk out whr you r from G : positiv n ngtiv V Countris n ntionlitis 1 LISTENING AND READING 1.13 Listn gin. Complt th onvrstion. Look t piturs f n nswr th qustions. 1 Wht sport o ll th popl lik? 2 Mth ountris 1 6 with piturs f. 1 Brzil 2 Spin 3 Grmny 4 Jpn 5 Russi 6 Frn 1.12 Listn n hk. Prtis sying th ountris Thoms n Ln r t th Worl Cup. Listn n tik ( ) th thr things thy tlk out. 1 footll 2 ountris 3 foo 4 ity 5 TV THOMAS Hi thr! My nm s Thoms. Wht s your 1? LENA I m Ln. THOMAS Hi, Ln! Whr r you 2? Russi? LENA Yh, you r right! I m Russin. I m from St Ptrsurg. THOMAS Oh ys! It s rlly utiful ity. LENA Ys, I think so too. So, 3 r you from, Thoms? THOMAS M? I m from 4. I m Frnh. LENA Oh, th Frnh tm s rlly goo! THOMAS Of ours, w r 5! Ar sntns 1 4 tru or fls? 1 Thoms n Ln r frins. 2 Ln is from Russi. 3 Thoms liks St Ptrsurg. 4 Ln sys th footll tm from Frn is vry. f Unrlin th two ntionlitis in th onvrstion in in this w srvi Cmrig Univrsity Prss

6 Cmrig Univrsity Prss Cmrig English Empowr Elmntry Arin Doff, Crig Thin, Hrrt Puht, Jff Strnks n Ptr Lwis-Jons Exrpt Mor informtion UNIT 1 2 VOCABULARY Countris n ntionlitis Thoms sys: I m from Frn. I m Frnh Fin othr pirs of ountris n ntionlitis in th ox low. Listn n hk. Ru ssi Br zil i n Sp nish J pn Ru ssin Gr mny Jp n s Gr mn Br zil Spin 1.14 Pronunition Noti how mny syllls h wor hs. Unrlin th strss sylll in h wor in th ox in Listn gin n rpt. Mk sntns out th popl low with th wors in 2. 1 Ln: Sh s Russin. Sh s from. 2 Th popl in piturs f: Thy r. Thy r from. Look t th onvrstion in 1 gin. Complt th qustion. Thn sk your prtnr. 3 GRAMMAR : positiv n ngtiv 1.17 Listn to th nxt prt of th onvrstion twn Thoms n Ln. Wht o thy tlk out? thir footll tms th town whr Thoms is from 1.17 Unrlin th orrt nswrs. Listn gin n hk. 1 Thoms is / isn t from Pris. 2 Ln s frins r / rn t Russin. 3 Hr frins r / rn t t th mth. 4 It s / It isn t 8:00. Look t th sntns n omplt th ruls. It s town nr Pris. It isn t vry ig. Thy r ll in th hotl. Thy rn t hr. I m from Frn. I m not from Pris. 1 To mk is n r ngtiv, w. 2 To mk I m ngtiv, w. Complt th tl with th orrt forms of th vr. r you from? I m from. I m. Positiv (+) Ngtiv ( ) I m from St Ptrsurg. I m Frnh. H rlly goo plyr. Sh from Mosow. Thy sy thy tir. Thy t th mth. f Now go to Voulry Fous 1A on p.160 for mor Countris n ntionlitis Now go to Grmmr Fous 1A on p.136 f Thoms n Ln tlk mor in th fé. A th vr to mk orrt sntns. Thoms sys: 1 My rothr t univrsity in Mri. 2 My mothr n fthr not hr. Ln sys: 3 Russi not vry hot in April. 4 My frins rlly intrsting n fun. g Writ two positiv n two ngtiv sntns out you with th vr. Mk two of th sntns fls. h R your sntns to prtnr n sy if your prtnr s sntns r tru or fls. 4 SPEAKING f Communition 1A Stunt A go to p.129. Stunt B go to p.132. Work in smll groups. Tll othr stunts: your nm your ountry n ntionlity your hom town. 11 in this w srvi Cmrig Univrsity Prss

7 Cmrig Univrsity Prss Cmrig English Empowr Elmntry Arin Doff, Crig Thin, Hrrt Puht, Jff Strnks n Ptr Lwis-Jons Exrpt Mor informtion 1B Sh s lovly prson G : qustions n short nswrs V Prsonlity jtivs READING 1 Lrn to tlk out popl you know Look t piturs. Whr o you think th popl r? Who o you think sys sntns 1 4? R th txts n mth thm with piturs. Ar your is in 1 orrt? I hv four lsss vry y. It s fun to trvl with frins. My fmily liv in iffrnt pls. Sh spks two lngugs Spnish n Portugus. Who woul you lik to mt: Suzi, Anry, Altn or Sh? Why? W O PHOTO N Suzi Altn This is m in Rio Jniro with my frin Clui. Sh livs in Brzil, ut sh s from Spin. Sh s lovly prson vry wrm n kin. In this photo, I m on holiy with my frin Tkor. H s fntsti frin n h s vry ool. H s grt prson to on holiy with. viw Suzi s photos viw Atln s photos lv Suzi mssg lv Atln mssg Anry Sh In this photo I m in St Ptrsurg with my ousin Olg. H s Russin, ut I m from Engln his fthr n my mothr r rothr n sistr. H s rlly plsnt guy n h s rillint otor. H s wllknown in his prt of St Ptrsurg. This is my ollgu Mrm. W r thrs n w work togthr in shool. Sh s quit, ut sh s rlly frinly. Sh s lso vry populr with hr stunts. viw Anry s photos viw Sh s photos lv Sh mssg lv Anry mssg 12 in this w srvi Cmrig Univrsity Prss

8 Cmrig Univrsity Prss Cmrig English Empowr Elmntry Arin Doff, Crig Thin, Hrrt Puht, Jff Strnks n Ptr Lwis-Jons Exrpt Mor informtion UNIT 1 2 VOCABULARY Prsonlity jtivs Look t th sntn. Th unrlin wors r jtivs. Ar thy out Rio Jniro or Clui? Sh s lovly prson vry wrm n kin! Unrlin nin mor jtivs in th txts. Thn put thm in th orrt gps. 1 vry goo:,,, 2 ni: lovly, wrm, kin,, 3 fmous: 4 h/sh osn t tlk muh: 5 popl lik him/hr: Pronunition Thr wors in th txts hv th /k/ soun: kin ool quit Unrlin th /k/ soun in ths wors. Whih two wors o not hv /k/? ol r hp kithn lik off quik k ky know om mk shool t Tlk out popl you know. Us jtivs from 2. My frin Emm s vry frinly n vry populr. My st frin Jo s ool guy. My unt Sophi s fntsti sh s vry wrm n frinly womn. Now go to Voulry Fous 1B on p.161 for mor Ajtivs 3 LISTENING 1.23 Listn to th onvrstion. Complt th ntionlitis (1 3) on th profils low. 4 GRAMMAR : qustions n short nswrs 1.24 Complt th nswrs with th vrs in th ox. Listn n hk. rn t isn t is r 1 Is sh Itlin? No, sh. Sh s from Spin. 2 Is h from Poln? Ys, h. 3 Ar thy mrri? Ys, thy. 4 Ar thy Spnish? No, thy. Thy r from Mxio. Complt th tl with th orrt forms of th vr. Qustions (?) Ar you Austrlin? you Spnish? h/sh Turkish? thy Russin? Short nswrs Ys, I m. Ys, w r. Ys, h/sh. Ys, thy. Now go to Grmmr Fous 1B on p.136 No, I m not. No, w rn t. No, h/sh. No, thy Complt th onvrstions. Us ontrtions s, r n isn t if possil. Listn n hk. A My frin Tony 1 s English. H 2 B 3 h from Lonon? A Ys, h 4. vry kin. A My frins, Jo n Ml, 5 Amrin. Thy 6 vry wrm n frinly. B 7 thy mrri? A No, thy 8. Thy 9 just goo frins. 5 SPEAKING Writ own wors out frins, fmily n fmous popl you know from othr ountris. Cmill British, ool, populr Gril Mxin, quit, kin Tlk out th popl you know. Look t th onvrstions in 4 to hlp you Listn gin. Complt th profils with prsonlity jtivs 4 6. Nm: Romn Ntionlity 1 Prsonlity 4 Nms: Digo n Mi Ntionlity 2 Prsonlity 5 Nm: Lur Ntionlity 3 Prsonlity 6 13 in this w srvi Cmrig Univrsity Prss

9 Cmrig Univrsity Prss Cmrig English Empowr Elmntry Arin Doff, Crig Thin, Hrrt Puht, Jff Strnks n Ptr Lwis-Jons Exrpt Mor informtion 1C Evryy English Wht s your surnm? Lrn to sk for n giv informtion S Chking unrstning P Consonnt groups 1 LISTENING Look t th piturs of Dn n Lo. Us prsonlity jtivs from pg 12 to sri thm Wth or listn to Prt 1. Choos th orrt nswr. 1 Dn wnts to: finish somthing o som xris 2 Lo wnts to: o n xris lss go for run. 3 Mrtin is: in th offi t th gym Wth or listn to Prt 2 gin. Ar th sntns tru or fls? Corrt th fls sntns. 1 Th lss strts t Tn popl n go to th fi tnss lss. 3 Th lss is in Stuio Lo tlks to th gym rptionist. Wth or listn to Prt 2. Wht os Lo wnt to o? Choos th orrt nswr. join th gym ook fi tnss lss py for fi tnss lss. Lo Dn 2 USEFUL LANGUAGE Asking for n giving informtion Who sys sntns 1 7 t gym: th rptionist (R) or visitor (V)? 1 Wht tim s th nxt lss? 2 An wht s your rss? 3 How n I hlp? 4 Thnks for your hlp. 5 Cn you spll tht, pls? 6 An whr s th lss? 7 Wht s your surnm? Symour. You r wlom. S E Y M O U R It s t twnty pst svn. It s in Stuio 1. f I lik to o fitnss lss. g 18 Nw Strt Mth 1 7 with g. Listn n hk. Unrlin th orrt nswrs. 1 It s in tn pst four / Room 6. 2 It s t ight o lok / Stuio A is rptionist n B wnts informtion. Complt th onvrstion. Look t 2 n 2 to hlp you. Listn n hk. A Hllo. How n I 1 you? B I 2 to o omputr ours. A No prolm. B Whn s th fi rst lsson? A It s tomorrow t ight o lok. B An 3 th lsson? A It s hr in Room 5. B Grt. Cn I ook pl? A Crtinly. 4 your surnm? B Moor. A Cn you 5 tht, pls? B M O O R E A Thnk you. Enjoy th lss. In pirs, prtis th onvrstion in 2. Us your own surnm. Tk turns ing A n B. 14 in this w srvi Cmrig Univrsity Prss

10 Cmrig Univrsity Prss Cmrig English Empowr Elmntry Arin Doff, Crig Thin, Hrrt Puht, Jff Strnks n Ptr Lwis-Jons Exrpt Mor informtion UNIT 1 3 LISTENING 1.31 Wth or listn to Prt 3. Lo tlks to Mrtin t th gym. Answr th qustions. 1 Who is Mrtin? 2 Wht os sh sy out Dn? H s vry usy. H s it lzy. Wht is goo tim to go to th gym? for work / shool ftr work / shool 4 CONVERSATION SKILLS Chking unrstning Complt th mini-onvrstions with th wors in th ox. so tht s sorry SONIA It s t twnty pst svn. 1 LEO? SONIA 7:20. SONIA It s in Stuio 1. LEO 2 7:20 in Stuio 1. t lunhtim nvr 5 PRONUNCIATION Consonnt groups 1.33 Listn to th tim. Noti how th mrk onsonnt groups r pronoun. ight o lok /t/ /kl//k/ 1.34 Listn to th wors low. How mny onsonnt souns o th mrk lttrs hv? thr six ighty 1.35 Prtis sying ths tims. Listn n rpt. 1 svn o lok (7:00) 4 thr forty (3:40) 2 six tn (6:10) 5 six thirty (6:30) 3 ight twnty (8:20) 6 twlv twnty (12:20) 6 SPEAKING Communition 1C Stunt A go to p.129. Stunt B go to p.132. Whih xprssion in 4 mns: 1 I m not sur n I wnt to hk. 2 I on t unrstn. Cn you sy tht gin? 1.32 Pronunition Listn to wht Lo sys in 4. Dos th ton go up or own on 1 n 2? Work in pirs. Us th ilogu mp to prtis hking unrstning. Tk turns ing A n B. A B Unit Progrss Tst CHECK YOUR PROGRESS You n now o th Unit Progrss Tst. 15 in this w srvi Cmrig Univrsity Prss

What do you know? Listen and find. Listen and circle. Listen and chant. Listen and say. Lesson 1. sheep. horse

What do you know? Listen and find. Listen and circle. Listen and chant. Listen and say. Lesson 1. sheep. horse Animls shp T h i nk Wht o you know? 2 2:29 Listn n fin. hors Wht s this? Wht s this? It s got ig nos. It s ig n gry. It s hors! YES! 2 Wht r ths? Wht r ths? Thy v got two lgs. Thy r smll n rown. Thy r

More information

3 Make words with the jumbled letters. 4 Match the questions and answers.

3 Make words with the jumbled letters. 4 Match the questions and answers. Unit Tst A n writ. son n nswr. My nm is Mr n I m rom Gon. I m tn yrs ol. My prnts r Mrln n Rul. My rothr is Sm. H s tn yrs ol, too. W r twins! My littl sistr is Lol n sh s only on. Sh s vry smll n vry

More information

a b c cat CAT A B C Aa Bb Cc cat cat Lesson 1 (Part 1) Verbal lesson: Capital Letters Make The Same Sound Lesson 1 (Part 1) continued...

a b c cat CAT A B C Aa Bb Cc cat cat Lesson 1 (Part 1) Verbal lesson: Capital Letters Make The Same Sound Lesson 1 (Part 1) continued... Progrssiv Printing T.M. CPITLS g 4½+ Th sy, fun (n FR!) wy to tch cpitl lttrs. ook : C o - For Kinrgrtn or First Gr (not for pr-school). - Tchs tht cpitl lttrs mk th sm souns s th littl lttrs. - Tchs th

More information

Family and friends 1.1 VOCABULARY. Family. 1 Who is who in Sally s family? Match a g to Match the word fragments to make family words.

Family and friends 1.1 VOCABULARY. Family. 1 Who is who in Sally s family? Match a g to Match the word fragments to make family words. VOCABULARY I n tlk out th po in fily Who is who in lly s fily? Mth g to COMMUNICATION u READING nd VOCABULARY grn r l s in ny Look t Mrk s fily tr Cot th sntns wh on word LISTENING nd WRITING Fily photo

More information

Contents. Practice Test Practice Test Practice Test Practice Test Practice Test Practice Test 8...

Contents. Practice Test Practice Test Practice Test Practice Test Practice Test Practice Test 8... Contnts How to Us This Book... 4 Prti Tst 1... 8 Prti Tst 2... 16 Prti Tst 3... 24 Prti Tst 4... 32 Prti Tst 5... 40 Prti Tst 6... 48 Prti Tst 7... 56 Prti Tst 8... 64 Prti Tst 9... 72 Prti Tst 10... 80

More information

UNIT 1. talk CAN DO OBJECTIVES GETTING STARTED

UNIT 1. talk CAN DO OBJECTIVES GETTING STARTED CAN DO OBJECTIVES tlk out iffrnt forms of ommunition Dsri xprins in th prsnt Giv n rspon to opinions Writ gui UNIT 1 tlk GETTING STARTED Look t th photo n nswr th qustions. 1 Whr o you think th oy is?

More information

1 Introduction to Modulo 7 Arithmetic

1 Introduction to Modulo 7 Arithmetic 1 Introution to Moulo 7 Arithmti Bor w try our hn t solvin som hr Moulr KnKns, lt s tk los look t on moulr rithmti, mo 7 rithmti. You ll s in this sminr tht rithmti moulo prim is quit irnt rom th ons w

More information

Module graph.py. 1 Introduction. 2 Graph basics. 3 Module graph.py. 3.1 Objects. CS 231 Naomi Nishimura

Module graph.py. 1 Introduction. 2 Graph basics. 3 Module graph.py. 3.1 Objects. CS 231 Naomi Nishimura Moul grph.py CS 231 Nomi Nishimur 1 Introution Just lik th Python list n th Python itionry provi wys of storing, ssing, n moifying t, grph n viw s wy of storing, ssing, n moifying t. Bus Python os not

More information

(2) If we multiplied a row of B by λ, then the value is also multiplied by λ(here lambda could be 0). namely

(2) If we multiplied a row of B by λ, then the value is also multiplied by λ(here lambda could be 0). namely . DETERMINANT.. Dtrminnt. Introution:I you think row vtor o mtrix s oorint o vtors in sp, thn th gomtri mning o th rnk o th mtrix is th imnsion o th prlllppi spnn y thm. But w r not only r out th imnsion,

More information

# 1 ' 10 ' 100. Decimal point = 4 hundred. = 6 tens (or sixty) = 5 ones (or five) = 2 tenths. = 7 hundredths.

# 1 ' 10 ' 100. Decimal point = 4 hundred. = 6 tens (or sixty) = 5 ones (or five) = 2 tenths. = 7 hundredths. How os it work? Pl vlu o imls rprsnt prts o whol numr or ojt # 0 000 Tns o thousns # 000 # 00 Thousns Hunrs Tns Ons # 0 Diml point st iml pl: ' 0 # 0 on tnth n iml pl: ' 0 # 00 on hunrth r iml pl: ' 0

More information

Math 61 : Discrete Structures Final Exam Instructor: Ciprian Manolescu. You have 180 minutes.

Math 61 : Discrete Structures Final Exam Instructor: Ciprian Manolescu. You have 180 minutes. Nm: UCA ID Numr: Stion lttr: th 61 : Disrt Struturs Finl Exm Instrutor: Ciprin nolsu You hv 180 minuts. No ooks, nots or lultors r llow. Do not us your own srth ppr. 1. (2 points h) Tru/Fls: Cirl th right

More information

A prefix word in each of these sentences is incorrect. Rewrite the prefix words correctly.

A prefix word in each of these sentences is incorrect. Rewrite the prefix words correctly. Spring Trm 2 Cirl th possssiv pronoun: Th hilrn wr thrill tht th i tht h n hosn or th inl prout ws thirs. Rwrit this sntn with th vril phrs t th ginning. Don t orgt omm! Thr wsn t on pi o pizz lt tr th

More information

Section 3: Antiderivatives of Formulas

Section 3: Antiderivatives of Formulas Chptr Th Intgrl Appli Clculus 96 Sction : Antirivtivs of Formuls Now w cn put th is of rs n ntirivtivs togthr to gt wy of vluting finit intgrls tht is ct n oftn sy. To vlut finit intgrl f(t) t, w cn fin

More information

ECE COMBINATIONAL BUILDING BLOCKS - INVEST 13 DECODERS AND ENCODERS

ECE COMBINATIONAL BUILDING BLOCKS - INVEST 13 DECODERS AND ENCODERS C 24 - COMBINATIONAL BUILDING BLOCKS - INVST 3 DCODS AND NCODS FALL 23 AP FLZ To o "wll" on this invstition you must not only t th riht nswrs ut must lso o nt, omplt n onis writups tht mk ovious wht h

More information

CD 1.24 MP p.m. 3 May 16

CD 1.24 MP p.m. 3 May 16 . Voulry Prsonlity jtivs Ajtiv + prposition I n sri popl n tlk out prsonl qulitis. SHOW WHAT YOU KNOW PERSONALITY Mth jtivs with thir opposits. lvr funny intrsting kin positiv oring ngtiv srious stupi

More information

QUESTIONS BEGIN HERE!

QUESTIONS BEGIN HERE! Points miss: Stunt's Nm: Totl sor: /100 points Est Tnnss Stt Univrsity Dprtmnt of Computr n Informtion Sins CSCI 710 (Trnoff) Disrt Struturs TEST for Fll Smstr, 00 R this for strtin! This tst is los ook

More information

Using the Printable Sticker Function. Using the Edit Screen. Computer. Tablet. ScanNCutCanvas

Using the Printable Sticker Function. Using the Edit Screen. Computer. Tablet. ScanNCutCanvas SnNCutCnvs Using th Printl Stikr Funtion On-o--kin stikrs n sily rt y using your inkjt printr n th Dirt Cut untion o th SnNCut mhin. For inormtion on si oprtions o th SnNCutCnvs, rr to th Hlp. To viw th

More information

Polygons POLYGONS.

Polygons POLYGONS. Polgons PLYGNS www.mthltis.o.uk ow os it work? Solutions Polgons Pg qustions Polgons Polgon Not polgon Polgon Not polgon Polgon Not polgon Polgon Not polgon f g h Polgon Not polgon Polgon Not polgon Polgon

More information

Graphs. CSC 1300 Discrete Structures Villanova University. Villanova CSC Dr Papalaskari

Graphs. CSC 1300 Discrete Structures Villanova University. Villanova CSC Dr Papalaskari Grphs CSC 1300 Disrt Struturs Villnov Univrsity Grphs Grphs r isrt struturs onsis?ng of vr?s n gs tht onnt ths vr?s. Grphs n us to mol: omputr systms/ntworks mthm?l rl?ons logi iruit lyout jos/prosss f

More information

UNCORRECTED SAMPLE PAGES 4-1. Naming fractions KEY IDEAS. 1 Each shape represents ONE whole. a i ii. b i ii

UNCORRECTED SAMPLE PAGES 4-1. Naming fractions KEY IDEAS. 1 Each shape represents ONE whole. a i ii. b i ii - Nming frtions Chptr Frtions Eh shp rprsnts ONE whol. i ii Wht frtion is shdd? Writ s frtion nd in words. Wht frtion is not shdd? Writ s frtion nd in words. i ii i ii Writ s mny diffrnt frtions s you

More information

Paths. Connectivity. Euler and Hamilton Paths. Planar graphs.

Paths. Connectivity. Euler and Hamilton Paths. Planar graphs. Pths.. Eulr n Hmilton Pths.. Pth D. A pth rom s to t is squn o gs {x 0, x 1 }, {x 1, x 2 },... {x n 1, x n }, whr x 0 = s, n x n = t. D. Th lngth o pth is th numr o gs in it. {, } {, } {, } {, } {, } {,

More information

1 I ( can / can t ) read a book, but I ( can / can t ) read a map. 2 They ( can / can t ) swim, but they ( can / can t ) pitch a tent.

1 I ( can / can t ) read a book, but I ( can / can t ) read a map. 2 They ( can / can t ) swim, but they ( can / can t ) pitch a tent. Avntur mp Writ t nms o t rtrs Flip Flo Hnn Mri Tom Cirl I lik ( ply / plyin ) sor, ut I ( on t / osn t ) lik mpin H osn t lik ( wt / wtin ) TV H ( lik / liks ) rin Ty r ( Brzil / Britis ) Ty r ( liv /

More information

b. How many ternary words of length 23 with eight 0 s, nine 1 s and six 2 s?

b. How many ternary words of length 23 with eight 0 s, nine 1 s and six 2 s? MATH 3012 Finl Exm, My 4, 2006, WTT Stunt Nm n ID Numr 1. All our prts o this prolm r onrn with trnry strings o lngth n, i.., wors o lngth n with lttrs rom th lpht {0, 1, 2}.. How mny trnry wors o lngth

More information

Grade 7/8 Math Circles March 4/5, Graph Theory I- Solutions

Grade 7/8 Math Circles March 4/5, Graph Theory I- Solutions ulty o Mtmtis Wtrloo, Ontrio N ntr or ution in Mtmtis n omputin r / Mt irls Mr /, 0 rp Tory - Solutions * inits lln qustion. Tr t ollowin wlks on t rp low. or on, stt wtr it is pt? ow o you know? () n

More information

S i m p l i f y i n g A l g e b r a SIMPLIFYING ALGEBRA.

S i m p l i f y i n g A l g e b r a SIMPLIFYING ALGEBRA. S i m p l i y i n g A l g r SIMPLIFYING ALGEBRA www.mthltis.o.nz Simpliying SIMPLIFYING Algr ALGEBRA Algr is mthmtis with mor thn just numrs. Numrs hv ix vlu, ut lgr introus vrils whos vlus n hng. Ths

More information

12/3/12. Outline. Part 10. Graphs. Circuits. Euler paths/circuits. Euler s bridge problem (Bridges of Konigsberg Problem)

12/3/12. Outline. Part 10. Graphs. Circuits. Euler paths/circuits. Euler s bridge problem (Bridges of Konigsberg Problem) 12/3/12 Outlin Prt 10. Grphs CS 200 Algorithms n Dt Struturs Introution Trminology Implmnting Grphs Grph Trvrsls Topologil Sorting Shortst Pths Spnning Trs Minimum Spnning Trs Ciruits 1 Ciruits Cyl 2 Eulr

More information

Present state Next state Q + M N

Present state Next state Q + M N Qustion 1. An M-N lip-lop works s ollows: I MN=00, th nxt stt o th lip lop is 0. I MN=01, th nxt stt o th lip-lop is th sm s th prsnt stt I MN=10, th nxt stt o th lip-lop is th omplmnt o th prsnt stt I

More information

5/9/13. Part 10. Graphs. Outline. Circuits. Introduction Terminology Implementing Graphs

5/9/13. Part 10. Graphs. Outline. Circuits. Introduction Terminology Implementing Graphs Prt 10. Grphs CS 200 Algorithms n Dt Struturs 1 Introution Trminology Implmnting Grphs Outlin Grph Trvrsls Topologil Sorting Shortst Pths Spnning Trs Minimum Spnning Trs Ciruits 2 Ciruits Cyl A spil yl

More information

CSE 373: More on graphs; DFS and BFS. Michael Lee Wednesday, Feb 14, 2018

CSE 373: More on graphs; DFS and BFS. Michael Lee Wednesday, Feb 14, 2018 CSE 373: Mor on grphs; DFS n BFS Mihl L Wnsy, F 14, 2018 1 Wrmup Wrmup: Disuss with your nighor: Rmin your nighor: wht is simpl grph? Suppos w hv simpl, irt grph with x nos. Wht is th mximum numr of gs

More information

Decimals DECIMALS.

Decimals DECIMALS. Dimls DECIMALS www.mthltis.o.uk ow os it work? Solutions Dimls P qustions Pl vlu o imls 0 000 00 000 0 000 00 0 000 00 0 000 00 0 000 tnths or 0 thousnths or 000 hunrths or 00 hunrths or 00 0 tn thousnths

More information

Graphs. Graphs. Graphs: Basic Terminology. Directed Graphs. Dr Papalaskari 1

Graphs. Graphs. Graphs: Basic Terminology. Directed Graphs. Dr Papalaskari 1 CSC 00 Disrt Struturs : Introuon to Grph Thory Grphs Grphs CSC 00 Disrt Struturs Villnov Univrsity Grphs r isrt struturs onsisng o vrs n gs tht onnt ths vrs. Grphs n us to mol: omputr systms/ntworks mthml

More information

DUET WITH DIAMONDS COLOR SHIFTING BRACELET By Leslie Rogalski

DUET WITH DIAMONDS COLOR SHIFTING BRACELET By Leslie Rogalski Dut with Dimons Brlt DUET WITH DIAMONDS COLOR SHIFTING BRACELET By Lsli Roglski Photo y Anrw Wirth Supruo DUETS TM from BSmith rt olor shifting fft tht mks your work tk on lif of its own s you mov! This

More information

Seven-Segment Display Driver

Seven-Segment Display Driver 7-Smnt Disply Drivr, Ron s in 7-Smnt Disply Drivr, Ron s in Prolm 62. 00 0 0 00 0000 000 00 000 0 000 00 0 00 00 0 0 0 000 00 0 00 BCD Diits in inry Dsin Drivr Loi 4 inputs, 7 outputs 7 mps, h with 6 on

More information

Add a suitable subordinating conjunction to this sentence: Alex sent a postcard from Scotland he was on holiday.

Add a suitable subordinating conjunction to this sentence: Alex sent a postcard from Scotland he was on holiday. Spring Trm 2 Complt th tal y turning ths ajtivs into s. Th irst on has n on or you. ajtiv simpl a A a suital suorinating onjuntion to this sntn: Alx snt a postar rom Sotlan h was on holiay. Writ on o th

More information

CSC Design and Analysis of Algorithms. Example: Change-Making Problem

CSC Design and Analysis of Algorithms. Example: Change-Making Problem CSC 801- Dsign n Anlysis of Algorithms Ltur 11 Gry Thniqu Exmpl: Chng-Mking Prolm Givn unlimit mounts of oins of nomintions 1 > > m, giv hng for mount n with th lst numr of oins Exmpl: 1 = 25, 2 =10, =

More information

CSE 373: AVL trees. Warmup: Warmup. Interlude: Exploring the balance invariant. AVL Trees: Invariants. AVL tree invariants review

CSE 373: AVL trees. Warmup: Warmup. Interlude: Exploring the balance invariant. AVL Trees: Invariants. AVL tree invariants review rmup CSE 7: AVL trs rmup: ht is n invrint? Mihl L Friy, Jn 9, 0 ht r th AVL tr invrints, xtly? Disuss with your nighor. AVL Trs: Invrints Intrlu: Exploring th ln invrint Cor i: xtr invrint to BSTs tht

More information

, each of which is a tree, and whose roots r 1. , respectively, are children of r. Data Structures & File Management

, each of which is a tree, and whose roots r 1. , respectively, are children of r. Data Structures & File Management nrl tr T is init st o on or mor nos suh tht thr is on sint no r, ll th root o T, n th rminin nos r prtition into n isjoint susts T, T,, T n, h o whih is tr, n whos roots r, r,, r n, rsptivly, r hilrn o

More information

On each of them are the numbers +6, 5, +4, 3, +2, 1. The two dice are rolled. The score is obtained by adding the numbers on the upper faces.

On each of them are the numbers +6, 5, +4, 3, +2, 1. The two dice are rolled. The score is obtained by adding the numbers on the upper faces. Cmrig Essntils Mthmtis Cor 8 N1.1 Homwork N1.1 Homwork 1 A thr shows hr lss 2 six-si i. On h of thm r th numrs +6, 5, +4, 3, +2, 1. Th two i r roll. Th sor is otin y ing th numrs on th uppr fs. Clult th

More information

Numbering Boundary Nodes

Numbering Boundary Nodes Numring Bounry Nos Lh MBri Empori Stt Univrsity August 10, 2001 1 Introution Th purpos of this ppr is to xplor how numring ltril rsistor ntworks ffts thir rspons mtrix, Λ. Morovr, wht n lrn from Λ out

More information

EE1000 Project 4 Digital Volt Meter

EE1000 Project 4 Digital Volt Meter Ovrviw EE1000 Projt 4 Diitl Volt Mtr In this projt, w mk vi tht n msur volts in th rn o 0 to 4 Volts with on iit o ury. Th input is n nlo volt n th output is sinl 7-smnt iit tht tlls us wht tht input s

More information

Outline. Circuits. Euler paths/circuits 4/25/12. Part 10. Graphs. Euler s bridge problem (Bridges of Konigsberg Problem)

Outline. Circuits. Euler paths/circuits 4/25/12. Part 10. Graphs. Euler s bridge problem (Bridges of Konigsberg Problem) 4/25/12 Outlin Prt 10. Grphs CS 200 Algorithms n Dt Struturs Introution Trminology Implmnting Grphs Grph Trvrsls Topologil Sorting Shortst Pths Spnning Trs Minimum Spnning Trs Ciruits 1 2 Eulr s rig prolm

More information

Aquauno Video 6 Plus Page 1

Aquauno Video 6 Plus Page 1 Connt th timr to th tp. Aquuno Vio 6 Plus Pg 1 Usr mnul 3 lik! For Aquuno Vio 6 (p/n): 8456 For Aquuno Vio 6 Plus (p/n): 8413 Opn th timr unit y prssing th two uttons on th sis, n fit 9V lklin ttry. Whn

More information

Designing A Concrete Arch Bridge

Designing A Concrete Arch Bridge This is th mous Shwnh ri in Switzrln, sin y Rort Millrt in 1933. It spns 37.4 mtrs (122 t) n ws sin usin th sm rphil mths tht will monstrt in this lsson. To pro with this lsson, lik on th Nxt utton hr

More information

QUESTIONS BEGIN HERE!

QUESTIONS BEGIN HERE! Points miss: Stunt's Nm: Totl sor: /100 points Est Tnnss Stt Univrsity Dprtmnt o Computr n Inormtion Sins CSCI 2710 (Trno) Disrt Struturs TEST or Sprin Smstr, 2005 R this or strtin! This tst is los ook

More information

FSA. CmSc 365 Theory of Computation. Finite State Automata and Regular Expressions (Chapter 2, Section 2.3) ALPHABET operations: U, concatenation, *

FSA. CmSc 365 Theory of Computation. Finite State Automata and Regular Expressions (Chapter 2, Section 2.3) ALPHABET operations: U, concatenation, * CmSc 365 Thory of Computtion Finit Stt Automt nd Rgulr Exprssions (Chptr 2, Sction 2.3) ALPHABET oprtions: U, conctntion, * otin otin Strings Form Rgulr xprssions dscri Closd undr U, conctntion nd * (if

More information

Nefertiti. Echoes of. Regal components evoke visions of the past MULTIPLE STITCHES. designed by Helena Tang-Lim

Nefertiti. Echoes of. Regal components evoke visions of the past MULTIPLE STITCHES. designed by Helena Tang-Lim MULTIPLE STITCHES Nrtiti Ehos o Rgl omponnts vok visions o th pst sign y Hln Tng-Lim Us vrity o stiths to rt this rgl yt wrl sign. Prt sping llows squr s to mk roun omponnts tht rp utiully. FCT-SC-030617-07

More information

N1.1 Homework Answers

N1.1 Homework Answers Camrig Essntials Mathmatis Cor 8 N. Homwork Answrs N. Homwork Answrs a i 6 ii i 0 ii 3 2 Any pairs of numrs whih satisfy th alulation. For xampl a 4 = 3 3 6 3 = 3 4 6 2 2 8 2 3 3 2 8 5 5 20 30 4 a 5 a

More information

Instructions for Section 1

Instructions for Section 1 Instructions for Sction 1 Choos th rspons tht is corrct for th qustion. A corrct nswr scors 1, n incorrct nswr scors 0. Mrks will not b dductd for incorrct nswrs. You should ttmpt vry qustion. No mrks

More information

More Foundations. Undirected Graphs. Degree. A Theorem. Graphs, Products, & Relations

More Foundations. Undirected Graphs. Degree. A Theorem. Graphs, Products, & Relations Mr Funtins Grphs, Pruts, & Rltins Unirt Grphs An unirt grph is pir f 1. A st f ns 2. A st f gs (whr n g is st f tw ns*) Friy, Sptmr 2, 2011 Ring: Sipsr 0.2 ginning f 0.4; Stughtn 1.1.5 ({,,,,}, {{,}, {,},

More information

Tangram Fractions Overview: Students will analyze standard and nonstandard

Tangram Fractions Overview: Students will analyze standard and nonstandard ACTIVITY 1 Mtrils: Stunt opis o tnrm mstrs trnsprnis o tnrm mstrs sissors PROCEDURE Skills: Dsriin n nmin polyons Stuyin onrun Comprin rtions Tnrm Frtions Ovrviw: Stunts will nlyz stnr n nonstnr tnrms

More information

Cycles and Simple Cycles. Paths and Simple Paths. Trees. Problem: There is No Completely Standard Terminology!

Cycles and Simple Cycles. Paths and Simple Paths. Trees. Problem: There is No Completely Standard Terminology! Outlin Computr Sin 331, Spnnin, n Surphs Mik Joson Dprtmnt o Computr Sin Univrsity o Clry Ltur #30 1 Introution 2 3 Dinition 4 Spnnin 5 6 Mik Joson (Univrsity o Clry) Computr Sin 331 Ltur #30 1 / 20 Mik

More information

COMPLEXITY OF COUNTING PLANAR TILINGS BY TWO BARS

COMPLEXITY OF COUNTING PLANAR TILINGS BY TWO BARS OMPLXITY O OUNTING PLNR TILINGS Y TWO RS KYL MYR strt. W show tht th prolm o trmining th numr o wys o tiling plnr igur with horizontl n vrtil r is #P-omplt. W uil o o th rsults o uquir, Nivt, Rmil, n Roson

More information

The Plan. Honey, I Shrunk the Data. Why Compress. Data Compression Concepts. Braille Example. Braille. x y xˆ

The Plan. Honey, I Shrunk the Data. Why Compress. Data Compression Concepts. Braille Example. Braille. x y xˆ h ln ony, hrunk th t ihr nr omputr in n nginring nivrsity of shington t omprssion onpts ossy t omprssion osslss t omprssion rfix os uffmn os th y 24 2 t omprssion onpts originl omprss o x y xˆ nor or omprss

More information

Integration Continued. Integration by Parts Solving Definite Integrals: Area Under a Curve Improper Integrals

Integration Continued. Integration by Parts Solving Definite Integrals: Area Under a Curve Improper Integrals Intgrtion Continud Intgrtion y Prts Solving Dinit Intgrls: Ar Undr Curv Impropr Intgrls Intgrtion y Prts Prticulrly usul whn you r trying to tk th intgrl o som unction tht is th product o n lgric prssion

More information

CS61B Lecture #33. Administrivia: Autograder will run this evening. Today s Readings: Graph Structures: DSIJ, Chapter 12

CS61B Lecture #33. Administrivia: Autograder will run this evening. Today s Readings: Graph Structures: DSIJ, Chapter 12 Aministrivi: CS61B Ltur #33 Autogrr will run this vning. Toy s Rings: Grph Struturs: DSIJ, Chptr 12 Lst moifi: W Nov 8 00:39:28 2017 CS61B: Ltur #33 1 Why Grphs? For xprssing non-hirrhilly rlt itms Exmpls:

More information

CSE 373. Graphs 1: Concepts, Depth/Breadth-First Search reading: Weiss Ch. 9. slides created by Marty Stepp

CSE 373. Graphs 1: Concepts, Depth/Breadth-First Search reading: Weiss Ch. 9. slides created by Marty Stepp CSE 373 Grphs 1: Conpts, Dpth/Brth-First Srh ring: Wiss Ch. 9 slis rt y Mrty Stpp http://www.s.wshington.u/373/ Univrsity o Wshington, ll rights rsrv. 1 Wht is grph? 56 Tokyo Sttl Soul 128 16 30 181 140

More information

Module 2 Motion Instructions

Module 2 Motion Instructions Moul 2 Motion Instrutions CAUTION: Bor you strt this xprimnt, unrstn tht you r xpt to ollow irtions EXPLICITLY! Tk your tim n r th irtions or h stp n or h prt o th xprimnt. You will rquir to ntr t in prtiulr

More information

Binomials and Pascal s Triangle

Binomials and Pascal s Triangle Binomils n Psl s Tringl Binomils n Psl s Tringl Curriulum R AC: 0, 0, 08 ACS: 00 www.mthltis.om Binomils n Psl s Tringl Bsis 0. Intif th prts of th polnomil: 8. (i) Th gr. Th gr is. (Sin is th highst

More information

0.1. Exercise 1: the distances between four points in a graph

0.1. Exercise 1: the distances between four points in a graph Mth 707 Spring 2017 (Drij Grinrg): mitrm 3 pg 1 Mth 707 Spring 2017 (Drij Grinrg): mitrm 3 u: W, 3 My 2017, in lss or y mil (grinr@umn.u) or lss S th wsit or rlvnt mtril. Rsults provn in th nots, or in

More information

Who is this Great Team? Nickname. Strangest Gift/Friend. Hometown. Best Teacher. Hobby. Travel Destination. 8 G People, Places & Possibilities

Who is this Great Team? Nickname. Strangest Gift/Friend. Hometown. Best Teacher. Hobby. Travel Destination. 8 G People, Places & Possibilities Who i thi Gt Tm? Exi Sh th foowing i of infomtion bot of with o tb o tm mt. Yo o not hv to wit n of it own. Yo wi b givn on 5 mint to omih thi tk. Stngt Gift/Fin Niknm Homtown Bt Th Hobb Tv Dtintion Robt

More information

Planar Upward Drawings

Planar Upward Drawings C.S. 252 Pro. Rorto Tmssi Computtionl Gomtry Sm. II, 1992 1993 Dt: My 3, 1993 Sri: Shmsi Moussvi Plnr Upwr Drwings 1 Thorm: G is yli i n only i it hs upwr rwing. Proo: 1. An upwr rwing is yli. Follow th

More information

Chapter 16. 1) is a particular point on the graph of the function. 1. y, where x y 1

Chapter 16. 1) is a particular point on the graph of the function. 1. y, where x y 1 Prctic qustions W now tht th prmtr p is dirctl rltd to th mplitud; thrfor, w cn find tht p. cos d [ sin ] sin sin Not: Evn though ou might not now how to find th prmtr in prt, it is lws dvisl to procd

More information

TOPIC 5: INTEGRATION

TOPIC 5: INTEGRATION TOPIC 5: INTEGRATION. Th indfinit intgrl In mny rspcts, th oprtion of intgrtion tht w r studying hr is th invrs oprtion of drivtion. Dfinition.. Th function F is n ntidrivtiv (or primitiv) of th function

More information

COMP108 Algorithmic Foundations

COMP108 Algorithmic Foundations Grdy mthods Prudn Wong http://www.s.liv..uk/~pwong/thing/omp108/01617 Coin Chng Prolm Suppos w hv 3 typs of oins 10p 0p 50p Minimum numr of oins to mk 0.8, 1.0, 1.? Grdy mthod Lrning outoms Undrstnd wht

More information

Graph Isomorphism. Graphs - II. Cayley s Formula. Planar Graphs. Outline. Is K 5 planar? The number of labeled trees on n nodes is n n-2

Graph Isomorphism. Graphs - II. Cayley s Formula. Planar Graphs. Outline. Is K 5 planar? The number of labeled trees on n nodes is n n-2 Grt Thortil Is In Computr Sin Vitor Amhik CS 15-251 Ltur 9 Grphs - II Crngi Mllon Univrsity Grph Isomorphism finition. Two simpl grphs G n H r isomorphi G H if thr is vrtx ijtion V H ->V G tht prsrvs jny

More information

Math 166 Week in Review 2 Sections 1.1b, 1.2, 1.3, & 1.4

Math 166 Week in Review 2 Sections 1.1b, 1.2, 1.3, & 1.4 Mt 166 WIR, Sprin 2012, Bnjmin urisp Mt 166 Wk in Rviw 2 Stions 1.1, 1.2, 1.3, & 1.4 1. S t pproprit rions in Vnn irm tt orrspon to o t ollowin sts. () (B ) B () ( ) B B () (B ) B 1 Mt 166 WIR, Sprin 2012,

More information

A Simple Code Generator. Code generation Algorithm. Register and Address Descriptors. Example 3/31/2008. Code Generation

A Simple Code Generator. Code generation Algorithm. Register and Address Descriptors. Example 3/31/2008. Code Generation A Simpl Co Gnrtor Co Gnrtion Chptr 8 II Gnrt o for singl si lok How to us rgistrs? In most mhin rhitturs, som or ll of th oprnsmust in rgistrs Rgistrs mk goo tmporris Hol vlus tht r omput in on si lok

More information

ME 522 PRINCIPLES OF ROBOTICS. FIRST MIDTERM EXAMINATION April 19, M. Kemal Özgören

ME 522 PRINCIPLES OF ROBOTICS. FIRST MIDTERM EXAMINATION April 19, M. Kemal Özgören ME 522 PINCIPLES OF OBOTICS FIST MIDTEM EXAMINATION April 9, 202 Nm Lst Nm M. Kml Özgörn 2 4 60 40 40 0 80 250 USEFUL FOMULAS cos( ) cos cos sin sin sin( ) sin cos cos sin sin y/ r, cos x/ r, r 0 tn 2(

More information

Page 1. Question 19.1b Electric Charge II Question 19.2a Conductors I. ConcepTest Clicker Questions Chapter 19. Physics, 4 th Edition James S.

Page 1. Question 19.1b Electric Charge II Question 19.2a Conductors I. ConcepTest Clicker Questions Chapter 19. Physics, 4 th Edition James S. ConTst Clikr ustions Chtr 19 Physis, 4 th Eition Jms S. Wlkr ustion 19.1 Two hrg blls r rlling h othr s thy hng from th iling. Wht n you sy bout thir hrgs? Eltri Chrg I on is ositiv, th othr is ngtiv both

More information

Winter 2016 COMP-250: Introduction to Computer Science. Lecture 23, April 5, 2016

Winter 2016 COMP-250: Introduction to Computer Science. Lecture 23, April 5, 2016 Wintr 2016 COMP-250: Introduction to Computr Scinc Lctur 23, April 5, 2016 Commnt out input siz 2) Writ ny lgorithm tht runs in tim Θ(n 2 log 2 n) in wors cs. Explin why this is its running tim. I don

More information

Garnir Polynomial and their Properties

Garnir Polynomial and their Properties Univrsity of Cliforni, Dvis Dprtmnt of Mthmtis Grnir Polynomil n thir Proprtis Author: Yu Wng Suprvisor: Prof. Gorsky Eugny My 8, 07 Grnir Polynomil n thir Proprtis Yu Wng mil: uywng@uvis.u. In this ppr,

More information

In order to learn which questions have been answered correctly: 1. Print these pages. 2. Answer the questions.

In order to learn which questions have been answered correctly: 1. Print these pages. 2. Answer the questions. Crystl Rports for Visul Stuio.NET In orr to lrn whih qustions hv n nswr orrtly: 1. Print ths pgs. 2. Answr th qustions. 3. Sn this ssssmnt with th nswrs vi:. FAX to (212) 967-3498. Or. Mil th nswrs to

More information

V={A,B,C,D,E} E={ (A,D),(A,E),(B,D), (B,E),(C,D),(C,E)}

V={A,B,C,D,E} E={ (A,D),(A,E),(B,D), (B,E),(C,D),(C,E)} Introution Computr Sin & Enginring 423/823 Dsign n Anlysis of Algorithms Ltur 03 Elmntry Grph Algorithms (Chptr 22) Stphn Sott (Apt from Vinohnrn N. Vriym) I Grphs r strt t typs tht r pplil to numrous

More information

Last time: introduced our first computational model the DFA.

Last time: introduced our first computational model the DFA. Lctur 7 Homwork #7: 2.2.1, 2.2.2, 2.2.3 (hnd in c nd d), Misc: Givn: M, NFA Prov: (q,xy) * (p,y) iff (q,x) * (p,) (follow proof don in clss tody) Lst tim: introducd our first computtionl modl th DFA. Tody

More information

Probability. Probability. Curriculum Ready ACMSP: 225, 226, 246,

Probability. Probability. Curriculum Ready ACMSP: 225, 226, 246, Proility Proility Curriulum Ry ACMSP:, 6, 6, 7 www.mthltis.om Proility PROBABILITY Proility msurs th hn of somthing hppning. This mns w n us mthmtis to fin how likly it is tht n vnt will hppn. Answr ths

More information

3 a b c km m m 8 a 3.4 m b 2.4 m

3 a b c km m m 8 a 3.4 m b 2.4 m Chaptr Exris A a 9. m. m. m 9. km. mm. m Purpl lag hapr y 8p 8m. km. m Th triangl on th right 8. m 9 a. m. m. m Exris B a m. m mm. km. mm m a. 9 8...8 m. m 8. 9 m Ativity p. 9 Pupil s own answrs Ara =

More information

Multipoint Alternate Marking method for passive and hybrid performance monitoring

Multipoint Alternate Marking method for passive and hybrid performance monitoring Multipoint Altrnt Mrkin mtho or pssiv n hyri prormn monitorin rt-iool-ippm-multipoint-lt-mrk-00 Pru, Jul 2017, IETF 99 Giuspp Fiool (Tlom Itli) Muro Coilio (Tlom Itli) Amo Spio (Politnio i Torino) Riro

More information

Chem 104A, Fall 2016, Midterm 1 Key

Chem 104A, Fall 2016, Midterm 1 Key hm 104A, ll 2016, Mitrm 1 Ky 1) onstruct microstt tl for p 4 configurtion. Pls numrt th ms n ml for ch lctron in ch microstt in th tl. (Us th formt ml m s. Tht is spin -½ lctron in n s oritl woul writtn

More information

MA1506 Tutorial 2 Solutions. Question 1. (1a) 1 ) y x. e x. 1 exp (in general, Integrating factor is. ye dx. So ) (1b) e e. e c.

MA1506 Tutorial 2 Solutions. Question 1. (1a) 1 ) y x. e x. 1 exp (in general, Integrating factor is. ye dx. So ) (1b) e e. e c. MA56 utorial Solutions Qustion a Intgrating fator is ln p p in gnral, multipl b p So b ln p p sin his kin is all a Brnoulli quation -- st Sin w fin Y, Y Y, Y Y p Qustion Dfin v / hn our quation is v μ

More information

Pupil / Class Record We can assume a word has been learned when it has been either tested or used correctly at least three times.

Pupil / Class Record We can assume a word has been learned when it has been either tested or used correctly at least three times. 2 Pupi / Css Rr W ssum wr hs b r wh i hs b ihr s r us rry s hr ims. Nm: D Bu: fr i bus brhr u firs hf hp hm s uh i iv iv my my mr muh m w ih w Tik r pp push pu sh shu sisr s sm h h hir hr hs im k w vry

More information

Outline. 1 Introduction. 2 Min-Cost Spanning Trees. 4 Example

Outline. 1 Introduction. 2 Min-Cost Spanning Trees. 4 Example Outlin Computr Sin 33 Computtion o Minimum-Cost Spnnin Trs Prim's Alorithm Introution Mik Joson Dprtmnt o Computr Sin Univrsity o Clry Ltur #33 3 Alorithm Gnrl Constrution Mik Joson (Univrsity o Clry)

More information

CS September 2018

CS September 2018 Loil los Distriut Systms 06. Loil los Assin squn numrs to msss All ooprtin prosss n r on orr o vnts vs. physil los: rport tim o y Assum no ntrl tim sour Eh systm mintins its own lol lo No totl orrin o

More information

Solutions for HW11. Exercise 34. (a) Use the recurrence relation t(g) = t(g e) + t(g/e) to count the number of spanning trees of v 1

Solutions for HW11. Exercise 34. (a) Use the recurrence relation t(g) = t(g e) + t(g/e) to count the number of spanning trees of v 1 Solutions for HW Exris. () Us th rurrn rltion t(g) = t(g ) + t(g/) to ount th numr of spnning trs of v v v u u u Rmmr to kp multipl gs!! First rrw G so tht non of th gs ross: v u v Rursing on = (v, u ):

More information

SOLVED EXAMPLES. be the foci of an ellipse with eccentricity e. For any point P on the ellipse, prove that. tan

SOLVED EXAMPLES. be the foci of an ellipse with eccentricity e. For any point P on the ellipse, prove that. tan LOCUS 58 SOLVED EXAMPLES Empl Lt F n F th foci of n llips with ccntricit. For n point P on th llips, prov tht tn PF F tn PF F Assum th llips to, n lt P th point (, sin ). P(, sin ) F F F = (-, 0) F = (,

More information

Improving Union. Implementation. Union-by-size Code. Union-by-Size Find Analysis. Path Compression! Improving Find find(e)

Improving Union. Implementation. Union-by-size Code. Union-by-Size Find Analysis. Path Compression! Improving Find find(e) POW CSE 36: Dt Struturs Top #10 T Dynm (Equvln) Duo: Unon-y-Sz & Pt Comprsson Wk!! Luk MDowll Summr Qurtr 003 M! ZING Wt s Goo Mz? Mz Construton lortm Gvn: ollton o rooms V Conntons twn t rooms (ntlly

More information

Walk Like a Mathematician Learning Task:

Walk Like a Mathematician Learning Task: Gori Dprtmnt of Euction Wlk Lik Mthmticin Lrnin Tsk: Mtrics llow us to prform mny usful mthmticl tsks which orinrily rquir lr numbr of computtions. Som typs of problms which cn b on fficintly with mtrics

More information

4.1 Interval Scheduling. Chapter 4. Greedy Algorithms. Interval Scheduling: Greedy Algorithms. Interval Scheduling. Interval scheduling.

4.1 Interval Scheduling. Chapter 4. Greedy Algorithms. Interval Scheduling: Greedy Algorithms. Interval Scheduling. Interval scheduling. Cptr 4 4 Intrvl Suln Gry Alortms Sls y Kvn Wyn Copyrt 005 Prson-Ason Wsly All rts rsrv Intrvl Suln Intrvl Suln: Gry Alortms Intrvl suln! Jo strts t s n nss t! Two os omptl ty on't ovrlp! Gol: n mxmum sust

More information

FINE JEWELRY & DESIGN STUDIO. 63 Haywood Street in Downtown Asheville North Carolina

FINE JEWELRY & DESIGN STUDIO. 63 Haywood Street in Downtown Asheville North Carolina FINE JEWELRY & DESIGN STUDIO 63 Hywoo Strt in Downtown Ashvill North Crolin 828.254.5088 www.jwlsthtn.om g i h. 14kw imon (0.21 tw) n $750. 14kw imon (0.46 tw) n $1,350. 14kw imon n spphir trrop rrings

More information

MAT3707. Tutorial letter 201/1/2017 DISCRETE MATHEMATICS: COMBINATORICS. Semester 1. Department of Mathematical Sciences MAT3707/201/1/2017

MAT3707. Tutorial letter 201/1/2017 DISCRETE MATHEMATICS: COMBINATORICS. Semester 1. Department of Mathematical Sciences MAT3707/201/1/2017 MAT3707/201/1/2017 Tutoril lttr 201/1/2017 DISCRETE MATHEMATICS: COMBINATORICS MAT3707 Smstr 1 Dprtmnt o Mtmtil Sins SOLUTIONS TO ASSIGNMENT 01 BARCODE Din tomorrow. univrsity o sout ri SOLUTIONS TO ASSIGNMENT

More information

CSE303 - Introduction to the Theory of Computing Sample Solutions for Exercises on Finite Automata

CSE303 - Introduction to the Theory of Computing Sample Solutions for Exercises on Finite Automata CSE303 - Introduction to th Thory of Computing Smpl Solutions for Exrciss on Finit Automt Exrcis 2.1.1 A dtrministic finit utomton M ccpts th mpty string (i.., L(M)) if nd only if its initil stt is finl

More information

Exam 1 Solution. CS 542 Advanced Data Structures and Algorithms 2/14/2013

Exam 1 Solution. CS 542 Advanced Data Structures and Algorithms 2/14/2013 CS Avn Dt Struturs n Algorithms Exm Solution Jon Turnr //. ( points) Suppos you r givn grph G=(V,E) with g wights w() n minimum spnning tr T o G. Now, suppos nw g {u,v} is to G. Dsri (in wors) mtho or

More information

RUTH. land_of_israel: the *country *which God gave to his people in the *Old_Testament. [*map # 2]

RUTH. land_of_israel: the *country *which God gave to his people in the *Old_Testament. [*map # 2] RUTH 1 Elimlk g ln M 1-2 I in im n ln Irl i n *king. Tr r lr rul ln. Ty r ug. Tr n r l in Ju u r g min. Elimlk mn y in n Blm in Ju. H i nm Nmi. S n Elimlk 2 *n. Tir nm r Mln n Kilin. Ty r ll rm Er mily.

More information

6202R. between SKY and GROUND. Statement sidewalk

6202R. between SKY and GROUND. Statement sidewalk twn SKY n GROUND Sttmnt siwlk wlkwy onnting rivrsi puli zons grnlin Lirris n musums in our tim r not only rsrv rtifts n ooks ut offr iffrnt vnts to visitors, host utionl n ivi progrms, nsur flxil sps for

More information

UNCORRECTED PAGE PROOFS

UNCORRECTED PAGE PROOFS 7 Shps 9 Unrstning lngth isovr n ojts Msurmnt n gomtry Wht informtion n w gthr from 2 shps n 3 ojts? 7 7 7 7 7E 7F 7G 7H 7I Tringl proprtis Quriltrl proprtis 2 shps n 3 ojts Isomtri rwings n plns Nts n

More information

V={A,B,C,D,E} E={ (A,D),(A,E),(B,D), (B,E),(C,D),(C,E)}

V={A,B,C,D,E} E={ (A,D),(A,E),(B,D), (B,E),(C,D),(C,E)} s s of s Computr Sin & Enginring 423/823 Dsign n Anlysis of Ltur 03 (Chptr 22) Stphn Sott (Apt from Vinohnrn N. Vriym) s of s s r strt t typs tht r pplil to numrous prolms Cn ptur ntitis, rltionships twn

More information

12. Traffic engineering

12. Traffic engineering lt2.ppt S-38. Introution to Tltrffi Thory Spring 200 2 Topology Pths A tlommunition ntwork onsists of nos n links Lt N not th st of nos in with n Lt J not th st of nos in with j N = {,,,,} J = {,2,3,,2}

More information

SAMPLE LITANY OF THE SAINTS E/G. Dadd9/F. Aadd9. cy. Christ, have. Lord, have mer cy. Christ, have A/E. Dadd9. Aadd9/C Bm E. 1. Ma ry and. mer cy.

SAMPLE LITANY OF THE SAINTS E/G. Dadd9/F. Aadd9. cy. Christ, have. Lord, have mer cy. Christ, have A/E. Dadd9. Aadd9/C Bm E. 1. Ma ry and. mer cy. LTNY OF TH SNTS Cntrs Gnt flwng ( = c. 100) /G Ddd9/F ll Kybrd / hv Ddd9 hv hv Txt 1973, CL. ll rghts rsrvd. Usd wth prmssn. Musc: D. Bckr, b. 1953, 1987, D. Bckr. Publshd by OCP. ll rghts rsrvd. SMPL

More information

d e c b a d c b a d e c b a a c a d c c e b

d e c b a d c b a d e c b a a c a d c c e b FLAT PEYOTE STITCH Bin y mkin stoppr -- sw trou n pull it lon t tr until it is out 6 rom t n. Sw trou t in witout splittin t tr. You soul l to sli it up n own t tr ut it will sty in pl wn lt lon. Evn-Count

More information

INTEGRALS. Chapter 7. d dx. 7.1 Overview Let d dx F (x) = f (x). Then, we write f ( x)

INTEGRALS. Chapter 7. d dx. 7.1 Overview Let d dx F (x) = f (x). Then, we write f ( x) Chptr 7 INTEGRALS 7. Ovrviw 7.. Lt d d F () f (). Thn, w writ f ( ) d F () + C. Ths intgrls r clld indfinit intgrls or gnrl intgrls, C is clld constnt of intgrtion. All ths intgrls diffr y constnt. 7..

More information

5/1/2018. Huffman Coding Trees. Huffman Coding Trees. Huffman Coding Trees. Huffman Coding Trees. Huffman Coding Trees. Huffman Coding Trees

5/1/2018. Huffman Coding Trees. Huffman Coding Trees. Huffman Coding Trees. Huffman Coding Trees. Huffman Coding Trees. Huffman Coding Trees /1/018 W usully no strns y ssnn -lnt os to ll rtrs n t lpt (or mpl, 8-t on n ASCII). Howvr, rnt rtrs our wt rnt rquns, w n sv mmory n ru trnsmttl tm y usn vrl-lnt non. T s to ssn sortr os to rtrs tt our

More information