3. Resolve into factors: (i) a3+b3—c3+3abc. b3+3abc=c3. (ii) (a+b)1+aa+ba. Show that if a+b=c then will a3+ (iii) a2(b+c)+b2 (c+a)+c2(a+b). 4. (a) Find the H.C.F and L.C.M. of the two terms of the fol3x2-5x+2 lowing fraction 4x3-4x2-4x+1 (b) What value of x will make both terms of the fraction in (a) equal? 5. (a) Define exponent. What kind of numbers is included in the definition of exponent? (b) Establish a meaning consistent with the definition of exponent for a positive fractional exponent. (c) Find the product of a+a-}−(a}}+a-})+1 by 1+(a}+a-}) (d) Extract the square root of: 4a+9b3-12a1b}+16ac1—24b{c}+16c1. 6. (a) Define a surd expression. (b) Find the value of V5 within less than of its exact value. From your solution show that the value of a real surd may be approximated as nearly as you please. (c) Simplify (3+V3) (3+V5) (V5—2) (b) If a, b, and c be unequal and 00 q show that ax+by+cz 0. Point out the necessity of the restriction in "unequal." 9. A man walks one mile an hour faster than a boy and takes one hour less in going 1534 miles? Find the boy's rate of walking. 10. (a) Construct an equation of two dimensions whose roots shall be 3 and 5. (b) What observations do you make regarding the value of each factor composing the equation? (c) Solve ax2+bx+c=0. From your result show (i) When the root are real and unequal. (ii) When the roots are imaginary. (iii) That surd roots occur in pairs. Solve 5x 3(x-1) =2x+ X- -3 3(x-2) Latin Authors. Time-Two and one-half hours. 1. Quibus rebus cognitis, principes Britannia, qui post proelium factum ad ea, quae jusserat Caesar, facienda convenerant, inter se colloquuti, quum equites et naves et frumentum Romanis deesse intelligerent et paucitatem militum ex castorum exiguitate cognoscerent, quae hoc erant etiam angustiora, quod sine impedimentis Caesar legiones transportaverat, optimum factu esse duxerunt, rebellione facta, frumento commeatuque nostros prohibere, et rem in hiemem producere, quod, iis superatis aut reditu interclusis, neminem postea belli inferendi causa in Britanniam transiturum confidebant. Itaque rursus conjuratione facta, paulatim ex castris discedere, ac suos clam ex agris deducere coeperunt. inem. (a) Translate. (b) Account for the case of: facienda, hoc, frumento, iis, nem (c) Give the grammatical relation: ea, colloquuti, angustiora, factu, interclusis. 2. Equites hostium essedariique acriter proelio cum equitatu nostro in itinere conflixerunt, tamen ut nostri omnibus partibus superiores fuerint atque eos in silvas collesque compulerint; sed compluribus interfectis cupidius insecuti nonnullos ex suis amiserunt. At illi intermisso spatio imprudentibus nostris atque occupatis in munitione castorum, subito se ex silvis ejecerunt impetuque in eos facto, qui erant in statione pro castris collocati, acriter pugnaverunt, duabusque missis subsidio cohortibus a Cæsare atque his primis legionum duarum, cum hae perexiguo intermisso á spatio inter se constitissent, novo genere pugnæ perterritis nostris per medios audacissime perruperunt seque inde incolumes receperunt. (a) Translate. erunt. (b) Give the principal parts of: compulerint, perruperunt, ejec (c) State definitely to whom each of the following refers: compluribus, suis, illi, eos, (in eos facto), his. (d) Write explanatory notes on: essedarii, his primis, novo genere pugnae. (e) Account for the mood of: fuerint, constitissent. 3. Diverso interea miscentur moenia luctu, et magis atque magis, quamquam secreta parentis ascensu supero atque arrectis auribus adsto: exoritur clamorque virum clangorque tubarum. (a) Translate. (b) Compare proximus. Give the principal parts of sternil. Account for the plural animi. (c) Write explanatory notes on: Anchisae, Danaum, Deïphobi; Vulcano. son is. (d) In segetem....pastor. Indicate clearly what the compari 4. 'Saepe fugam Danai Troia cupiere relicta fecissentque utinam; saepe illos aspera ponti praecipue cum iam hic trabibus contextus acernis (a) Translate. (b) Account for the case of: reditus, anima; and the mood of parent. (c) Parse ponti, adytis, ima. (d) Give the principal parts of: staret, caesa, obstipuere. caesa." What is the reference Latin Grammar, Prose and Sight Translation. Time-Two and one-half hours. 1. Give with reasons the gender of: Olympus, fagus, poeta, nefas and margarita. 2. (a) Decline in the singular: jus, bos, nubes, agger. (b) Decline in the plural: pes, mare, nix, radix. (c) Give genitive and gender of: homo, carmen, hiems, corpus. 3. (a) Write in full: fem. plur. of miser; neut. sing. of alius; neut. plur. of idem. (b) Compare: malus, gracilis, primus. (c) Write the Latin numeral adjectives (cardinal and ordinal) from one to five. Give the corresponding numeral adverbs. 4. Give (a) 3rd sing. perf. ind. act. of: possum, coepi. (b) 3rd plur. pres. subj.. act. of: volo, sum. (c) 2nd plur, plup. subj. pass. of: dedo, fero. (d) 2nd sing. and plur. imperative of: eo, nolo, edo (to eat). 5. Express in Latin: two forts; ten miles; they came to see; we eat to live; at home. 6. Translate into Latin: (a) The scouts brought word that the enemy would pitch his tent at the foot of the hill. (b) They all promised to come into camp with their baggage. (c) At the fourth hour of the day he reached Britain and there beheld armed troops on all the hills. (d) Do not think that you will often have as good an opportunity. 7. Illustrate in Latin sentences: (a) A verb governing the dative. (b) The partitive genitive. (c) The use of fido. (d) The dative of possession. 8. Translate into Latin: (a) When these things had been accomplished a ten days' thanksgiving was decreed by the senate. (b) At that time all the soldiers were afraid that they would be surrounded by the enemy, that they would be defeated and the city taken. (c) He himself in the meanwhile, until he learned that the legions had assembled, made up his mind to remain in Gaul. 9. Translate: Tria bella Romani cum Poenis gesserunt. Primo Regulus consul Romanus maxima cum laude tera marique pugnabat. Poeni perterriti de pace agere volebant. Ille tamen, nisi duris condicionibus, pacem dare noluit. Poeni tandem, commutatione rerum facta, Romanos magna clade vicerunt et Regulum ceperunt. Utrique jam captivos inter se reddere cupiunt. Regulus igitur a Poenis Romam missus est pollicitus nisi civibus suis ut captivos redderent persuaderet sese ad supplicium perferendum rediturum esse. Ubi ad urbem pervenit, captivorum permutationem incommodo rei publicae arbitratus, uxoris precibus liberorumque immotus, Carthaginem rediit. Paucis post diebus omnibus suppliciis necatus est. Poenus-Carthaginian. Time-Two and one-half hours. 1. Translate: French Authors. Et, ceci l'ayant étonné, il se cacha pour observer ce qui se passerait. Et, après un peu de temps, il entendit un léger cri, et il aperçut la seconde mère rapportant en hâte la nourriture qu'elle avait recueillie, et elle la distribua à tout les petits indistinctement, et il y en eut pour tous, et les orphelins ne furent point délaissés dans leur misère. Et le père qui s'était défié de la Providence raconta le soir à l'autre père ce qu'il avait vu. Et celui-ci lui dit: "Pourquoi s'inquiéter? Jamais Dieu n'abandonne les siens. Son amour a des secrets que nous ne connaissons point. Croyons, espérons, aimons, et poursuivons notre route en paix. "Si je meurs avant vous, vous serez le père de mes enfants; si vous mourez avant moi, je serai le pére des vôtres. "Et si l'un et l'autre, nous mourons avait qu'ils soient en âge de pourvoir eux-mêmes à leurs nécessités, ils auront pour père le Père qui est dans les cieux." (a) Distinguish passer, se passer, se passer de. (b) Cieux.-What is the singular of this noun? (c) Meurs. Give the past participle. Write in full the present indicative. |