5. Decline-σεαυτοῦ, ἐκεῖνος, ὅστις. Give the meaning of—πότερος, πόσος, ποῖ, ἕτερος, πού. Give the gen. and dat. plur. of-alter, idem, quivis, and Gen. and dat. sing. of-nemo and totus. 6. Parseἑλοῦσι, ἐτρώθην, πλήσωνται, ἔδεσθε, βεβηκόσι, edant, messus, rebare, pepulerit, coegeris. 7. Give the first pers. sing. subj. and opt. 2 sing. imper., inf. and partic. of— ἐτάφην, ἤμυνα, πέπυσμαι. Also the perf. ind. and past partic. of-rideo, tango, tero, traho, carpo. 8. Write down-3 pl. pf. ind. pass. of kaλéw; Perf. act. partic. nom. dual fem. of TÚTT; 3 pl. pres. opt. pass. of Xpurów; I aor. mid. imper. 2 dual of Toléw; Pres. partic. mid. dat. plur. fem. of Tμáw; 2 plur. fut. perf. of jubeo; Fut. inf. pass. of moneo; 2 pl. plpf. subj. of volo; 3 pl. impf. subj. of nequeo; 2 pl. fut. pf. of fero. 9. Give the meaning of the following terminations, with examples-Latin. -ax, -osus, -bundus, -sco, urio. Greek. -ινος, -τος, «όω, -ίκος, -είω. 10. Translate into Latin :— (1) He said that he should have laughed if he had been present. (2) Though he is a good man, he sometimes does wrong. (3) The more hidden a danger is, the greater is the difficulty of avoiding it. (4) Caesar must be consulted. The interests of Caesar must be consulted. (5) He said that he would go out and see what they wanted. 11. Translate into Greek : δέομαι ἄγω (1) Seuthes requested Medocades to bring the army to him by sea. ἐκπίπτω (2) After this having been driven out of that land ἐκτρέφω παρὰ I was brought up at the court of the king. (3) It was evident that the soldiers were hungry. τρέχω (4) Some ran one way, some another. νόσος (5) In the time of Darius he perished of disease πορεύομαι while journeying towards Athens. 4 34371 by 6.7. 3. Express as a decimal fraction, and add together •02, ·03, ·303. 4. Reduce 158. 4d. to the decimal of 17., and find the value of .0125 of a ton. 5. Find the value of (1) 2359 articles at 14s. 8d. each; (2) 180 acres 3 roods 15 poles at 17. 6s. 8d. per acre. 6. Find the square root of (1) 18671041; (2) 122-1025. 7. A bankrupt's debts amount to 600l. and his assets to 410l. What can he pay in the pound, and what will a creditor receive to whom he owes 1257.? 8. If 3500 baskets are purchased at råd. each and sold at 2d. apiece, what will be the total gain and the gain per cent. 9. If 60 men can build a wall in 8 days, working 10 hours a day, how many men can build a wall of the same size in 20 days, working 7 hours a day? 10. Find the cost of papering a room 30 feet long, 16 feet 3 inches broad, and 12 feet high, with paper 2 feet wide at 6d. a yard, allowing for two windows each 8 feet by 4 feet, a door 7 feet by 4 feet, and a fireplace 6 feet by 4 feet. 11. A man holds 14000l. Three and a-half per Cent. Stock. He sells out the whole at 91 and invests the proceeds in a Five per Cent. Stock at 105. Find the difference in his income. 12. Find the compound interest on 3000l. for 3 years at 4 per cent. per annum. IV. [N. B. Two Propositions at least from the Second Book 1. Define-rhombus, diameter, plane angle, superficies, scalene triangle, hypotenuse. 2. Draw a straight line at right angles to a given straight line, from a given point in the same. 3. If two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other, the base of that which has the greater angle shall be greater than the base of the other. 4. Parallelograms on the same base, and between the same parallels, are equal to one another. 5. To a given straight line apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle. 6. Describe a square on a given straight line. 7. If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square on the aforesaid part. 8. If a straight line be bisected, and produced to any point, the rectangle contained by the whole line thus produced, and the part of it produced, together with the square on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced. 9. If a straight line be divided into two equal, and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line and of the square on the line between the points of section. 10. In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle, by twice the rectangle contained by the side on which, when produced, the perpendicular falls, and the straight line intercepted without the triangle, between the perpendicular and the obtuse angle. V. 1. If a = 2, b = 1, c = −3, find the value of ab (a+b) + ac (a + c) + bc (b + c). (1) a2 + b2+c2 ; 3. (1) Multiply x3 —a3 +3α2 x − 3 ax2 by x-a. (2) Multiply together a+mb, ma+b, a+b. 4. Divide 2 a3+6a2b−4a2c −2 ab2 + 3 ac2 — 6 b3+4b2 c (1) +9bc2-6c3 by a+3b-2c. a2+a2x2+x4 a2 x2 5. Resolve into their simple factors (1) x2-3x-4 ; (2) x2-2xy-15y2; 6. (1) Find the G. C. M. of 3 2 n3 — 3 n2 - 8 n + 12 and 6 n2-15n+6. (2) Find the L. C. M. of 4a+4b, 6a2-2462, a2-3 ab+262. (2) Divide (x+y)2 x2 + y2 by (x2 — xy + y2) (x1 −y1) 8. Find the square root of (1) 4x1 −12x3 + 25x2 −24x+16 ; (x− y) (x2 + y3). 10. (1) A man was three times as old as his son on his birthday in 1870, and is twice as old as the same son on the same day in 1882. In what year was the father born? (2) A garrison of 1000 men, having provisions for 60 days, was reinforced after 10 days, and from that time the provisions lasted only 20 days. Find the number of the reinforcement. (3) Two pounds of tea and three pounds of sugar together cost 6s. ; but if sugar were to cost half as much again, and tea rose 3d. a pound, the same quantities would cost 78. Find the present price per pound of tea and sugar respectively. |