the numbers examined are 1000, 840, 900, 1260, 1400; what is the average number of candidates per annum and the average number of failures? 9. B undertook to cut and harvest the corn on 241 a. 2 r. 20 p. at 17. 3s. 6d. per acre on condition that 27. per acre be deducted for all the land not cleared by Sept. 1. At that date 35 acres were still not cleared. What did B receive? 10. Four labourers undertook to excavate a pit 24 feet by 20 feet, 3 yards deep, at 18. per cubic yard for the first yard in depth, 28. for the second yard, 4s. for the third yard; what did each of them receive? 11. A merchant bought 3000 quarters of wheat at 40s. per quarter. At the end of 3 months he sold the wheat again at 458. per quarter; what was his gain per cent. after deducting 5 per cent. per annum on capital invested and 18. 6d. per quarter for warehouse charges? 12. A bankrupt owing 4000l. pays his creditors at the rate of 138. 4d. in the pound. If this sum of money is allowed to accumulate at 5 per cent. simple interest, in how many years will it reach the amount of the original debt? 13. A capitalist sold out 8oool. (stock) 3 per cent. Consols at 96 and invested the proceeds in 5 per cent. French Rentes at 112. Find the difference of income. IV. [N. B. Two propositions at least from the Second Book 1. Define-superficies, semicircle, acute-angled triangle; and state the three postulates. 2. If two triangles have two sides of the one equal to two sides of the other, each to each, and have likewise their bases equal; the angle which is contained by the two sides of the one shall be equal to the angle contained by the two sides equal to them of the other. 3. Draw a straight line at right angles to a given straight line, from a given point in the same. 4. Make a triangle of which the sides shall be equal to three given straight lines, any two of these being greater than the third. 5. Parallelograms upon the same base, and between the same parallels, are equal to one another. 6. 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. 7. If the square described upon one of the sides of a triangle be equal to the squares described upon the other two sides of it, the angle contained by these two sides is a right angle. 8. If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts. 9. If a straight line be divided into two equal parts and also into two unequal parts, the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line. 10. Divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts shall be equal to the square of the other part. 11. In every triangle, the square of the side subtending either of the acute angles is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle. V. 1. If a = 0, b = 1, c = 2, d = 3, find the value of (2) c2d2 - {b2+d2 [b+c+d(b−d+c)a2]} ; 2. From a+b+(a+b)3 subtract a (3ab +3b2+1). 3 ab and Divide 4a5-a3+4a by 2a2+3a+2. 4. Find the G.C.M. of (1) x3+2x2-2x-1 and 3 +x2 — 5 x — 2 ; (1) a-b-c, a+b+c, a2 —b2 -2bc-c2; a с e a3 + c3+e3 5. Shew that if %==7' b3+d3 +ƒ3 6. Simplify ху d (1) (∞ + *** y) × (∞ 3 (x X 7. Shew that the sum of the cubes of any two numbers is less than the sum of those numbers cubed by three times the product of the numbers multiplied by their sum. 8. Find the square root of (1) 9a2+30ab + 12a +2562+206+4; (1) 4(x+1)−22(x − 3) = x−3(x − 2); 10. A certain quantity of bacon is bought at rod. per lb., and sold at 11d. If the total profit is 5., how many pounds of bacon were purchased? A bag contains a certain number of sovereigns. A takes out half and 10 more, B then takes out half the remainder and 20 more, and there are exactly 100 sovereigns left. How many were in the bag at first? A number consists of two digits, their sum being 11. If the digits are transposed the new number falls short of doubling the old by 20. What was the original number? Translate : (I. 357-363.) (ΙΙ. 411-418.) (V. 290–296.) (VI. 494-502.) (VII. 234-241.) (VIII. 245-252.) (ΙΧ. 182–189.) VI. ....... “Ως φάτο δακρυχέων......εἴδομεν ἄμφω. ......... Ω φίλοι ἥρωες Δαναοὶ πατρίδος αἴης. (XVI. 275–283.) Ως εἰπὼν ὤτρυνε.........αἰπὸν ὄλεθρον. (XVII. 333-341.) Ως ἔφατ', Αἰνείας...πελασαίατο τεθνηώτα. (XVIII. 497-506.) Λαοὶ δ ̓ εἰν ἀγορῇ ...ἀμοιβηδὶς δὲ δίκαζον. (ΧΙΧ. 357–364.) Ως δ ̓ ὅτε ταρφεια......διος ̓Αχιλλεύς. (ΧΧ. 144–252.) “Ως ἄρα φωνήσας......"Αρηα πτολίπορθον. (ΧΧΙ. 331-341.) Ορσεο, κυλλοπόδιον......ἀκάματον πῦρ. (ΧΧΙΙ. 450-459.) Δεῦτε, δύω μοι ἕπεσθον......οὐδενὶ εἴκων. (XXIII. 448-455.) Αργεῖοι δ' ἐν........περίτροχον ἠΰτε μήνη. (XXIV. 349-357.) Οἱ δ' ἐπεὶ οὖν μέγα......αἴ κ' ἐλεήσῃ. Translate : (I. 127–134.) (X. 410-415.) (ΧΙ. 584-590.) (ΧΙΙ. 407-414.) VII. HOMER, Odyssey. Ἔγχος μέν......ὑπερφιάλοισι μετελθὼν. Στεῦτο δὲ διψάων......ἐλαῖαι τηλεθόωσαι. Ἡ δ ̓ ἔθει οὐ μάλα.........θυμὸς ἀγήνωρ. (ΧΙΙΙ. 433-438.) Κνύζωσεν δέ οἱ ὄσσε.........ἦεν ἀορτήρ. (XIV. 348–352.) Αὐτὰρ ἐμοὶ δεσμὸν.........ἀμφὶς ἐκείνων. (XV. 160-165.) Ως ἄρα οἱ εἰπόντι......φρεσὶ θυμὸς ἰάνθη. (XVI. 284–290.) Οσσα τοι ἐν.......... πυρὸς ἵκετ ̓ ἀϋτμή. (XVII. 291-296.) *Ἂν δὲ κύων... ἀποιχομένοιο ἄνακτος. (XVIII. 370-374.) Εἰ δ ̓ αὖ και......διηνεκέα προταμοίμην. (ΧΙΧ. 467-472.) Τὴν γρηὺς χείρεσσι......ἔσχετο φωνή. (ΧΧ. 296–302.) (ΧΧΙ. 42-50.) ̓Αλλ ̓ ἄγε οἱ καὶ ἐγώ........βάλε τοῖχον. Ἡ δ' ὅτε δὴ θάλαμον.........δέ οἱ κα. (ΧΧΙΙ. 297-301.) Δή τότ' Αθηναίη......μακρὰ πέλονται. (XXIII. 195-201.) Καὶ τότ' ἔπειτ'......βοὺς φοίνικι φαεινόν. (XXIV. 226-231.) Τὸν δ ̓ οἷον πατέρ'.........πένθος ἀέξων. |