3. Write out the persons (pres. iudic.) of— malo, orior, prosum, ἄπειμι (absum), ἄπειμι (abeo), ἀφίημι. 4. Give the comparatives and superlatives of— μέγας, τάλας, ἡδύς, parvus, facilis, superus, and positives of the adverbs μάλιστα, θᾶσσον, ἀπωτάτω, melius, citissime, celerrime. 5. Parse the following words προὔδοσαν, εἰδόσιν, μεθέντες, ταὐτόν, πράξειας, 6. Write down 3 plur. 2 aor. imper. of yíyvoμai. 2 sing. 2 aor. opt. mid. of μeðíστnμi. 7. Give the Latin and Greek for 11-29-14th-2000 Greeks-how?-somehow-how many?-so many-who? -somebody. 8. Give examples, in Latin, of Ablative Absolute, Cognate Accusative, Objective Genitive, and in Greek, of Genitive Absolute, Attic Attraction, Attic Reduplication. 9. Translate into Latin (1) Caesar had determined to carry his forces over the Rhine to strike fear into the Germans. (2) The quicker you go, the safer will the road be. (3) I can't understand, why they were spared. (4) You may do what you like with them, provided you don't kill them. 10. Translate into Greek, using the proper parts of ópáw and κτείνω (1) If they see him, they will kill him. (2) If they saw him, they would kill him. (3) If they had seen him, they would have killed him. 11. Turn into Oratio Recta the following sentence: "Si Gallia omnis cum Germanis consentiret, unam esse in celeritate positam salutem. Cottae quidem atque eorum, qui dissentirent, consilium quem haberet exitum? And into Oratio Obliqua :— "Vincite, inquit, si ita vultis; neque is sum, qui gravissime ex vobis mortis periculo terrear; hi sapient, et si gravius quid acciderit, abs te rationem reposcent." III. I 1. The driving wheel of a bicycle is 3 yds. 2 ft. in circumference. (1) If it revolves twice in a second for 1 hr. 5 m., how many miles does it travel in that time? (2) How many times must it revolve in a minute to travel 10 miles an hour? 2. Find the value of 501 lbs. 1 oz. Avoirdupois at 168. 10 d. per oz. 3. Find the value of (+++12)—(31—2§); and 4. Find the Greatest Common Measure of 3264, 4896, 28560; and the Least Common Multiple of 11, 22, 28, 33, 44, 56. 92 5. Find the Square Root of 42436, and of 41°21. 6. Find the value of .0032 × 23.45; 15.625÷2·5; ·03÷ 13 250, 17 7. Express as decimal fractions 2010; and as vulgar fractions in their lowest terms 0625, 145. 8. Reduce 2 miles 1100 yds. to the decimal of a league; and find the amount of 325 of 1 lb. Troy. 9. If ale brewed with 3 bushels of malt costs Is. 3d. per gallon, when malt is 378. 6d. per quarter, how much must ale be per gallon brewed with 5 bushels, when malt is 318. 6d. per quarter? 10. It is determined to remove the wainscoting which entirely covers the walls of a room that is 5 yds. square and 3 yds. I ft. high, and to apply it to covering the walls of another room that is 6 yds. 2 ft. long, 5 yds. 2 ft. 6 in. broad, and 8 ft. high. How much old wainscoting will be superfluous, or how much new required to complete the work? 11. (1) At what rate of interest will 7557. amount to 11327. 108. in 10 years? (2) What is the compound interest on 50l. for 3 years at 5 per cent.? 12. M. invests 8280l. cash in the 5 per cents. at 120. At the end of a year he sells out at 115, and exchanges into the 4 per cents. at 90. What is the difference in his annual income? IV. [N.B. Two Propositions at least from the Second Book are required.] 1. Define an acute angle, a diameter of a circle, a rhombus, parallel straight lines, a gnomon. 2. The angles at the base of an isosceles triangle are equal to each other; and if the equal sides be produced, the angles on the other side of the base shall be equal. 3. Bisect a given finite straight line, that is, divide it into two equal parts. 4. If from the ends of a side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle. 5. The opposite sides and angles of parallelograms are equal to each other, and the diameter bisects them, that is, divides them into two equal parts. 6. The complements of the parallelograms which are about the diameter of any parallelogram, are equal to each other. 7. If there be two straight lines, one of which is divided into any number of parts; the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line and the several parts of the divided line. 8. 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. 9. Divide a given straight line into two such parts that the rectangle contained by the whole and one of the parts shall be equal to the square of the other part. 10. Describe a square that shall be equal to a given rectilineal figure. 2. From a3-(a + b) c2 + (a + c) d2+b3 subtract —a3 +(a−b)c2 + cd2 + b3. 3. Multiply 23—2x2+6x-12 by 2x3 +4x2-4x−8. 4. Divide x6 −5x1+3x3+6x2-7x+2 by x3-3x2+3x-1. 5. Find the G. C. M. of (1) -2x+1 and x3-3x+2 ; (2) 4a3-17a+12 and 6a2-17a+12. 6. Find the L. C. M. of (1) 4ab3 +4b3d and a2b2-b2d2 and 36; x2+6x-7 x2+3x-4 (3) (x2+xy+y2)2 — (x2 + xy — y2)2. 8. Extract the square root of (1) x1−6x3y+15x2 y2 — 18xy3 +9y1; 10. (1) The length of a tramway is five miles. Two cars start at the same time from opposite ends. One travels eight miles an hour, the other seven. How far will each have gone when they meet? And what time will have elapsed since they started? (2) A wine-merchant blends a dearer and a cheaper kind of sherry in a cask which contains 236 gallons, and adds a certain quantity of brandy. There are five gallons more of the dearer wine than of the cheaper, and ten times as much of the cheaper wine as of the brandy. How many gallons are there of each in the cask? (3) A and B are reading the same Greek book. A uses a translation, B does not. A reads the whole book at a uniform rate, and gets through the first half in twothirds of the time that B takes to read the same amount. The second half of the book B reads at the same rate as A. B spends three hours more over the whole book than 4. How many hours does it take each of them to read it? |