2 ROYAL MILITARY COLLEGE, SANDHURST. . 4. Reduce 49. to its lowest terms. Find the value of 1 of (1 + 13), and prove it equal to şof 201 divided by 10%. 5. Reduce 1š to a decimal that terininates. Express 11 in the form of a recurring decimal. Add together 13.57, 004, 34. Divide 6.25 by00003, prove the last result by vulgar fractions. 6. If one metre French = 39. 371 English inches, show that 32 metres = 35 yards nearly. Express, by means of decimals, 71. 128. 6d. in pounds. Find the value of 3.5 of a pound. 7. Find the interest on 1,5521. 108. for 18 months at 5 per cent. simple interest. If I buy into the three per cent. stock at 75, what rate of interest do I receive for the money I invest? 8. If the army and navy of a country together cost 26 millions sterling, and the cost of the army exceed that of the navy by three fifths the cost of the navy, what is the cost of each ? Euclid. 1. Make a triangle of which the sides shall be equal to three given straight lines, but any two whatever of these must be greater than the third. How does the construction in this proposition fail when the condition in italics is not fulfilled. 2. To a given straight line apply a paralellogram which shall he equal to a given triangle, and have one of its angles equal to a given rectilineal angle. Could a rectangle be described on a line of any magnitude equal to any given equilateral triangle. - VOLUNTARY PORTION. 1. Inscribe an equilateral and equiangular pentagon in a given circle. If A B C D E be the angles of the pentagon taken in order, and C A and C E be joined, prove (1.) The angle BCD is trisected. C 2. When is a straight line said to be divided in extreme and mean ratio; divide a given line in extreme and mean ratio. If in the figure of question (1.) A D be joined, cutting C E in F, show that C E is divided in F in extreme and mean ratio. MATHEMATICS. 3 3. Solve the equations : ху (1.) y2 = 3 x + 2 y + 2 (2.) 20* + y = 337 | + y = 7 S 4. A garrison besieged loses 5 men on the first day, 10 on the second, 15 on the third, and so on, and at this rate the garrison would be all destroyed in 50 days. How many men must be introduced at the end of the fifteenth day of the siege to bring the garrison up to a strength of 8,000 men ? 5. Prove log. 35 x 46 = } log. 3 + 6 log. 4. (1.) (-0874)s. MATHEMATICS. Afternoon Paper. DISTRIBUTION OF MARKS. Obligatory Portion (in both papers) Max. Marks. 1,200 2,400 Total 3,600 Part of the Obligatory Portion, and part of the Voluntary, are given in each of the papers (morning and afternoon). Of the 1,200 marks allotted to the Obligatory Questions, 400 will be required for qualification. OBLIGATORY PORTION. Algebra. (1.) What signs are used in Algebra to express addition, subtraction, multiplication, division ? How does it appear that ab = ba, and a = b = b. a 4 ROYAL MILITARY COLLEGE, SANDHURST. b b a a a +3 (2.) Subtract (a – +c) from the sum of (a+;) and ( +c). 2a2_22 a Reduce + 20 a -2 Divide 49xy by - 7x*y:. *. a-6 (3.) If x= a +6 a-b a + b and y= Reduce to its lowest terms 3x2 — 3-4 63+70-20 (4.) What is the rule for transferring an algebraical quantity from one side of an equation to another? Solve the equations2 (x-4) 1 (1.) + 5.1= x 3 3 2.1 –72 I-25 + =x-44. 5 2 + 3y. (5.) There are two sorts of wine, one worth 5 shillings a quart, and the other worth 3 shillings a quart; how much of each must be taken to mix a quart that shall be worth 38. 6d. ? 十 VOLUNTARY PORTION. Euclid. If a straight line be divided into two equal and also into two unequal parts, the squares of the unequal parts are together double the square of half the line and of the square of the line between the points of section. (1.) How many square yards of sheet iron would be required to make a pipe 14 feet in diameter and 48 feet long, and what would be its weight if the iron was t'th of an inch thick, the weight of a cubic foot of iron being 486 pounds ? a MATHEMATICS. — LATIN. 5 sec 45° Prove (1.) sin 45° + sin 30° (2.) What is the complement of an angle or arc? Prove the sine of an angle is equal to the cosine of its complement. If the sine of an angle is }, what is the cosine, and what the tangent? sin 45° sin 30° tan 45o sec 45° + tan 450 2 sin A (2.) tan 2A – tan A= = cos A + cos 3A (3.) From the top of a tower 150 feet high, the angles of depression of the top and bottom of a vertical column standing on the same horizontal plane were observed to be 22° 15' and 46° 30'; find the height of the column. (4.) Find the centre of gravity of four heavy particles, situated in the same plane. Ex. Weights of 1, 3, 5, 7 ounces, placed in order in the angles of a rigid square, whose side is 10 inches, the weight of the square itself being 4 ounces. (5.) If a body be projected with a given velocity down a smooth inclined plane, find the space it will describe in a given With what velocity must a body be projected down an in clined plane of given length whose angle of inclination is 30°, so that the time down the plane may be equal to the time of a body falling freely through the vertical height ? tine. LATIN. Rev. N. POCOCK, M.A. DISTRIBUTION OF MARKS. Marks. No Candidate will be allowed for Translation more than 800 For Composition in Prose or Verse, or in both, more than - 600 For Grammatical Questions more than 600 Grammatical Questions. 1. Give the rules for the formation of comparatives and super latives, with instances and such exceptions as you know of. Do adverbs admit of degrees of comparison ? 6 ROYAL MILITARY COLLEGE, SANDHURST. 2. What are the principal tenses of adimo, defero, decerno, lugeo, malo, proficiscor, prosum, sepelio, solvo, sterno, tollo ? 3. What is meant by the three concords in grammar? Give some explanation of them, with examples ? 4. What is the meaning of the military terms calo, matara, testudo, pilum, sudes, sagulum, tragula, and vinea? 5. What is the rule for the formation of the perfect tense in the second conjugation of verbs ? Mention all the exceptions you know. 6. Parse the words dederet, dederit, domitam, fusus, fugavit, compagibus, positurus. 7. What is the derivation of consuetudo, crudus, eloquentia, finitimus, locuples, pernicies, necopinatus ? 8. Distinguish between angustus, exiguus, parvus, exilis, gracilis, and tenuis, and quote any passages you may remember in which these epithets are used. 9. Explain the following constructions Labienus, quid sui consilii sit, proponit. Tu autem abes longe gentium. 10. Mark the quantities of the following words : similis, tutela, comes, dedecus, lorica, libertas, miles, humidus, and quote as many lines as you can to prove them. 11. What is the quantity of a vowel before a vowel, and a vowel a before two consonants ? Give examples in verse, and state what exceptions there are to the rule. 12. Give such account as you can of the metres used by Horace, with examples of each. The whole number of marks allowed for translation will be assigned to correct translations of the three passages marked with an asterisk. Passages for Translation. Eutropius. Desperans. Hannibal, Hispanias contra Scipionem ducem diutius posse retineri, fratrem suum Hasdrubalem in Italiam cum omnibus copiis evocavit. Is veniens eodem itinere, quo |