Examination conducted in behalf of the TRUSTEES of the RHODES BEQUEST, January, 1907, by the Delegacy of Local Examinations, Oxford, England.

The time allowed for each Paper is two hours.

I. ARITHMETIC.

1. A merchant began business with $100,000. In the first year he made 10 per cent., which he added to his capital. In the second year he made 20 per cent. and added the profits to his capital. In the third year he again made 20 per cent., and laid out $60,000 on real estate. How much capital would he have left in the business at the beginning of the fourth year?

2. Find the difference between

9⅕ - 1⅔ × 3⅜ and 2¾ × 1⅙ - ⅘.

3. Find the square root of 4⅑ to four places of decimals.

4. If, by selling an article for $2, a man gains ⅐ of the cost price, at what price must he sell it so as to gain 8 per cent.?

5. The area of one side of a cubical cistern is 14·0625 square feet; find to the nearest gallon the amount of water which it will hold when full, assuming that one cubic foot weighs 1,000 ounces and that one gallon of water weighs 10 lb.

6. Find the cost of a carpet to cover a floor 22 ft. 6 in. long and 18 ft. 9 in. wide at 5s. 4d. per square yard.

7. Divide £37. 10s. 4½d. by 4⅐ and express £3. 14s. 7½d. as the decimal of £10.

8. A sum of $2,500 is lent at compound interest at 3½ per cent. per annum. What is due to the lender at the end of three years?

9. A can do a piece of work in 24 days which B can do in 36 days. What fraction will remain to be done if both are engaged upon the work for 6 days?

II. ALGEBRA OR GEOMETRY.

(a) Algebra.

The full working must be shown in all cases.

1. If 2p - 3q = 8, ½q = p - 6, find the value of

(p - q)² - 7(p² - q²) + 12(p + q)².

2. Divide

x⁶ + ax⁵ - 12a²x⁴ + 19a³x³ + 15a⁴x² - 14a⁵x + 2a⁶

by

x² + 4ax - 2a².

3. Find the highest common factor of

54p⁵ - 11p²q³ - q⁵ and 12p⁵ + 11p⁴q + q⁵,

and the least common multiple of

a²c(ab - b²), 4(a² - b²)c³, 6b²c. 3(ab² + a²b).

4. Simplify:

(1) ((p + 3)/(p² + 2)) + (1/(2p + 2)) - (1/(p - 1));

(2) {p(p + q) - q(p - q)} {p(p - q) - q(q - p)} ÷ (p³ - q³).

5. Solve the equations:

(1) (x + 3)/6 - (11 - x)/7 = (⅖)(x - 4) - (⅟₂₁)(x - 3);

(2) 1/(x + 1) + 2/(x + 2) = 3/(x + 3);

(3) 17x/a + 3y/b = 9, 3x/a - 2y/b = 37.

6. Find the remainder (free from x) when ax² + bx + c is divided by x - p. What inference is suggested by the result?

7. By the investment of £400, partly in a 2½ per cent. stock at 75 and partly in a 4 per cent. stock at 96, a total income of £15. 8s. 4d. is obtained. How much money is spent on each stock?

8. The perimeter of a room is a feet, and the height of its walls is b feet: find the cost of papering the walls of the rooms with paper x inches wide at y pence per foot, the area of the windows, door, and fireplace being (⅒)ab square feet in all.

(b) Geometry.

The use of reasonable symbols and abbreviations is permitted.

1. If two angles of a triangle are equal, the sides opposite to them are equal.

2. Find the locus of points which are equidistant from two given points.

3. The sum of any two sides of a triangle is greater than the third side.

4. Make a triangle equal in area to a given triangle and having one of its angles equal to a given angle.

5. Show that the bisector of the exterior angle at the vertex of an isosceles triangle is parallel to the base.

6. A ladder erected against an inner wall of a shed just reaches a window 18 feet from the ground, and, on being turned over through a right angle (the foot not being moved), it reaches a point on the opposite wall 7 feet 6 inches from the ground. Find the distance between the walls.

7. D is the middle point of the hypotenuse BC of a right-angled triangle BAC. Show that DA = DB.

8. AB, CD are two equal chords in a circle. Show that they are equidistant from the centre.

9. Show that, if two tangents are drawn to a circle from an external point, the tangents (1) are equal in length, (2) subtend equal angles at the centre of the circle.

III. LATIN PROSE COMPOSITION.

Translate into Latin:—

When the bridge was nearly all cut away, Horatius made his two companions leave him, and pass over into the city. Then he stood alone on the bridge, and defied all the army of the Etruscans: and they showered their javelins upon him, and he caught them on his shield and stood yet unhurt. But just as they were rushing at him, to drive him from his post by main force, the last beams of the bridge gave way, and it all fell with a mighty crash into the river. While the Etruscans wondered, and stopped in their course, Horatius turned and prayed to the god of the river: ‘O father Tiber, I pray thee to receive these arms and me who bear them, and to let thy waters befriend and save me.’ Then he leaped into the river, and though the darts fell all around him, yet they did not wound him, and he swam across to the city safe and sound.

IV. GREEK AND LATIN GRAMMAR.

(a) Latin Grammar.

1. Give (a) the meaning, gender, and genitive singular of—pes, domus, lex, opus;

and (b) the meaning, genitive case, and comparative of—parvus, niger, vetus, senex.

2. Give the meaning, present infinitive, and 1st person sing. of the perfect indicative of—pono, capio, morior, iuvo, audeo, reor.

3. Explain what impersonal verbs are, and give instances to show the constructions used with them.

4. Translate into Latin:—

(a) Having lost his horse, he was obliged to go on foot.

(b) I hope that he will come quickly.

(c) He will return home to-morrow.

(d) I am afraid that the girl will die.

(e) Whatever happens, we must go away.

5 What is the meaning of the following prepositions and what cases do they take—penes, coram, apud, instar?

6. What classes of verbs cannot ordinarily be used in the passive voice, and why?

(b) Greek Grammar.

1. Give (a) the meaning, gender, and genitive singular of—πόλις, χρώς, κέρας, σῶμα:

and (b) the meaning, genitive singular, and comparative of—ταχύς, μέγας, φίλος.

2. Decline in the singular—οὐδείς, ὅστις, and in the plural—σύ, οὗτος, πᾶς.

3. Give the 1st person singular of the future and of the 2nd aorist indicative active of—αἱρέω, φέρω, πάσχω, δίδωμι, θνήσκω.

4. Translate into English:—μὴ γένοιτο, πέμπτος αὐτός, οἴκαδε, οἱ σὺν αὐτῷ, ἔλεξε τοιάδε.

5. What is the Greek for—the same man, myself, upwards, as if, therefore, thirty years?

6. Name all the prepositions which govern the dative case, and give their meanings.

V and VI. TRANSLATION FROM LATIN AND GREEK INTO ENGLISH.

V. Translation from Latin into English.

The Paper contains the following Sections:—

N.B.—Candidates must select one and only one of the Sections numbered 1-12.

VI. Translation from Greek into English.

The Paper contains the following Sections:—

N.B.—Candidates must select one and only one of the Sections numbered 1-8.

Each of the above Sections comprises from three to eight passages from the Books or Sources mentioned, and the total amount of translation required averages between fifty and sixty lines of ordinary text. No questions on context or grammar are set; translation only.