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4. Turn into Oratio Obliqua :

Hanc ego et vivus multos per annos magnâ diligentiâ defendi et nunc moriens eadem fide Caesari restituo. Nolite, obsecro, committere, quod ante in exercitu Caesaris non accidit, ut rei militaris dedecus admittatur.' And, into Oratio Recta :

Hos, praecipue in victoriâ insolentes, praecursuros et loca excelsiora atque aedificia occupaturos; ita fugâ navibusque nostros prohibituros. Proinde ejus consilii obliviscerentur atque omni ratione esse vincendum cogitarent. 5. Decline in the singular-oú, où, outos.

Give the meaning of–πόσος, που, όπως, μήποτε, τηλικουτος.

Give the gen. and dat. plur. of—ambo, ipse, quivis. Give the gen. and dat. sing. of-aliquis, iste. 6. Parse:-ομείσθε, έαγε, θορούσης, πέφανται, ώσας.

:, , , , . obliviscere, adfore, pexum, fisus, manâsses.

7. Give the first pers. sing. subj. and opt., 2nd sing. imper., the inf. and part. of -- οίδα, έλαθον, πέπωκα, έγνων, είλημμαι.

Give the perf., inf., and supine of-arcesso, fateor, pungo, caedo, excutio. 8. Write down :

(1) 3rd sing. fut. ind. of Táoxw.
(2) 2nd plur. ist fut. ind. pass. of tiuáw.

τιμάω.
(3) 2nd dual perf. ind. pass. of lavoávw.

λανθάνω
(4) 3rd sing. opt. pres. of pnuí.

.
(5) ist aor. pass. part. dat. plur. masc. of tréuTW.

3rd plur. perf. subj. of expergiscor.

Acc. fem. plur. perf. part. pass. of tundo. (8) 3rd sing. plupf. subj. act. of aufero. (9) 3rd plur. fut. ind. of reor. (10) 2nd fut. ind. pass. of tollo. 9. Explain and illustrate by examples

Historic infinitive, impersonal verb, conjunction, dativus ethicus, genitive of quality.

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φημί.

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10. Translate into Latin :

(1) He hoped that the war would soon be over.

(2) He cried out "Why do you not seize your arms and escape

to
your

tents ?' (3) He went to Rome to study literature at the house of Sulpicius.

(4) He said that he could have persuaded the king to spare the prisoners.

(5) We must not lose the opportunity of consulting the priestess of Apollo.

11. What prepositions in Greek govern two cases only ? Shew by examples the difference of meaning.

-C

III.

Arithmetic. 1. Find the G.C.M. of 49728 and 20424 and L.C.M. of 3, 7, 12, 15, 32. 2. Simplify:

of 11 of 31

+

31-2 and divide (1}+33 +}) by (1š - +34).

3. Reduce 2.05 of half-a-crown to the fraction of a pound and add together 2.2 of five shillings + •22 of ten shillings.

4. Reduce 105, 3to decimals; and .02565 and .0546 to vulgar fractions of the lowest terms.

5. Multiply 4.017 by 003 and divide 26.57565 by 7281.

6. Find the square root of 2.01668401 and of (3+*+16+).

7. How many tiles 6 inches square will be required to pave a footpath 4 feet wide carried round a grass-plot 25 yards long by 13 yards wide ?

8. In an examination for the civil service 60 per cent. of the candidates pass in each year. In 5 successive years

. 5

2 2

5

6

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 il. 34. 61. per acre on condition that 2l. 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 408. per quarter. At the end of 3 months he sold the wheat again at 45%. 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 soool. (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.

Euclid.
[N.B. Two propositions at least from the Second Book

are required.] 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.

a

V.

Algebra. 1. If a = 0,6 = 1, c= 2, d=- 3, find the value of

I
acd + 2 bc+d-cad 20-bd + 2 ac 7

i
20-36

40-cd +3 bc
(2) cod? {b2+d2[b+c+d(6-d+c)a?]} ;

(1)

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3 ab

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a

с

e

ace

38(6+c)(c,d)
(3)

b-
+
62 + c

(6+c)d2
2. From a + b +(a + b)3 subtract a(3ab +362 + 1).

3 ab 3. Multiply a+ -62 by a2

+62, 5

5 and Divide 4a - a3 + 4a by 2 a2 + 3a + 2. 4. Find the G.C.M. of

(1) 23 + 2x-— 23 — 1 and x3 + x2 – 5X— 2;

(2) 4x3 + 4y3 and 8x8 + 24xưy + 24 xy2 + 8y3, and the L. C. M. of

(1) a-b-c, a +b+c, a? — 62 — 260 —c2;
(2) x2 + x-6, x2 + 4x— 12, x2 +9x + 18.

a3 +68+e3 5. Shew that if

7 def' 63 +d3 +f3 = bdf 6. Simplify

XY
(1) (x + x (x

Y

x+y
a+b
(2)

+
a2 + ab +62 a? - ab +62

3x + 2y 3x – 2y 16 y?
(3)

32 - 24 3x + 2y 9.22 — 4y2 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 + 30 ab + 12a + 2562 + 206+4; 81 22 3630

4

+ 49 74 9. Solve the equations : (1) 4(x + 1)-22(x-3) = x-3(x-2);

30 (2)

3 =

145; 40

2

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202

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ab

(2)

+

5(98+15)

= 246 — 9(3®+2)

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