Hapsburg and Bourbon (in Spain); Romanoff (in Russia). 5. Mark on the map by asterisks, with the names written by the side of the asterisks, the situation of Orleans, Poitiers, Toulouse, Valladolid, Treves, Munich, Pesth, Modena, Adrianople. Moscow, MATHEMATICS. Morning Paper. REV. CANON HEAVISIDE, M.A. OBLIGATORY PORTION. (N.B.-Questions in the remaining part of the Obligatory Section will be set in the Afternoon Paper.) 1. Multiply 5 tons 13 cwt. 23 lbs. by 71, and divide 51757. 18. 1ąd. by 91. 2. How many guineas are there in 2117. 1s.? 3. If 14 English miles are equal to 11 Irish miles, how many Irish miles are there in 154 English miles? 4. If 15 pumps working 8 hours a-day can raise 1260 tons of water in 7 days, how many pumps working 12 hours a-day will be required to raise 7560 tons of water in 14 days? 5. A brick is 9 inches long, 4 inches wide, and 3 inches thick, how many bricks will it require to build a wall 520 yards 9 inches long, 15 feet high, and 14 feet thick? 6. Find the amount of 39681. 15s. in six years at 51 per cent., simple interest. 7. Divide 17 11 7 8. Reduce 1s. 1d. to the decimal of a pound. Add together 1.3625 of £1, ·75 of 13s. 4d. and of £20. 9. In the extraction of the square root, state the rule for pointing whole numbers and decimals. Extract the square roots of (1) 12345-4321 (2) 8·1. Euclid. 1. If two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of the one greater than the angle contained by the two sides equal to them of the other, the base of that which has the greater shall be greater than the base of the other. 2. If a straight line be divided into any two parts, the squares of the whole line and of one of the parts are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. VOLUNTARY PORTION. 1. Describe a square about a given circle. Point out how an equilateral and equiangular octagon may be described about a circle, and find its area, in terms of the radius. 2. Find a mean proportional between two given straight lines. Find an harmonic mean between the same two straight lines. 3. Find the sum of a geometrical progression of (n) terms. If (s) be the sum of a geometrical progression whose first term is (a) and last term (7) and (s1), the sum of the reciprocals of the same series prove 4. Find by the aid of the logarithmic tables: (2) The number of years in which a sum of money will treble itself at 6 per cent. compound interest. 5. Find the area of the sector of a circle when the radius is 10 feet, and the angle at the centre 45°. Afternoon Paper. REV. CANON HEAVISIDE, M.A. OBLIGATORY PORTION. 1. Find the value of a2+2ab+b2 when a=0 and b5, find the value of a2+2ab+b2 when a=3 and b=2, account for the identity of the results. 2. Add together (3a−4b + 5c), (4b−3a + 2c), (a + −7c) Subtract (x+2x2y + 3xy2 + 2y3). Prove (x+y)3. (x − y)2 = (x + y). (x2 —y2)2. 4. Solve the following equations: 5. Two regiments consisted of the same number of men; after two companies, of 60 men each, were added to one regiment, and 60 men were disbanded from the other, it was found that the number of men in one regiment were to the number in the other as 4 to 3, how many men were there in each regiment originally? Euclid. 1. Describe a parallelogram that shall be equal to a given triangle and have one of its angles equal to a given rectilineal angle. 2. The angles in the same segment of a circle are equal to each other. VOLUNTARY PORTION. 1. If three straight lines meet all in one point and a straight line stand at right angles to each of them in that point, these straight lines are in one and the same plane. 2. Prove Tan 22° 30', and Sin 22° 30′. 3. One side of a right angled triangle is 20 feet, and the hypothenuse is 140 feet, find the angle subtended by the least side of the triangle. An observer ascends 140 yards up a slope of 1 in 3 from the edge of a river, and observes the angle of depression of an object on the edge of the opposite bank to be 2° 15', find the breadth of the river. 4. If (P) support (W) on an inclined plane, the direction of (P) making a given angle with the plane, find the relation between (P) and (W) in the case of equilibrium, (1) When the plane is smooth; (2) When the plane is rough, (W) being on the point of sliding down the plane. 5. (M) and (M,) are two inelastic balls, (M) impinges on (M,) at rest on direct impact, find the velocity of each ball after impact. Ex. M-3 M, the velocity of M after impact is (ths) of its velocity before impact, find the modulus of elasticity. |