9. Write the Irish of-1 am, thou art, he is, she is, we are, ye are, they are-using the emphatic forms as táim-se, etc. 10. Write all the persons singular and plural of ní pabar. MATHEMATICS. FIRST PAPER. ARITHMETIC AND ALGEBRA. PROFESSOR GIBNEY. 1. Find, to the nearest penny, the present worth of a bill of £552 14s. 3d. due three years hence, allowing compound interest at the rate of 22 per cent. per annum. 2. A train whose length is 50 yards, and whose rate is 25 miles an hour, meets a train going in the opposite direction whose length is 60 yards. The trains take 5 seconds to pass one another by. Find the rate of the second train. and divide the result by the sum of the fractions Show that the fraction that you arrive at finally is a perfect square. 4. Find, in their simplest forms, the values of x, y, z, from the equations x + y z = 2a + 2b, ax + by + bz = ab — b2, bx + ay + bz = a2 – ab. 5. Find the values of x that satisfy the equation 7. A contractor has to complete a piece of work by a certain date, and if he has not got it done in time he will have to pay a fine for each day that he is late. He will have to pay £1 for the first day, £2 for the second day, £3 for the third day, and so on. He is late, and the amount of his fine is £186 more than if he were fined a uniform £10 for each day that he is late. How many days is he late? 8. Insert three geometrical means between 05 and 2·45, and calculate each to two places of decimals. 9. A society consists of 20 senior members and 10 junior members. The council consists of 10 members of whom 7 are to be seniors and 3 are to be juniors. In how many ways may the council be selected? In how many ways might the council be selected if the rule were that at least 7 of its members must be seniors. 10. (a) Write down the sixth term in the expansion of according to the binomial theorem. (b) If (1 + x)21 be expanded according to the binomial heoretm, find which is the greatest term when x is ths. SECOND PAPER. GEOMETRY AND TRIGONOMETRY. PROFESSOR BROMWICH; PROFESSOR MCWEENEY. 1. PQR is a right-angled triangle, P being the rightangle; prove that the squares on QP, PR are together equal to the square on QR. Let PQ be greater than PR, and let O be the centre of the square on PQ; draw, through 0, lines parallel and perpendicular to QR. Show that the square on PQ is then divided into four equal parts which can be placed round the square on PR, so as to make up a square whose side is equal to QR. 2. Find the locus of the centre of a circle of given radius which touches a given circle. 3. Construct a regular pentagon in a given circle. If the radius of the circle is 40 inches, prove, in any way, that the side of the pentagon is very approximately 47 inches. 4. Give Euclid's definition of proportion; and explain why it is more comprehensive than the ordinary arithmetical definition. Prove, directly from the definition, that the diagonals of any two squares are to one another as the sides of the squares. 5. If two triangles are equiangular, prove that their sides are proportional. A circle is described through A to touch the base BC, of a triangle ABC, at the point C; the circle cuts AB again in D: prove that CD. AB = AC, BC. 6. Prove that cos (a + B + y) = cosa cosẞ cosy × (1 - tanẞ tany - tany tana - tana tanß); and deduce the relation between tan a, tan ẞ, tan y, if a + B + y = {π. 7. Find sec 15° and tan 224°, giving your answer both in surds and in decimals (two places only). 9. In a triangle ABC, a = 6, b = 7, A = 45°: find the two values of c, proving that their difference is 6.78 (to two places of decimals). 10. Find all values of 0, & between which satisfy sin (0-4) = 1, tan (0 + $) = √3. EXPERIMENTAL PHYSICS. FIRST PAPER. PROFESSOR MCCLELLAND. 1. Explain the meaning of the terms-mass,' 'weight,' 'momentum,' 'energy,' and' force.' 2. Describe a method of determining the value of the acceleration produced by gravity. 8. Explain the nature of a sound-wave, and point out what characteristics of the wave-motion determine the pitch and loudness of a musical note. 4. What effect is produced in a musical note when the observer begins to move rapidly towards the source of the sound, and why? 5. How is the air vibrating in an organ-pipe open at both ends (a) when it is giving its fundamental note, (b) when giving its first harmonic? 6. State the laws of the refraction of light. 7. An object is placed 20 inches in front of a concave mirror of 5 inches focal length. Where will the image be formed, and what will be its size as compared with the object? 8. Describe how you would measure the angle of a prism. Illustrate by a sketch how a ray of light is deviated by passing through a prism. 9. What arrangement of apparatus would you use to obtain a pure spectrum? 10. Why does a red rose appear red when viewed in sunlight? If only green light falls on the rose, what colour will it appear to be? SECOND PAPER. MR. HENRY. 1. Define a degree centigrade.' 2. How would you demonstrate experimentally the difference between the radiating powers of a dark and a bright surface? A piece of copper weighing 15 grams, and at a temperature of 60° C. is dropped into a calorimeter containing 14 c.cm. of water at 13° C. Find the final temperature of the calorimeter and contents, given the specific heat of copper 0.1, and the water equivalent of the calorimeter 1 c.cm. 4. Explain why, when a thaw comes after heavy frost, water-pipes are found to be burst. 5. Define the terms latent heat,' boiling point,'' dewpoint,' and thermal conductivity.' ་ |