7. (a) Let s sum, d = common difference,+8x+15)x+3x3-31x-123x-90(x2-5x-6 a = first term. s=(2a+4d) (I) 2+8x+15x Hence the rent is £120, the poor-rate £20, and the water rate £10 per annum. EXAMINATION FOR ENGINEER STUDENTS. There is an Examination held every year in the month of April, for the purpose of selecting candidates desirous of entering one of Her Majesty's Dockyards as Engineer Students. For the last few years the competition has been. open, but under a recent regulation, the Lords of the Admiralty reserve to themselves the right of nominating a certain number of students not exceeding one-fifth of the whole number to be selected. Candidates eligible for nomination are(a) Sons of officers of the Navy, Army, or Royal Marines, who have been killed in action, or who have been lost at sea on active service, or killed on duty, or who have died of wounds received in action, or injuries received on duty within six months of such action or injury; or (b) Sons of Officers of the Navy or Royal Sons of Officers of the Navy or Royal Marines desirous of obtaining nominations must apply to the Secretary of the Admiralty; sons of officers of the Army, to the Military Secretary, the Horse Guards; and sons of officers of the Indian Army, to the Military Secretary, India Office. These applications must be made before the 1st of February in each year. Candidates successful in obtaining a nomination will be appointed on passing the following examination : 1. Arithmetic, the maximum number of marks being ... 2. Hand writing 3. Writing from Dictation,, 4. English Composition The above subjects constitute a test; and candidates failing to satisfy the examiners in each of them are rejected. Besides the test subjects, nominated candidates will be examined with a view of ascertaining the extent of their knowledge and their relative merit in: 5. English Grammar, maximum number of marks ... 150 6. French, or German or Italian translation 7. Latin, Translation into English ... ... 150 150 ... 100 300 ... 300 No nominated candidate will be eligible who obtains less than 700 marks out of the 1,750 shown above. Candidates (whose parents must be British citizens) who intend going in for the Open Competitive Examination must apply for a form (a copy of which for the present year is printed below) to the Civil Service Commissioners on or after the 1st of January in each year. This form must be duly filled up and returned to the Commission before the 15th March. The subjects of the Competitive Examination are the same as for nominated candidates, and unless the proficiency is shown in each of the first four subjects, the candidate will be disqualified, and the examination of his other papers will not be proceeded with. Further, it is to be particularly remarked that candidates will be tested as to their ability to read aloud with clearness, distinctness, and accuracy, and without hesitation. Stammering, or any im perfection of utterance, will be regarded as a disqualification. The course of instruction extends over seven years, and, as regards two specially selected students, over a longer period. Annual payments of £30 for the first two years, and £20 each year for the two subsequent years have to be made for each student, besides the cost of outfit, which amounts to about £22 per annum. Students who are well reported on by their officers receive 1s. per week for the first year, 2s. for the second, 3s. u week for the third, 5s. for the fourth, 8s. for the fifth, and 10s. for the sixth year. Candidates must not be less than fourteen, nor more than sixteen years of age, on the 1st of May in the year in which they offer themselves for examination. We have printed many of the questions given at last examination, and appended the answers, which we trust may be found useful to intending candidates: If you have never been examined, insert here the word "never." If you have been examined give the date, &c., of the last occasion. t State the place at which you wish to be examined, FORM TO BE FILLED UP BY ALL CANDIDATES FOR ENTRY. The Order for admission to the Examination (which will be posted on the 22nd March) will not be issued unless this Form, filled up by the Candidate himself, is received by the Secretary of the Civil Service Commission on or before the 15th March, 1883. SIR,-I beg to inform you that I wish to be a Candidate at the Examination appointed to be held on the 3rd and 4th April, 1883, for entry as Engineer Students in Her Majesty's Dockyards. If successful in the competition, I shall be prepared to satisfy the Commissioners that I am of the prescribed age, and of good character. I beg to inform you that I was* examined before the Civil Service Com missioners in the month of t in the year 18, as a Candidate for the situation of. I desire to be examined at + which must be Name in full. I am, SIR, Your obedient Servant, either London, Address to which it is desired that the Liverpool, Portsmouth, Order for Examination should be sent Devonport, Bristol, Leeds, Newcastle-on Tyne, Edin burgh, Glas- The Secretary, gow, Aber deen, Dublin, Belfast, or Cork. Civil Service Commission. Evidence of age, &c., need not be supplied until the result of the Examination is known. ENGINEER STUDENTS. ARITHMETIC. Time-2 Hours. 1. Write out in words the number 560,109,031. Answer-Five hundred and sixty millions, one hundred and nine thousand, and thirty one. 2. Write down in figures forty-five millions nineteen thousand and forty. Answer-45,019,040. 3. Write down in figures seven hundred and ten millions nine hundred and seven. Answer-710,000,907. 4. Multiply £834 19 11 by 17. £834 19s. 11d. Add 835 17 £14,195 Less, 8 d. d. £14,194 19s. 31d., Answer. 5. Divide £9,346 14s. 11d. by 63. £148 7s. 2d. Answer. 6. From £873,473 2s. 81d., take £385,982 17s. 8 d. £487,490 4s. 113d. Answer. 7. Multiply 368,245 by 19,073, 7,023,536,885 Answer. 8. Multiply £748 13s. 43d. by 81. £60,642 3s. 4d. Answer. 9. Divide £1,760,917 12s. 93d. by 45. £39,131 10s. 03d. Answer. 10. Divide £5,354,833 10s. Od. by 432. £12,395 8s. 111d. 11. In 9,785,743 square inches, how many acres, roods, &c. 1a., 2r., 9 poles, 18 yds., 4 feet, and 43 in. Answer. 12. If 7 oz., 12 dwts., 2 grs. of silver plate cost £1 18s. 01d., how much will 1 oz., 10 dwt., 10 grs. cost? 7 oz., 12 dwts., 2 grs.: 1 oz., 10 dwts., 10 grs.:: £1 18s. 04d., or 5:1:: £1 18s. 01d. : £0 7s. 74d. Answer. 13. Find (by Practice) the cost of 1 ton, 17 cwt., 3 qrs., 21 lbs., at £2 6s. 8d. per ton. £4 8s. 6d. Answer. 14. Find the simple interest on £4,730 for 3 years at 41 per cent. per annum. a(a+bc)—b{(c—a)—(b—a)}—{a(bc—a)+ 28. A person holding £12,500 stock in the 3 per cents. sells out at 80, sufficient to buy an estate for £7,500 which brings in 4 per cent. Find And the difference in his income. £100 invested in 3 per cents. at 80 produces £4 7s. 6d.; invested in an estate it produces £4 only; there is consequently a loss of 7s. 6d. per 100, and on £7,500 there will be a loss of £28 2s. 6d. Answer. 29. Multiply (by duodecimals) 7 ft., 6 in., 5 pts., by 2 ft., 9 in., 3 pts., and the product by 6ft., 6 in. Express the result in cubic feet, cubic inches, and the fraction of a cubic inch. √a2+1+√a2—1√a2+1—√ aa—1 √a+1-va-1 √aa+1+√a2—1 4. Find the greatest common measure of 5. Find the least common multiple of 6. Extract the square root of (1) 9a1+12a3+22a2+12a+9 EUCLID-Books I.-IV. and VI. with definitions of Book V. 1. Straight lines which join the extremities of equal and parallel straight lines, towards the same parts, are themselves equal and parallel. Euclid, Book I., Prop. 33. 2. The square described upon the hypotenuse of a right-angled triangle is equal to the sum of the squares described upon the sides which contrin the right angle. Euclid, Book I., Prop. 47. 3. (a) The opposite angles of any quadrilateral figure inscribed in a circle are together equal to two right angles. (b) Show that a circle cannot be described about any parallelogram which is not rectangular. (a) Euclid, Book III., Prop. 22. (b) The opposite angles of a parallelogram are equal to one another (I. 34). Let a circle be described about a parallelogram with (1) an acute and (2) an obtuse angle. In case (1) the opposite angles of a quardrilateral inscribed in a circle are less than two right angles in (2) they are greater, contrary to Euc. III. 22. 4. Inscribe a circle in a given equilateral and equiangular pentagon. Euclid Book IV. Prop. 13. 5 (a) What is meant by duplicated ratio ? (6) Similar triangles are to one another in the duplicate ratio of their homologous sides. (a) When three magnitudes are proportionals, the first is said to have to the third the duplicate ratio of that which it has to the second. (Definition, Book V.) (6) Euclid, Book VI., Prop. 19. 6. If the four sides of any quadrilateral be bisected, the quadrilateral formed by joining the middle points will be a parallelogram. Let E F G H be the figure formed by joining the points of bisection; draw B C; join EC and F B; the triangle B E F is equal to A E F (Euc. 1, 38). Similarly, FEC is equal to A E F; therefore B E F is equal to F E C, but they are on the same base, E F; they are (I. 39) between the same parallels; E F is therefore parallel to B C. In a similar manner it can be shown that GH is parallel to BC, therefore EF and GH are parallel (I. 30). By joining A D, E G can be shown to be parallel to F H, the figure EFGH is therefore a parallelogram. Q.E.D. |