ALGEBRA AND MENSURATION. The solution must be given at such length as to be intelligible to the Examiner, otherwise the answer will be considered of no value. SECTION V. Find the difference in value between the arithmetical expression 57 and the algebraical expression ab when a= 5, b=7. Simplify the expression(2a - {3b-a-c}+{46 – 3a – c}). -a Reduce (1 a) + (a 1) b + (1 – a) (6 - 1) c +(1 — a) (1 - 0) (0 – 1) d to one expression consisting of factors of the form (1 a). 1 1 3 Divide 24+ + 4x2 + + 6 by 203 + + 3x + aca (These form one question.) SECTION VI. 1. Simplify the expression1 За 3x 8a? — 22 ax 10m2 + (5x + a) (5x + a)2 (5x + a) Show that (y + % - 2)2 + (x + a y)2 + (a + y x)? =(w? — Y-%) (y2 — % a ) (do – y) 2. Reduce to lowest terms ac? X + 3 9x — 357 – 6aży?. ; 9x + 20y + 27a?y? 2 3. Show that 24 + 81 is never less than 18x2; and that (13 + =9ab — 27 if a +b + 3=0. SECTION VII. Solve the equations 4x + 1 5 — 3 700 - 4 6x - 5 13 + -2 2 2 +3 1 ( (2) 5w3 — 56 = 6x2 (22 + yo) (a - b)=a3. - 63 (These three equations form one question.) SECTION VIII. 1. (a) One number is the square of another, and their sum equals six times the smaller of the two; find the numbers. (b) A and B exchange purses; A has as many halfsovereigns as B has half-crowns, and as many sixpences as B has shillings; find the ratio of the number of halfsovereigns to the number of half-crowns, that neither may lose by the exchange. 2. Two trains, A and B, are despatched from opposite termini of a railway at the same time, with speeds of 20 and 30 miles per hour respectively; a third train, C, is despatched after B three hours later, with a speed of 40 miles per hour: what is the length of the railway, if A pass Ở half an hour after passing BP SECTION IX. 1. The sides of a five-sided rectilineal figure ABCDE taken in order, AB, BC, etc., are 18, 24, 30, 24, 18 feet respectively; the angles ABC, AED, are right angles; find the area in feet to two places of decimals. 2. From two of the opposite angles of a parallelogram, whose sides are 75 and 120, perpendiculars can be dropped such that the two triangles so formed are together equal to the remainder of the parallelogram : find the altitude of the parallelogram. 3. Find the cost of gilding the surface of a cone, whose radius of base is 48 feet, and whose height is 36 feet, at 3 d. per square foot. : MALE AND FEMALE CANDIDATES. Candidates are not permitted to answer more than one question in each section. One full map only is to be drawn. a GEOGRAPHY AND HISTORY. GEOGRAPHY. Section 1. Draw a full map, (a) of the west coast of Great Britain from Land's End to Great Orme's Head. Or (6) Of Ireland. SECTION II. Define the terms “estuary," "strait," "archipelago,” “valley." Illustrate your definition of the first from America, of the second from Asia, of the third from Europe, of the fourth from Great Britain. 2. Give accurately the shape of the earth, its equatorial and polar diameters, the proportion of land and water on its surface, the positions of the polar and tropical circles, the latitudes of London and Edinburgh. 3. State clearly how deltas and glaciers are formed. Draw your illustrations from the continents of Europe and Africa. SECTION III. 1. Name the chief rivers which drain the eastern slope of Great Britain, and the heights in which they rise; distinguish also those that are navigable for some considerable distance above their mouths, and explain why the other rivers are not equally navigable. 2. Give the position of, and some of the historical associations connected with, the following towns :-Win. chester, Peterborough, Shrewsbury, Boston, Scarborough, Cardiff, Stirling, Aberdeen, Cork, and Drogheda. Point out in each case the natural advantages of situation which suggested their first establishment. 3. Select one of these counties—Hampshire, Staffordshire, Durham; and one of these-Perth, Lanark, Argyll; give an account of the industrial occupations, the chief towns, and the rivers of the two selected. Explain the terms county and shire. Section IV. Select one out of each of the following groups : (a) Switzerland, Sweden, Austria. Give an account of the manufactures of the first, of the mineral and vegetable productions of the second, of the races or nations who inhabit the third. Section V. Supply the blanks in one of the following passages : (a) The of Canada now includes the various provinces known as etc., in fact the whole of North America, except The territory stretches from the to the ocean, and contains an area of 3,580,310 The capital of the is in the province of Canada proper contains the two provinces of and comprising also the basin of ; it is thc - on the north side of that river, and of the and on the south side north of the parallel of and extends from 42° to 53° lat. and 60° to 90° long. (6) Australia is a term equivalent to a large and most important chiefly in the southern -, between the - and oceans. Australia, the largest in the world, is sometimes called the sixth it is included between 11° and 39o – lat. and 113° and 154° - long. This island includes sepa. rate colonies, viz., etc. The chief towns of these colonies are etc. ܪ HISTORY. SECTION I. Give the dates of some remarkable events that took place between the years (a) 1250 and 1350, Or (6) 1450 and 1550. SECTION II. 1. How were armies raised in the days of the Norman kings? What were the chief causes of the anarchy in England after the death of Henry I. ? 2. Relate the events of the minority of Henry VI. Give instances of minors who were rightful heirs to the throne being set aside in favour of persons of full age. 3. How were the affairs of Scotland administered during the minority of James V.? What effect had the defeat of Flodden on the Government during that period ? Section III. 1. Trace the descent of Henry VII. from Henry III. Why was Henry VII. afraid of the claims of the Earls of Warwick and Lincoln ? 2. Write short accounts of Prince Rupert and David Leslie. 3. What difficulties had William III. to encounter in England and Scotland on bis accession to the throne ? SECTION IV. 1. What were the chief terms of the Union between England and Scotland ? Show that both countries have benefited by the Union. 2. Name some of the great writers and statesmen towards the close of the eighteenth century, and write a brief life of one of them. 3. What were the chief events of the years 1800-1805P Write a full description of one. SCHOOL MANAGEMENT. than one question in any section. Candidates who have not be selected for notes of lessons. No Candidate is to answer more than seven questions. SECTION I. 1. Describe the desk accommodation of your school. What space should be reserved for each child for writing, what for reading, in desks ? Whicl lessons should be given out of desks? Give your reasons. . 2. How was your schoolroom warmed and ventilated ? Explain clearly the action by which the vitiated air was removed from the room. What are the chief difficulties attending ventilation in the winter? 3. Explain why erasures should never be permitted in any of the registers or other school documents. If a mistake were made in marking or casting up the registers, how should it be corrected ? Explain the uses of an admission book. (For Females only.) 4. By what graduated steps would you teach hemming to very young children? In what order would you teach hemming, felling, stitching, seaming, and gathering ? What other kinds of stitch are required for a plain nightshirt ? SECTION II. 1. Which are the silent letters in the following words :-often, would, answer, track, lambkin, friend, know, furious ? How is the type of printed books sometimes varied to assist young children in overcoming this difficulty ? 2. Divide the following words into two classes, accord. ing as the letters which compose them do or do not represent the same sounds in a considerable number of other words :-pen, who, screen, eyes, plague, only, two, too, would, cough, there were. Give your reasons. 3. Before reading the following paragraph with older children, what words should be previously explained ? Give your explanation of each. |