SECTION VIII. 1. What decimal of a guinea is of 12s. 6d.? 2. How many paces of 2.16 feet are there in 3-25 miles ? 3. An estate is divided between two claimants in the ratio of 51 to ·025; the money value of the smaller share is £238 28.: express in guineas tho corresponding value of the larger share. SECTION IX. 1. If the value of £1 sterling varies from 25.15 francs to 26.75 francs, what is the corresponding variation in value of 100 guineas ? 2. A B C D is a quadrilateral; A B=845 feet, BC= 613 feet, CD=810 feet; A B is parallel to C D, and the angle at A is a right angle: find the area. 3. The wheels of a locomotive are 2 metres asunder, and the inner wheel describes the circumference of a circle whose radius is 120 metres. Find the difference of the length of the paths of the els, having it given that the circumference of a circle equals 3.1416 its diameter. SECTION X. 1. Define ratio and proportion. Show that when four numbers are in proportion the product of the means is equal to the product of the extremes. 2. Explain, as to a class, the object and the process of reducing fractions to a common denominator. Reduce to the least common denominator , , , , explaining the work. 3. State as precisely as possible your views as to the value of Mental Arithmetic simply as an educational instrument; explain how you would employ it for this purpose in the different classes of a mixed school of 120 children of from 7 to 14 years of age, and point out any faults which you have noticed in the ordinary treatment of this subject. 3 4 EUCLID, ALGEBRA, AND MENSURATION. EUCLID. Capital letters, not numbers, must be used in the diagrams. Not more than two questions to be answered in each section. The only signs allowed in geometry are + and =. The square on A B may be written sq. on A B,” and the rectangle contained by Å B and CD, “rect. A B, C D.” SECTION I. 1. Define the terms—“plane superficies,” "right angle," "segment of a circle," and “rhombus”; and write down Euclid's 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. To make a triangle of which the sides shall be equal to three given straight lines, but any two of which are together greater than the third. What is the reason for the limitation in the data ? SECTION II. 1. If the square described on one side of a triangle be equal to the squares described on the other two sides, the angle contained by these two sides is a right angle. 2. If a straight line be divided into two equal, and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line and of the square on the line between the points of section. 3. The diagonals of a rhombus bisect each other at right angles. ALGEBRA. The solution must in every instance be given at full length. A correct answer, if unaccompanied by the solution, or if not obtained by an intelligible method, will be considered of no value. SECTION III. 1. Define the terms “factor," "COefficient, exponent,” and “binomial,” and explain the use of brackets. 2. Multiply 4a3 – 2ab2 — 313 by 2a2 ab + 4b2; and divide a2b + (a - b)2x — 2axa 23 by b + x. 3. Find the G.C.M. of a2 + 5ab + 462 and a3 + 4a2b + Gab? + 263; and the L.C.M. of a'b + ab), and a472 – a2b4. power," + = 0. ac + SECTION IV. 1. Find the square root of (1) 4x4 + 12x®y + 5xy– 6xy3 + y*. (2) } to 4 places of decimals. 2. Solve the equations 11 (x + 3) 13 — 30 3x – 1 78 5 3 =/5. a + 20 Y Y (4) 3x2 + 5ax 2a2 = 0. 3. The ages of two men are now as 4 to 3, but 9 years ago they were as 3 to 2: find their present ages. a a =1. al =1. MENSURATION. SECTION V. 1. Find the area in acres of a field, the sides of which are 270, 360, and 450 yards respectively, 2. Find the diagonal of a square that shall be equal in area to a rectangle of which two adjacent sides are 30 and 20. 3. The chord of an arc is 24 feet, and its height is 8 feet : find the diameter of the circle of which the arc is a part. a GEOGRAPHY AND HISTORY. Candidates are not permitted to answer more than one question in each section. One full map only is to be drawn. GEOGRAPHY. SECTION I. 1. Draw a full map of Wales, marking the rivers, lakes, mountains, principal towns, and boundaries between the counties. 2. Describe in words the south coast of England, the west coast of Ireland, and the coast of Scotland, from Cape Wrath to Kinnaird's Head. 3. Name in order, beginning at the South Foreland, the islands and groups of islands in the British Seas (not including Great Britain or Ireland). Give a brief account of one of the largest, or draw a little sketch map of it. SECTION II. 1. Draw a full map of Russia in Europe. 2. Describe, as fully as you can, the course of a traveller from London to Calcutta, by Paris, Turin, Brindisi, Athens, Suez, Bombay, and Ceylon. Give a brief account of two of these places. 3. Describe fully the courses of the Danube, the Ganges, and the Nile, and their tributaries. SECTION III. 1. Write a short account of the cotton trade and cotton manufacture of Great Britain. What great war affected this trade? And what was the effect on the growth of cotton in other countries ? 2. From what countries do we import tea, coffee, sugar, fruit, rice, and spices ? Give a short account of the manner of obtaining each of these articles. 3. In what parts of England and of Europe are iron, lead, and tin found ! And what countries are noted for gold, silver, pearls, and precious stones ? Say what you know of the manner of obtaining each of them. SECTION IV. 1. Draw a full map of the shores of the Gulf of Mexico and the Caribbean Sea, with the West India Islands. 2. Describe the great physical features and vegetation of South America. 3. Where and what are Patagonia, Santiago, La Plata, Lima, Chimborazo, Hong Kong, Savannah, Albany, Huron, Quebec, Fraser, Etna, Mozambique, Gondar, Munich, and Penang? HISTORY. SECTION I. 1. Describe, with dates, the condition of England during the reign of Alfred. 2. Describe, with dates, the condition of England during the reign of William the Conqueror. 3. Describe, with dates, the condition of Scotland after the death of Alexander III. SECTION II. 1. What is a civil war? Which of the following battles were fought during civil wars : :-Eve. sham, Falkirk, Nevill's Cross, Shrewsbury, Bosworth, Worcester, and Dunbar? Give dates, and say by whom each of them was fought. 2. Which of the kings of England, or of Scotland, were famous as warriors ? Describe the wars in which they were engaged. 3. Which kings or queens of England or Scotland were ever prisoners ? By whom was each of them imprisoned ? And when ? And where? SECTION III. 1. Name, with dates, any great British royagers or travellers; and mention any discoveries made by them. 2. Name two distinguished authors in the reign of Queen Elizabeth, two in that of Queen Anne, and two in that of Queen Victoria ; and describe the character of their works. 3. In whose reign did each of these events take place; -The invention of printing; the discovery of America; the founding of the first English colony; the invention of the steam engine; the opening of the first railroad; the invention of the electric telegraph ? Show briefly the importance of each of them. SECTION IV. 1. Name, with dates, the sovereigns of the house of Hanover. Show what was their title to the throne; and state how each of them was related to his or her predecessor. 2. Sbow, by a table, that Queen Victoria is descended from William the Conqueror. 3. Compare the reign of Queen Victoria with that of George III. MUSIC. The Tonic Sol-fa questions are printed in italics. Candidates must keep entirely to one set of questions or the other. You are not permitted to answer more than four questions. 1. Write over each of the following notes its pitch name (A, B, Do, Ré, or other); and under it its duration name (crotchet, quaver, or other). 1. Describe pitch. Give the octave marks used in bass and soprano parts. |