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In what particular case will the quadrilateral figure required by the construction be a rhombus ?
2. Given two points, find two other points that shall be at the same given distance from each of them. What is the least possible length of the given distance ?
3. Any two sides of a triangle are together greater than the third side. Construct the triangle when each side is equal to half the sum of the other two.
SECTION III. 1. The three interior angles of every triangle are together equal to two right angles. What ratio does the angle of a regular hexagon bear to a right angle ?
2. Triangles upon the same base and between the same parallels are equal. A line drawn through the middle points of the sides of a triangle is parallel to the basc.
3. In any right-angled triangle the square described on the side subtending the right angle is equal to the squares described on the sides which contain the right angle.
Section IV. 1. If a straight line be divided into two equal parts and also into two unequal parts, the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line. Construct a rectangle equal to the difference of two given squares.
2. If a straight line drawn through the centre of a circle cut a straight line in it which does not pass through the centre at right angles, it shall bisect it. Lines drawn at right angles to the sides of any figure inscribed in a circle from their middle points meet in one point.
3. The angles in the same segment of a circle are equal to one another. Given three points in the cir. cumference of a circle, required to find a fourth.
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 V. 1. If a = 2, b=3, c= 0, find the ralue of 3a + 4b, 3a - 4c, a' + 2? + c, abc (a + b + c)
x (a + bc)(a + 12 + ( + 3).
y by x}
a + b
2. Multiply 03 5x2 3x – 18 by a2 + 3x – 4. 3. Divide a
yš: SECTION VI. 1. Find the G.C.M. and L.C.M. of 22 + 5x + 4, x3 + 4x2 – 2x – 8.
2. Simplify the expressions,-
26 a? — 462 a? - 2ab
and b a? - 62 aa + 4ab ab + 462 3. If show that 6 d
- ď SECTION VII. Solve the equations1. (a) 5x + 6 = 7x - 10.
(6) 3 (2x — 1) + 4 (3x − 2) = 5 (3x + 2). Or 2. 2x 3y + 2 = 7x — By – 3 = 0. Or 3. 32x2 3 20x.
SECTION VIII. 1. The length of a garden exceeds its breadth by 50 yards; the garden contains 9375 yards : find its length and breadth.
2. Two numbers are in the ratio of 5: 6; show that four times their sum = 44 times their difference, whatever the numbers may be.
3. A labourer can save out of his weekly wages 10 per cent.; his wages rise one shilling a week, but, his expenses increasing also 10 per cent., he can now only save 5 per cent. of his increased wages. Find his weekly wages.
MENSURATION. SECTION IX. 1. Find the number of turfs, 4 feet by 8 inches, required for a garden plot, 50 feet by 75 feet, allowing for four circular beds, diameter 6 feet.
2. A triangular piece of ground, whose sides are 800, 500, and 500 yards respectively, is let for £30 a year : find the letting price per acre.
3. A schoolroom is 60 feet long, 20 feet broad, 10 feet high to the wall plate, 16 feet high to the ridge of the roof. How many children would it contain, allowing 80 feet of cubic space for each childp By how much does this exceed the workable number at 8 square feet
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. Draw a map, —
1. Of the east coast of Great Britain between the estuaries of the Forth and Thames.
Or 2. Of the Spanish Peninsula.
SECTION II. 1. Define cape, zone, watershed, peninsula, volcano.
2. What are parallels of latitude and longitude ? Give the latitude of some of the chief cities of the world.
3. Give in miles the length of the earth's diameter, of the equator, of the sun's distance from the earth, and of England.
SECTION III. Describe fully-
SECTION IV. Describe the position, and claims to notice in a lesson on geography, of not more than six of the following:
1. A manufacturing town in Cheshire.
3. A town in Scotland famous for its linen manufactures.
4. A seaport in the west of Ireland. 5. A frontier town of India. 6. A seaport of France on the Mediterranean. 7. A city on the St. Lawrence. 8. The chief town of the Cape Colony. 9. The chief town of New South Wales. 10. An inland town of Russia in Asia. 11. A British island in the Mediterranean. 12. A place within the Arctic circle. 13. A large commercial city of the United States.
SECTION V. 1. In what countries are raw silk, cotton, indigo, and hemp chiefly produced ?
2. Name the countries rich in iron, gold, or salt.
3. What are the chief manufactures of Franco and Austria ?
HISTORY. SECTION 1. 1. Give the dates of some remarkable events (not more than eight) that took place between the years 1200 and 1400.
Or 2. 1400 and 1600.
SECTION II. 1. What were the chief provisions of Magna Charta relating to taxation and the administration of justice Relate the circumstances under which it was forced upon King John.
2. What was the claim of Edward III. to the throne of France ? How long did the war begun in this reign continue ? Name, with dates, the chief battles.
3. On the death of the Maid of Norway, who were the chief claimants to the throne of Scotland ? On what ground was appeal made to the king of England ?
SECTION III. 1. What were the remote and imme. diate causes of the Spanish Armada ? Give a short account of the expedition.
2. Name some of the leading statesmen of Charles the First's reign, and the sides they took before and after the outbreak of the Civil War.
3. What was the immediate cause of the Revolution of 1688. Describe briefly the occurrences of that year.
SECTION IV. 1. Name some of the most striking actions of the Seven Years' War. What countries were engaged in it? What were the results to England ?
2. Give some account of the events that led to the American War of Independence. What was the chief right that the colonists were determined to uphold ? Which of our leading statesmen took opposite sides on the question ?
3. How are the colonies and possessions of England governed ? Illustrate your answer by the cases of Ceylon, Victoria, and Malta.
SCHOOL MANAGEMENT. Three Hours allowed for this paper with that on Music. Those who are or have been pupil teachers are not to answer more
than one question in any section. Candidates who have not been pupil teachers may answer any seven questions they think fit. No candidate is to answer more than seven ques. tions. SECTION I. 1. What registers were kept in your school, and what share had you in keeping them? How did you test their accuracy ? At each meeting of a school what entries should be made in the daily register of attendance before it can be considered to be closed ?
2. Point out the advantages of having one or more classrooms attached to a school containing four or more classes. Which lessons may be given with advantage in separate classrooms? Give your reasons.
3. When a child is admitted, by what considerations would you classify it ? For what subjects would you suggest a separate classification of the whole school, and why?
(For Females only.) 4. If you have been a pupil teacher in a girls' school, draw up a series of standards (not less than four) of needlework suitable to your school.
Or, if you have not been a pupil teacher, make out a list of articles of summer and winter clothing for girls of ten years old, with the price and material of each article. What part of the work of each article would you expect a girl of twelve years of age to be able to do ?
SECTION II. 1. Name some of the qualities of good reading.
2. What peculiarities of pronunciation of vowels or consonants have you observed in your scholars or in your own locality ? Name some words beginning with the aspirate in which it should not be sounded.
3. What special help should be given to an older child backward in reading, to obviate his being placed in a class of younger children? What harm would it do a child to be so placed ?
SECTION III. 1. A class of infants understand the notation of numbers up to (but not including) ten. How