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SECTION VII. Solve the equations
3 - 1
5x + 3
a + a +b a + ctd
Q2 + 2x
(These form one question.) SECTION VIII. 1. Find a number such that when it is divided into 4 and into 3 equal parts, the continued product of the former shall equal eighty-one times the continued product of the latter.
2. Two trucks whose wheels are of different sizes are in motion; one makes 2002 revolutions more than the other in 7 miles, whereas if its wheels had been twice as large in circumference, it would have made 770 less than the other : find the circumference of the wheels.
MENSURATION. SECTION IX. 1. A rectangular park, one side of which is twice as long as the other, contains 500 acres : how much ground will be occupied by a road 15 feet wide, running round it ?
2. Two equal chords, 15 inches in length, are drawn from a point in the circumference of a circle, and form an angle equal to two-thirds of a right angle : find the area of the circle to three places of decimals.
Females. The solution must in every instance be given at such length as
to be intelligible to the Examiner, otherwise the answer will be considered of no value. SECTION I. Add together nine hundred and seventy thousands seven hundre and nine; three millions thirty thousands and thirty-three; fifty-nine thousands five hundred and ninety; eight millions eight hundred and eight thousands and eighty-eight; sixty-seven thousands and seventy-six. Multiply thesum by seventynine, and divide by eighty-four.
SECTION II. Divide 6061 tons 11 cwt. 2 qrs. 18 lbs. 5 ozs. 5 drams by 69; and prove your sum by multiplication. SECTION III. Work out the following bill of parcels :-
137 reading books at 5 d. each.
at 1s. 9 d. each.
7 dozen slates at 2d, each. SECTION IV. Find, by Practice, the value of 191 acres 3 roods 37 poles of land at £42 3s. 4d. per acre.
SECTION V. 1. What sum of money, invested in 33 per cent. stock at 872, would produce 50 guineas per annum ? and what increase of income would be obtained by selling out the stock at par and investing in stock at 105 paying 54 per cent. ?
2. A person has an income of £122 10s. from 3} per cent. consols; he sells at 92, and invests his principal in stock at 95, which yields 57 per cent. : what will his income be?
SECTION VI. 1. The carriage of one lot of goods weighing 3 tons 1 cwt. 16 lbs. cost £1 158. 8d. : what would be the cost of carriage for 8 other lots weighing each 1 ton 13 cwt. 8 lbs. 2 oz.?
2. If 18 men can dig a trench 17 yards long and 2 yards broad in 17 days, working 5 hours a day, how many men will dig a trench 12 yards long and 4 yards broad in 9 days, working 8 hours a day?
SECTION VII. 1. Arrange the following fractions in order of magnitude :13, 1, $, b, and 2.
3 33 2. Multiply 34. by 71, and divide
5 together their sum and difference.
SECTION VIII. 1. Find the value of •732 + 4.96 + 2 X 2:395+ 13•798543 - 21131.
by , and add
2. Multiply 3.05 by .203, and '1787 by :373, and divide 14:4 by .012.
SECTION IX. 1. Find the expense of carpeting a room 31 ft. 6 in. long, and 16 ft. 6 in. broad with carpet of yd. wide at 58. 3d. a yard.
2. What would be the cost of coverirg a space 14 yards by 10 with lead of 2} lbs. to the square foot at 4d. a pound?
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, exc in Section VII., from which only one
subject should be selected for notes of á lesson. No Candidate is to answer more than seven questions.
SECTION I. 1. For what number of children were desks provided in your school ? Describe the desks used, and state how much space was allowed for each child for writing. What lessons were given out of desks? or in a standing position ? Why were they so given ?
2. What movements of drill were required in your school for entering or leaving the room, and for changing class ? What are the objects of school drill? Show that it has an influence upon the character of children and their behaviour out of school.
3. In what different shapes may classes be arranged for reading, arithmetic, and geography lessons ?
State which shape you consider best for each purpose, and why you would employ that arrangement. What should be the position of the teacher in regard to his class ?
(For Females only.) 4. Name the parts of a boy's shirt of simple pattern, the proportions required in cutting it out, and the various kinds of work required for each part.
SECTION II. 1. In the following sentence explain the peculiar difficulties presented by the words printed in italics in the early stages of reading :
He would take no pains to teach any boy, who could not at least write what boys of eight years old can write. 2. What especial care would
the less advanced readers in your class, before, during, or after the reading lesson? How can home lessons be utilized for teaching reading ?
3. What preparation is required in a reading lesson, both for the individual words and for the general sense of the passage? How may a reading lesson be divided to secure both the mechanical and intelligent mastering of a passage ? State the proportions of time given to each division.
SECTION III. 1. How can mental addition and sub. traction of money be used to illustrate the first steps in simple addition and subtraction? What other illustrations would you employ?
2. The Education Code states : “The weights and measures taught in public elementary schools should be only such as are really useful.” To what common uses may the avoirdupois, liquid, and square measure tables be applied ? Give examples of such mental problems as you would employ in each of these tables for fourth standard children.
3. Write down the rules for working mentally the following sums-prices of dozens, of scores, multiplying by 99, and dividing by 60.
SECTION IV. 1. What elements are common to the written letters, p, q, h, g, d, y? In what order and in what combinations would you teach these elements to infants ?
2. By what rules would you be guided in selecting the extracts for transcription, or the subjects for com. position, for a class whose handwriting was well formed ?
3. Give some examples of a child's first steps in learning to draw, and explain the progressive nature of each step.
SECTION V. 1. By what illustrations have you given