SECTION VI. 1. If a pane of glass 18 inches long and 122 inches wide cost 10d., what will be the cost at the same rate of a pane 22} inches long and 15 inches wide ? 2. If 5 oxen are worth 24 sheep, and 4 sheep are worth £13, what are 55 oxen worth? Section VII. 1. Reduce to a simpler form (t + } + 3) (9X 1 X 1%): 2. Multiply £2 198. 01 d. by 71. SECTION VIII. 1. How often will a wheel, 2 metres 9 decimetres 7 centimetres in circumference, revolve in passing over a distance of 2 kilometres 7 hectometres 2 decametres 9 metres 4 decimetres 3 centimetres ? 2. Add together 3-754, 4:63, 2.4, and 5.2i. 3. Multiply 31.5 by 27:9, and divide the product by 9-765, giving the reason for the position of the decimal point in each result. SECTION IX. 1. Reduce £104 38. 31d. to farthings; and explain, as you would to a class, each step of the process. 2. Define “Ratio ” and “Proportion," and work an example in Proportion in illustration of your definitions. 3. Explain the terms “Principal," "Principal," "Interest," “ Amount," and work an example, such as you would give to a class, in illustration. EUCLID AND ALGEBRA. THREE Hours allowed for this Paper. EUCLID. Capital letters, not numbers, must be used in the diagrams. Not more than ten questions to be answered. 1. Give Euclid's definitions of a plane rectilineal angle, and of a triangle. Prove that if two triangles have two sides of the one equal to two sides of the other, each to each, and have also the angles contained by those sides equal to one another, they shall also have their bases or third sides equal; and the two triangles shall be equal, and their other angles shall be equal, each to each, namely, those to which the equal sides are opposite 2. When is one straight line said to be perpendicular to another ? Draw a straight line perpendicular to a given straight line of an unlimited length, from a given point without it. Why must the given straight line be of unlimited length ? 3. Make a triangle of which the sides shall be equal to three given straight lines ; but any two whatever of these must be greater than the third. Why is it made a condition, in working this problem, that any two of the given lines must be greater than the third ? 4. What are parallel straight lines ? The straight lines which join the extremities of two equal and parallel straight lines towards the same parts, are also themselves equal and parallel. 5. What is a parallelogram? Describe a parallelogram which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal triangle. 6. In any right-angled triangle, the square which is described on the side subtending the right angle is equal to the squares described on the sides which contain the right angle. 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. 1. Add together 2x3 + 3x2y + 3xy2 + y?, 523 – 15x2y + 15xy2 – 5y3, 1033 + 10 yo, 17xʻy — 17xy? ; and from their sum take away 13x3 39x2y + 39xya 13y. 2. What is a vinculum, and what effect has it when preceded by a minus sign? Collect the following, 12 (ab cd) - bd) - 5 (ab - cd) — 7 (ac - bd) + 3ab 2 (ac + bd - cd). 3. Multiply a* + 49a2 + 2401 by a’ — 49, and divide 203 — 2x2 + 3x – 6 by a . 2. 4. Multiply as 2a2b + 3ab2 + 468 by a? 2ab 3b?, and divide æ4 + (262 — a2)xa + 64 by ocz + ax + b*. 6 (ac 5. Solve the equations, - 7 x + 7 (a) + 2 9 3 (6) (3x - 5) (6x — 7) – 2(3x - 5)2 = 75. 6. A man starts on a journey on foot, and walks 3 miles an hour. Two hours later his friend follows him on horseback and rides 7 miles an hour. Where will the latter overtake the former ? DOMESTIC ECONOMY. THREE Hours allowed for this paper. You are not permitted to answer more than one question in each Section. SECTION I. (Househoid Work.) 1. State the materials required for cleaning, brass and copper vessels, also for cleaning glass and china, and explain the way in which these materials should be used. 2. Mention any industrial work in which you have yourself been trained, and state the benefit of such training for future life. 3. What are the duties of a “maid of all work" ? In what do they differ from the work of a housemaid ? SECTION II. (Investment.) 1. What are the peculiar benefits of the Post Office Savings Bank, and in what do they differ from those of the old Savings Banks ? 2. Name any safe investments for a school teacher; and compare the benefits to be derived from one of them with the benefits to be gained from the Post Office Savings' Bank. SECTION III. (Cooking.) 1. What instruction bave you received in cooking ? Describe the advantage of such instruction for the comfort and health of a school teacher. 2. Name six inexpensive dinners for a school mistress and two pupil teachers; the cost of providing each dinner, and the amount of each ingredient required. 3. Give the recipes for making pea soup, for boiling potatoes, for an Irish-stew, and for cooking a shecp's head. SECTION IV. (Sickness.) 1. What instructions have you received to help you in your attendance on the sick? What should be done in the following cases :a person fainting: a child suffering from a fit of epilepsy; insensibility after à fall; a child rescued from drowning ! 2. What precautions have you been instructed to take upon the breaking out of any infectious disease in your neighbourhood ? Describe any simple remedies for a severe chill, for å sick headache, for a troublesome cough. SECTION V. (Clothing and Washing.) 1. What instruction have you received with regard to laundry work? Explain the benefit of such teaching. 2. What would be the cost of fitting out a girl of 13 years of age for service ? Make out à bill of such charges, showing the quantity and price of each article. 3. To what extent has cutting out been taught in your school ? Explain any successful plan which has been adopted to give children a practical knowledge of this subject. a a erasures. DICTATION AND PENMANSHIP. TWENTY MINUTES allowed for these Exercises. Candidates are not to paint their letters in the Copy-setting Exercise, but to take care that the copy is clean and without Omissions and erasures in the Dictation Exercise will be counted as mistakes. The words must not be divided between two lines; there is plenty of room for the passage to be written. Write in large hand, as a specimen of penmanship, the word, Originality. Write in small band, as a specimen of penmanship, the sentence, “One truth is clear: whatever is, is right.” : DICTATION. Write the passage * dictated to you by the Examiner, and punctu. ate it correctly. Az " It is natural to suppose that a Government thus arbitrary and vigilant must have looked with extreme jealousy on the diffusion of free inquiry through the press. The trades of printing and book-selling, in fact, though not absolutely licensed, were always subject to a sort of peculiar superintendence. Besides protecting the copyright of authors, the Council frequently issued proclamations to restrain the importation of books, or to regulate their sale.”—Hallam. Az "The king at length sent a message, requesting that a supply might be granted, with a threat of dissolving Parliament unless it was done. But the days of intimidation were gone by. The House voted that they would first proceed with the business of impositions, and postpone supply till their grievances should be redressed Aware of the impossibility of conquering . their resolution, the king carried his measure into effect by a dissolution.”—Hallam. * The passages A1, A2, were given alternately where the number of Candidates was large, and there was danger of copying. |