3. A block of land, containing 40380 ac. 2 ro. 32 per., is divided into sections, each containing 380 ac. 3 ro. 32 per. ; how many sections are there? 4. Find in yards, to two dec. places, the sides of a square which shall contain an acre. 5. Express £27 17s. 94d. in dollars, assuming one dollar to equal 4s. 2d. 6. Find the value of 2731 articles at £4 8s. 93d each, in two ways, one being by Practice. 7. Distinguish between complex and compound fractions. Compare the value of of £1, of a guinea, and of 11s. 10d. 8. A four-penny loaf weighs 3.5 lbs., when wheat is 4.75s. the bush.; how much would be paid for 22.5 lbs., when wheat is 14s. the bush.? 9. What is meant by the square root of a quantity? Find the square root of 89680900. D. 1. Explain the meaning of the terms Addend, mutiplier, factor, dividend, minuend. Find the sum of 486 +390 +462 + 98, and explain clearly each step in the process. 2. What is the difference between seven millions ninety-eight thousand five hundred and twelve, and three hundred and eighty-seven thousand six hundred and nine? Write the answer in words. 3. Write out the table of Square Measure. 4. If a silver spoon weighs 15 dwts. 11 grs., how many dozen of such spoons can be formed out of 122 oz. 9 dwt. 1 gr. ? 5. What is meant by ascending reduction? Reduce 52073 sheets of paper to reams; and 351 sevenshilling-pieces to half-guineas. 6. Define Ratio and Proportion, and give numerical examples. If 42 yards of cloth which is 18 in. wide cost £59 14s. 2d., what will 118 yards of yard-wide cloth of the same quality cost? 7. Define Interest and Insurance. What is the simple interest on £47 10s. for four years and 52 days at 4 per cent. per annum? 8. Find by Practice the value of 235 oz. of gold at £3 17s. 101d. an oz. Prove by Multiplication. THE ART OF TEACHING. (Two hours allowed for answering this Paper.) 1. Distinguish between the Individual and Simultaneous methods of teaching; point out the advantages and disadvantages of each. 2. Explain clearly the difference between Explanation, Description, and Illustration. 3. What do you mean by "Notes of Lessons"? State their advantages and the principles on which they should be constructed. 4. Give a synopsis of the "First Reading Book." 5. State fully how you would give elementary lessons in Arithmetic. 6. Write a short essay on "Questions and Answers." 7. What are the objects of transcription and dictation? 8. Describe the methods of conducting these in the school with which you are connected. EUCLID-BOOKS, I., II., AND III. (Three hours allowed for this Paper.) 1. Define a plane angle, a circle, and parallel straight lines. How does a plane angle differ from a plane rectilineal angle? Under what circumstances may two lines never meet when produced and yet not be parallel? 2. Prove that upon the same base, and upon the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity. Construct the figure for the third case, and shew why it "needs no demonstration." 3. Prove that any two sides of a triangle are together greater than the third side. Show from this proposition that the difference of any two sides of a triangle is less than the third side. 4. Prove that in any right-angled triangle, the square which is described upon the side subtending the right angle is equal to the squares described upon the sides which contain the right angle. Exhibit to the eye the truth of this proposition in the case of a triangle whose sides are 3, 4, and 5 units respectively. 5. Prove that if a straight line be divided into any two parts, the squares on the whole line, and on one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square on the other part. Give Euclid's demonstration of this proposition; also, prove it algebraically. 6. Describe a square that shall be equal to a given rectilineal figure. 7. Distinguish between the angle of a segment and the angle in a segment. What is meant by the distance of a point from a line? When is a circle said to be given? 8. Prove that one circle cannot touch another in more points than one, whether it touches it on the inside or outside. 9. Prove that the angle in a semicircle is a right angle; but that the angle in a segment greater than a semicircle is less than a right angle, and the angle in a segment less than a semicircle is greater than a right angle. PROBLEMS. PROBLEMS. 10. Divide a right angle into three equal angles. 11. In the base of a triangle, find the point from which lines drawn parallel to the sides of the triangle, and limited by them, are equal. 12. Prove that if two circles cut each other, the straight line joining their centres will bisect their common chord at right angles. ALGEBRA. (Three hours allowed for this Paper.) 1. What is Algebra? Explain the meaning of the terms-negative quantity, coefficient, like quantities. Distinguish between an identity and an equation. 2. Simplify the expression, 5x { 3x — (2x + 3)}, and find its value, when x=-1. 3 3. If a=5, b=3, c=1, find the numerical value of 5ab + √9bc-2√3a+b-2c. 5. Resolve into elementary factors, 12a2+7ab-10b2, 15a2+2ab- 86, and 15a 5ab-106. What is their G. C. M.? 6. What is Evolution? State and explain the law respecting the sign of the root after evolution. Extract the square root of 16x + 24x2 + 25x* + 12x2 + 4, and the cube root of 64a3 144a2b+108ab 2763. 3z + 2x 1 8 4 3x + 2y = (ii) 3y+2z 5 9 8 = 2 9. A and B begin trade, A with three times as much stock as B. three times A's stock is exactly equal to seven times B's. 10. A person sells a acres more than the mth part of his estate, and there remain b acres less than the Of how many acres does the estate consist? nth part. 11. The slope of a hill is 1 in 8. A man, whose usual pace on level ground is 4 miles an hour, ascends and descends in 5 hours. His pace uphill: pace on level: 3:4, and pace downhill to pace on level: 5:4 What is the height of the hill? [Price, 1s. 1d.] By Authority: JAMES C. BEAL, Government Printer, William street, Brisbane. 1874. QUEENSLAND. REPORT OF THE BOARD OF GENERAL EDUCATION FOR THE YEAR 1873. Presented to both Houses of Parliament by Command. To His Excellency The Most Honorable GEORGE AUGUSTUS CONSTANTINE, Marquis of Normanby, Earl of Mulgrave, Viscount Normanby, and Baron Mulgrave of Mulgrave, all in the County of York, in the Peerage of the United Kingdom; and Baron Mulgrave of New Ross, in the County of Wexford, in the Peerage of Ireland; a Member of Her Majesty's Most Honorable Privy Council, a Knight Commander of the Most Distinguished Order of St. Michael and St. George, Governor and Commander-in-Chief of the Colony of Queensland and its Dependencies. MAY IT PLEASE YOUR EXCELLENCY, The Board of General Education beg to submit this their Fourteenth Annual Report, together with a Statement of Accounts. GENERAL. 1. The condition of the school departments during the year was on the whole satisfactory, and the applications received for aid towards the establishment of new schools were unusually numerous. 2. The following is a Comparative General Statement of Statistics during the years 1872 and 1873 : |