ARITHMETIC. REV. CANON HEAVISIDE, M.A. 1. If a pound of meat cost 7 d., how many pounds may be bought for one sovereign? 2. 40 pounds troy of standard gold are coined into 1869 sovereigns, determine the weight in grains of one sovereign. 3. Find the value of 19 yards 2 feet 8 inches of cloth at 5s. 74d. a-yard. 4. If 70 men mow 110 acres in 8 days, working 11 hours a-day; how many men, working 7 hours a-day, will mow 150 acres in 10 days? 5. When 5000l. amounts to 66877. 10s. in five years at simple interest, find the rate per cent. 6. Find the expense of lining a cistern with lead at 21. 2s. the cwt., the cistern being 10 feet 9 inches long, 10 feet 3 inches wide, and 6 feet 6 inches deep; each square foot of lead weighing 8 lbs. 7. If a proper fraction be divided by a proper fraction, show that the quotient must be greater than the fraction that is divided. By what fraction must (++) be divided to give for a quotient the whole number 12 ? 8. Express 17. 13s. 4d. as the fraction of 57.; and find the value of of 12 guineas added to 20 of 50001. 9. In the division of decimal fractions, state and explain the rule for pointing the quotient when the number of decimal places in the dividend falls short of the number in the divisor. Express as a finite decimal, the quotient of 3:078 by 0144. 10. Find in its simplest form the product of 1.83 multiplied by 54. Find the value of 009 of 1167. 11s. 11. Prove (002)2 × (·05)2 = (·01)*. 12. A square tract of land contains 400000 acres, what is the length of a side of the square, it being given that 640 acres make a square mile? MATHEMATICS. REV. CANON HEAVISIDE, M.A. Voluntary Paper, No. 1. 1. Explain briefly the principle of keeping accounts by "double entry." Give some description of a "waste book," "journal," and "ledger." Rule a cash book and enter in it the following transactions, and strike a balance : 1864. Jan. 1. Cash in hand £ S. d. 501 10 11 Cash at bankers 1,602 0 1 3. Paid John Evans (by cheque) 204 3 2 4. Paid into bank 400 0 0 5. Paid John Smith 12 13 4 6. Received of Evan Jones 100 10 6 9. John Woornan's draft on me 11. Paid to my account at bank by John Evans ARITHMETIC. REV. CANON HEAVISIDE, M.A. 1. If a pound of meat cost 74d., how many pounds may be bought for one sovereign? 2. 40 pounds troy of standard gold are coined into 1869 sovereigns, determine the weight in grains of one sovereign. 3. Find the value of 19 yards 2 feet 8 inches of cloth at 5s. 7d. a-yard. 4. If 70 men mow 110 acres in 8 days, working 11 hours a-day; how many men, working 7 hours a-day, will mow 150 acres in 10 days? 5. When 5000l. amounts to 66877. 10s. in five years at simple interest, find the rate per cent. 6. Find the expense of lining a cistern with lead at 21. 2s. the cwt., the cistern being 10 feet 9 inches long, 10 feet 3 inches wide, and 6 feet 6 inches deep; each square foot of lead weighing 8 lbs. 7. If a proper fraction be divided by a proper fraction, show that the quotient must be greater than the fraction that is divided. By what fraction must (++) be divided to give for a quotient the whole number 12 ? 8. Express 17. 13s. 4d. as the fraction of 57.; and find the value of of 12 guineas added to 50001. of 9. In the division of decimal fractions, state and explain the rule for pointing the quotient when the number of decimal places in the dividend falls short of the number in the divisor. number of combinations of 10 things taken 3 at a time. 9. Expand (x+a)6 by the Binomial Theorem. MATHEMATICS. Voluntary Paper, No. II. REV. CANON HEAVISIDE, M.A. 1. Define a parallelogram; describe a parallelogram equal to a given triangle, and having of its angles equal to a given rectilineal angle. 2. In an acute-angled triangle show that the square of the side subtending one of the acute angles is less than the squares of the sides containing that angle by twice the rectangle contained by either of those sides, and the straight line intercepted between the acute angle and the perpendicular let fall upon it from the opposite angle. 3. Show that the angle in a semicircle is a right angle, 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. 4. Define similar rectilineal figures. If the sides of two triangles about each of their angles be proportional, show that the triangles are similar according to the definition. 5. The straight lines joining the points of bisection of the sides of a regular hexagon will form a regular hexagon; prove this, and compare the sides of the two hexagons. 6. Prove the sine of an angle equal to the sine of its supplement. Find sine 120°. Prove sin (A+B)=sin A cos B+cos A sin B, and deduce from this formula the corresponding expression for sin (A-B). 7. Three sides of a plane triangle are respectively 107.2, 85.2, 66 feet; find the least angle. 8. If a side of a rhombus is 29.5 feet, and one of its angles 62°, find its area. 9. What is meant by the coefficient of friction? A power P acting at a given angle to an inclined plane just prevents a weight W sliding down the plane; find the equilibrium relation of P to W. (1.) When the plane is smooth. (2.) When friction is considered. 10. An elastic ball (A) impinges on another elastic ball (B) at rest, in direct impact; find the velocity of each ball after impact. GEOGRAPHY. G. W. DASENT, D.C.L. 1. Enumerate the chief colonial possessions of Great Britain, and state how and when each of them was acquired. 2. Name the principal seaports of Great Britain and Ireland, and give some particulars as to the physical position, population, and commerce of each. 3. What metals and what minerals have most influence on the commercial prosperity and political |