University of the State of New York 108th examination ARITHMETIC Tuesday, March 14, 1893-9: 15 a. m. to 12:15 p. m., only 100 credits, necessary to pass, 75 NOTE- Give all operations (except mental ones) necessary to find results. Reduce each result to its simplest form and mark it Ans. I Define fraction, power, root, ratio, percentage. JO 3 Find the sum of 1, X 1, 3, . Express the result decimally. 6 4 Find the cost of 20 boards each 14 ft long, 8 in. wide, 14 in. thick at $24 per M. ΙΟ 5 How many cubic yards of masonry in the walls of a cellar 30 ft long, 21 ft wide and 9 ft deep, inside measurement, if the walls are 18 in. thick? (Make no allowance for openings.) I 2 6 Find the amount of $265 at 41% simple interest from July 12, 1892 to March 14, 1893. 7 Bought 240 barrels of apples at $1.75 a barrel; lost 40 barrels through frost; at what price a barrel must I sell the remainder to gain 25% on the money invested? ΙΟ 8 School bonds bearing 41% interest sell at 10% premium; what rate per cent does the buyer get on his investment? ΙΟ 9 If 2 men plow 15 acres in 5 days working ten hours a day, how many acres will 3 men plow in 4 days working 8 hours a day? ΙΟ 10 Find the square root of 243.121 correct to three decimal places. 6 II Find the face of a 60 day note which when discounted at a New York bank will yield $250. 6 12 Find the weight of the water that can be contained in a cubic vessel whose edge is 4 decimeters. 6 University of the State of New York 111th examination ARITHMETIC Tuesday, June 13, 1893-9:15 a. m. to 12:15 p. m., only 100 credits, necessary to pass, 75 NOTE- Give all operations (except mental ones) necessary to find results. Reduce each result to its simplest form and mark it Ans. I Divide the sum of 18 thousandths, 106 ten thousandths, 84 hundredths, and 509 ten thousandths by 15 millionths. ΙΟ 2 State two methods of proving subtraction and illustrate each by an example. 4 3 What number divided by the sum of and 2 will give a quotient of 25% ? 230 IO 4 Define greatest common divisor, least common multiple, and illustrate by finding the greatest common divisor and least common multiple of 12, 15 and 18. I 2 5 If 14 quarts of grass seed are required for an acre of ground, what will be the cost of the seed for a field 36 rods by 24 rods, the seed being worth $31⁄2 a bushel? I 2 6 Find the cost of a stone walk 4 rods long and 5 feet wide, at 60 cents a square foot. 6 7 Find the amount of $436 at 4% % simple interest, from January 1, 1893, to the present time. ΙΟ 8 I buy oranges at the rate of 15 cents a dozen and sell them at the rate of 3 for 10 cents; find the gain per cent. ΙΟ 9 Find the distance between the diagonally opposite corners of a rectangle 60 feet long and 50 feet wide. (Result correct to two places of decimals.) IO 10 If it costs $80 to plow a field 40 rods by 80 rods, when we pay $5 a day for man and team, how much will it cost to plow a field 30 rods by 60 rods, if we pay $4 a day? (Solve by proportion.) ΙΟ II Assuming that 1 kilogram equals 2 pounds, find the weight in pounds of the water that can be contained in a tank 1 meters long, 8 decimeters wide and 5 decimeters deep. 6 University of the State of New York Examinations Department 107th examination ADVANCED ARITHMETIC Monday, January 23, 1893-9: 15 a. m. to 12:15 p. m., only 100 credits, necessary to pass, 75 NOTE- Give each step of solution, indicating the operations by appropriate signs. Use cancelation when possible. Reduce fractions to lowest terms. Express final result in its simplest form and mark it Ans. I Name the principal unit of length, of surface, of capacity and of weight in the metric system and show the relation between these units. 9 2 The sum of two numbers is 260 and their difference is 12; find the numbers and demonstrate the principle involved. ΙΟ 3 A and B can do a piece of work in three days; B and C can do it in four days; A and C can do it in six days; if all work together for the same length of time what part of the sum paid to all should each receive? 4 Demonstrate the following: I 2 If the greater of two numbers be divided by the less and the less be divided by the remainder, and this process be continued till there is no remainder the last divisor will be the greatest common divisor. ΙΟ 5 Add the following repetends and convert the sum into a common fraction: .103, .2432, .11224. Give reasons for each step. ΙΟ 6 Find the fourth term of the following proportion and demonstrate the principle on which the operation is based: 8:12=10:x. ΙΟ 7 Columbus discovered America October 12, 1492. Explain why the four hundredth anniversary of that event was celebrated October 21, 1892. 8 8 A cylindric cistern is 8 ft in diameter; how deep must it be to contain 75 barrels of water? 9 9 A note for $250, due in one year, with interest at 6%, is dated January 1, 1892; what is the true value of this note October 1, 1892? 8 10 Find the diagonal of a right parallelopiped whose edges are 6 ft, 8 ft and 4 ft. 8 II Find in inches to two places of decimals the diagonal of a cube whose volume is 9 cubic feet. 6 University of the State of New York Examinations Department 108th examination ADVANCED ARITHMETIC Monday, March 13, 1893-9:15 a. m.to 12:15 p. m., only 100 credits, necessary to pass, 75 NOTE- Give each step of solution, indicating the operations by appropriate signs. Use cancelation when possible. Reduce fractions to lowest terms. Express final result in its simplest form and mark it Ans. : I Indicate the following operations by signs in one connected expression the sum of the square roots of 3 and 5 multiplied by 7; this product increased by 4 times the square of the sum of 4 and 6; the 4th power of the entire sum. 8 2 Find the sum of 1⁄2 and 23 and illustrate by means of lines each step of the operation. 14 3 Demonstrate the common rule for multiplying a fraction by a fraction. 16 4 Compare the bank discount of any given sum with the true discount (days of grace not included in either case) and deduce a method of finding either from the other. 14 5 The diameter of the base of a cone is double that of the base of a cylinder of the same volume; find the ratio of their altitudes. ΙΟ 6 Find the square root of 104976 and give a reason for each step in the process. 14 7 Deduce a rule for finding the sum of an arithmetic series and illustrate its use by finding the sum of 10 terms of the series whose first term is 2 and whose common difference is 4. I 2 8 State a method of finding (a) the 6th root of any number; (b) the 5th root of an integral number known to be a perfect 5th power. I 2 University of the State of New York Examinations Department 111th examination ADVANCED ARITHMETIC Monday, June 12, 1893-9: 15 a. m. to 12 :15 p. m., only 100 credits, necessary to pass, 75 NOTE Give each step of solution, indicating the operations by appropriate signs. Use cancelation when possible. Reduce fractions to lowest terms. Express final result in its simplest form and mark it Ans. 1 Define power, root, true discount, standard of measure, uniform scale. ΙΟ 2 Compare the standard units of money of the United States, England, France and Germany as to relative value. Find the value of $100 in each of the other units. 15 3 A locomotive runs of a mile in of a minute; at what rate an hour does it run? (Give analysis in full.) ΙΟ 4 The base of a certain triangle is 40 feet, its altitude is 30 feet; find the area of a similar triangle whose base is 25 feet. ΙΟ 5 The edges of a rectangular parallelopiped are in the proportion of 3, 4 and 6, its volume is 720 cubic inches; find its entire surface. 15 6 Derive the rules for converting difference of longitude into difference of time and vice versa. Indicate the application of these rules in finding time or longitude. 15 7 Derive a rule for marking goods so that a given reduction may be made from the marked price and a given profit still be made on the cost. 8 Find the sixth root of 191102976 and explain the process. 15 ΙΟ |