III. LITTLE EXAMINATIONS i. 1. Two men hire a pasture for $132. One puts in 7 cattle and the other 15. How much rent should each pay ? 2. How much will 360 ft. of iron pipe cost if listed at $1.50 a foot, a discount of 40%, 10%, being allowed? 3. How much will 4 gross of jars of mixed pickles cost at $6 a dozen, a discount of 20%, 10%, being allowed? 4. A man's salary of $2100 a year was increased 10% and later was decreased 10%. How much was it then? 5. If the ratio of cream to the rest of the milk of a certain quality is 1: 5, how many pounds of cream in 750 lb. of milk? 6. If in. on a map represents a distance of 750 mi., how many miles will 14 in. represent? ii. 1. A triangular gable to a house has a base of 36 ft. and a height of 12 ft. 8 in. Find the area of the gable. 2. If a tree casts a shadow 45 ft. long when a post 3 ft. high casts a shadow 3.6 ft. long, how high is the tree? 3. If 72 reams of paper are used in printing 3800 books, how many reams of paper will be needed for printing 9800 books, each 18 as large? 4. If the ratio of butter fat to the rest of the milk of a certain quality is 1:24, how many pounds of butter fat in 1050 lb. of milk of that quality? 5. If the ratio of solid matter to the rest of the milk of a certain quality is 33: 217, how many pounds of solid matter in 375 lb. of milk of that quality? 6. After deducting a discount of 331%, 25%, and paying $5 cartage and $19.50 freight, 30 stoves cost $504.50. At what price was each stove listed? 17. 5. Express the following as decimals and also as per cents: 13. 1. 14. 3. 15. §. 16. . 18. Find the area of a circle of radius 4.9 in. 19. What is the area of a circle of radius 6.3 ft. ? 20. Find the curve surface of a cylinder 18.9 in. high and 1 ft. in diameter. 21. Find the volume of the cylinder in Ex. 20. 22. Find the entire surface of the cylinder in Ex. 20. Add these numbers without writing them in columns : PROBLEMS WITHOUT NUMBERS All work oral 1. If you know the number of cups of flour needed for a certain number of loaves of bread, how do you find the number cups of flour needed for a certain other number of loaves ? of 2. If you know how much water flows through a pipe in a minute, how do you find the amount of water that will flow through the pipe in a whole day, at the same rate? 3. If a boy wishes a piece of board to make a bookshelf, how do you find the cost of the board, knowing the size of the shelf and the cost of the lumber per M? 4. If you know how much per foot an iron rod expands in length when heated from the ordinary temperature to red heat, how do you find the amount of expansion of an iron rod a given number of inches in length when heated to red heat? 5. If you know the number of hours per day that a man works, for each day of the week, and his rate of wages per hour, how do you find the amount of money due him at the end of the week? 6. How would you calculate the cost of a concrete walk in front of the schoolhouse? 7. Suppose that your school has a playground in the form of a rectangle, how would you find the area in acres? 8. If you know the weight of two volumes of a substance, and one of the volumes, how do you state the proportion? 9. How can you find the height of your school building by means of shadows and the height of a pole? 10. How can you find the height of a tree by sighting over the top of a pole of known length? PROBLEMS FOR COMPLETION 1. A man bought 5 loads of coal containing respectively 2475 lb., 2830 lb., 1970 lb., 2150 lb., 1950 lb. The coal cost him $11.45 a ton. Complete the problem and solve it. See the note after Ex. 1, page 81. Complete and solve the following problems: 2. A grocer sold Mrs. Pratt the following items: 41 lb. butter @ 52¢; 3 bunches celery @ 18¢; 12 lb. beans @ 16¢; 8 cans corn @ 184; and 2 bottles olives @ 60¢. 3. An electric meter indicated 198 K.W.H. on May 1 and 251 K.W.H. on June 1. Electricity costs 11¢ per K.W.H. 4. A bill of goods amounts to $170. There are discounts of 10% and 8%. 5. A cow gave 675 lb. of milk in a month. The milk tested 4.2% butter fat. House Orchard and Barns Garden 44 rd. Pasture Meadow 30 rd.30 rd. 10 ft. in diameter and 8 ft. high. There are 231 cu. in. in 1 gal. 8. A grain bin is 18 ft. long, 14 ft. wide, and 6 ft. deep. There are 11 cu. ft. in 1 bu. 9. A city lot is in the form of a rectangle. The frontage of the lot is 22 ft. 6 in. The area of the lot is 1080 sq. ft. ALERTNESS TEST Copy the following on paper as rapidly as possible, canceling in each case the numbers (if any) that should be omitted so that the numbers shall run along in a regular order according to some kind of rule or law. For example, Ex. 1 should appear as 9 8 7 6 5 4 2. 11. 42 40 38 36 34 32 30. 18. 7 7 6 7 7 7 7 7 7 7. The teacher should have all the pupils begin at the same instant and should call all papers in at the end of 4 min. The teacher should then score for each pupil (1) the rights and (2) the wrongs and should repeat the test at least once a month during the term to see if the score is improved. To have the test at its best, the teacher should write it on the blackboard, with the order of the lines changed and with occasional new combinations, so that it cannot be worked out in advance. As in the case of all these alertness tests, it is in the discretion of the teacher to omit the work if the class does not have the time for taking it. Nevertheless, it should be understood that such a test not only furnishes an interesting game but also furnishes a valuable exercise in becoming familiar with number relations. Not many of the pupils in an ordinary class should be expected to complete any given test in the time specified. It is such tests that enabled the army to rank its men according to mental alertness and that are coming to be used in determining the fitness of applicants for positions requiring alertness, speed, and accuracy. |