IV. LITTLE EXAMINATIONS i. 1. Find the premium on a fire-insurance policy for $12,500 at $1.24. 2. Find the premium on a life-insurance policy for $15,000 at $32.75. 3. Find the cost of 250 shares of stock at 967, including the brokerage of $15 per 100 shares. 4. Find the income from 41% bonds of par value $9500. 5. Draw a graph of the changes of temperature during a day when the thermometer indicated the following: 8 A. M., 60°; 9 A. M., 65°; 10 A. M., 68°; 11 A. M., 70°; noon, 75°; 1 P. M., 76°; 2 P. M., 78°; 3 P. M., 75°; 4 P. M., 70°; 5 P. M., 70°; 6 P. M., 68°; 7 P. M., 65°; 8 P.M., 58°. Find, to the nearest hundredth, the square roots of: 6. 13. 7. 17. 8. 30. 9. 125. 10. 5. iii. Find the circumferences, given the following diameters: 1. 34.1 in. 2. 32.2 ft. 3. 3.5 in. 4. 4 in. Find, to the nearest hundredth, the square roots of: 6. 19. 7. 15. 8. 50. 9. 675. 5. 9 in. 10. 12 iv. Find the discounts and the proceeds on the following notes: 1. $500, for 60 da., at 6%. 4. $825, for 90 da., at 4%. 5. $675, for 90 da., at 41%. 6. $575, for 30 da., at 5%. Multiply, and also divide these numbers: 10. by. 11. 2 by . 12. by . 13. 37 ft. 8 in. by 2. ខ 1. Find, to the nearest hundredth, the values of the following: 14. 35% of $23,468.25. 15. 7.2310.643. 16. 2÷0.6234. Add these numbers without writing them in columns: 17. $4.48 $5.92+ $1.75 +$5.75 + $9.50 +$19+ $8.75. 18. $24.17+ $25.29 + $41.50 + $65.70 + $79.85 + $82.50. 19. $42.96 $58.37+ $87.62 + $54.63 +$42.85+ $53.75. 20. $58.17+ $65.42 + $96.54 + $84.90 + $68.79 + $48.70. 21. $63.44+ $88.96+ $17.28 + $62.95 + $78.69+ $42.55. 22. Add 125% of 5280 ft. to mi., using a short method. 23. Find the value of √138 to the nearest hundredth. 24. Which will bring the better income, a 5% note or 6% stock, par value $100, which costs, including brokerage, $120 ? 25. A manufacturer pays $5642.40 for materials, labor, and overhead charges on a certain contract, and makes a profit of 121% on these costs. Find the amount of the contract. PROBLEMS WITHOUT NUMBERS All work oral 1. If you know the face of a fire-insurance policy and the premium per $100, how do you find the premium? 2. There are companies that insure employers against accidents to the workmen. If you know the annual pay roll of an employer and the per cent of the pay roll that the insurance company charges, how do you find the total premium ? 3. If you know the newspaper quotation on some railroad stock, how do you find the cost of a share? 4. If you know the newspaper quotation on a certain stock, how do you find the amount you would receive for a share? 5. How do you find the square of a number? 6. If you know the side of a square, how do you find the area? Illustrate by an example. 7. If you know the area of a square, how do you find the side? Illustrate by an example. 8. How do you find, by factoring, the square root of a number which is a perfect square? Illustrate by an example. 9. How do you find the hypotenuse of a right triangle when you know the other two sides? 10. If you know the base and height of a pyramid, what else can you find, and how do you find it? 11. If you know the height of a cylinder and the diameter of the base, what other measurements can you find relating to the cylinder, and how do you find them? 12. How do you find the area of a circle? the volume of a cube? the volume of a sphere ? PROBLEMS FOR COMPLETION 1. A man takes out a 20-payment limited life insurance policy for $15,000. The premium at his age is $26.40 annually. 2. A man buys 50 shares of stock when it is quoted at 108. The brokerage is $15 per 100 shares. 3. A man owns 25 shares of stock. A dividend of $2.75 a share is declared. 4. A man buys 30 shares of Western Union Telegraph stock at 87 and sells it at 90. The brokerage is as usual on each transaction. 5. Suppose that you have $3000 to invest and that with it you can buy 44% Liberty Bonds of par value $3200, including brokerage. 6. Mr. Huntington invests $12,500 in some property that pays him 53% a year. 7. Mr. Driscoll buys a house for $9800 and rents it at $68 a month. In a certain year he pays $56 for taxes, $32 for insurance, and $75 for repairs. 8. A square has an area of 22 sq. in. 9. Another square has a diagonal of 10 in. 10. A third square has a perimeter of 17 in. and it is to be covered with gold leaf at a cost of 3¢ per square inch. 11. A ladder 28 ft. long leans against a building. The foot of the ladder is 8 ft. from the building. 12. The edge of a cube is 16 in. 13. The area of one side of a cube is 289 sq. in. 14. The area of a circle is 44 sq. in. 15. The area of the surface of a sphere is 154 sq. in. ALERTNESS TEST Beginning at a signal from the teacher, copy the following on paper, insert in each set of parentheses the number which the teacher announces, then place a cross (+) before each statement that is correct, and a circle (0) before each one that is incorrect : = 1. 3+() 20. 2. ( )-4=12. 3. 2x()= 30. 4. 10 x ( )÷ 2 = 80. 5.5+()= 4 x 5. 6. 9 x()= 153. 7. ( )+( ) = 40. The teacher should see that the pupils have copied all eight exercises, and should then say, "Take the number 15 and begin." The number given may be 15, 16, or 17, and should be changed as the test is repeated. The teacher should score the results as directed on pages 82, 144, and 214. Allow 10 sec. Proceed as in the exercises above, using the following statements and inserting the numbers which the teacher directs: 1. ( )÷ 2 = 24 +1. 2. ( )÷ 2 = 51–1. 3. ( )÷7=10 – 3. 4. ( )-3=47+1. 5. 3×( )=153. 6. 2+()=50. 7. ( )-9= 40. As before, the teacher should give a number when the class is ready. This number may be 48, 49, 50, or 51. Allow 15 sec. By the aid of such tests a teacher's records will soon show the degree of alertness of each member of the class, and the work can be adjusted according to the individual powers of the pupils. Such psychological-arithmetical tests are extensively used in the army and at present are becoming common in the placing of men and women in industrial positions that require alertness. As already stated in connection with alertness tests, the work omitted at the discretion of the teacher. may be |