SET I. COOK COUNTY, ILLINOIS. Eighth Grade Examination for County Superintendent's Diploma. June, 1897. O. T. BRIGHT, Supt. Time, 9:30 to 12. 1. What is the ratio of (a) .2% to 2%? (b) 5 ÷ 5 = ? (c) .05÷5=? (d) .5÷.05=? (e) .005÷.5=? (e) .005+.5=? (f).05÷ .005 = ? 2. A girl spelled correctly 95% of 60 words. How many words did she miss? 3. When a vessel sails 160 miles a day, she completes her voyage in 14 days. In what time would she complete it if she sailed 196 miles a day? 4. A three inch cube was painted on all sides. It was then cut into inch cubes. (a) How many of the inch cubes were painted on three sides? (b) How many on two sides? (c) How many on one side? (d) How many were not painted at all? 5. Fill the blanks in the following: A boy had a fish pole 15 feet long. A piece equal to 20% of its length was broken off while catching fish. % of the whole pole. % of the part remaining. % of the part broken off. of a certain section of land (a) The part remaining was (b) The part broken off was (c) The part remaining was 6. The, N.E. of the N.W. was fenced off into four equal fields. (a) What is the shortest length of fence necessary? (b) How much land in each field? 7. A straight pole 72 feet high is broken 20 feet from the ground, but is not detached. How far from the foot will the top reach? SET II. NEW HAVEN (CONN.) PUBLIC SCHOOLS. (Answer 10 entire questions.) 1. (a) 13 oz. is what per cent of 5 lb. avoirdupois? (b) A man added 18 cows to his herd, thereby increasing the number 25 per cent. How many cows has he now? 2. If lead pencils that cost 3 cents each, are sold for 5 cents each, what is the per cent of profit? 3. Find the interest on a note for $330 at 6 per cent, given August 3, last year, and due to-day. 4. Write a negotiable, interest-bearing, promissory note. 5. (a) Divide of 8 of 73 by 33. (b) Subtract 8 from the sum of 51, 21, 4. 6. A rectangular field is 86 rods long and 46.875 rods wide. How much wheat will it produce at the rate of 20 bushels per acre? 7. A rectangular park, the sides of which are respectively 45 rods and 60 rods long, has a walk crossing it from How long is the walk? corner to corner. 8. If of 9 bushels of wheat cost $131, what will § of a bushel cost? 9. If hay sells for $14 a ton at a loss of 121 per cent, what must it sell for to gain 15 per cent? 10. How many pounds of cotton at 7 cents a pound can a broker buy for $9225, and retain his commission of 21 per cent? 11. Find the proceeds of a 3 months' note for $500 discounted at a bank at 6 per cent. 12. If a building 20 feet high casts a shadow of 6 feet, what length of shadow will a church spire 114 feet high cast? SET III. COOK COUNTY, ILLINOIS. Applicants for Teachers' Second Grade Certificates. June, 1898. O. T. BRIGHT, Supt. 'Mental Arithmetic." Time, 20 minutes. Fill the blanks: 1. By a sale of goods, I lost 121%. The cost was % of its % of the selling price. 2. The circumference of a 3-in. circle is radius. 3. A five-inch square is inch square. % greater than a four 4. I buy apples four for three cents and sell them three for four cents. I gain per cent. 5. A and B are 78 miles apart and walk toward each other; A walks 3 miles an hour and B 3 miles an hour. When they meet B will have walked miles. 6. A stick of timber 15 inches square and 32 feet long contains board feet. 7. A horse trots 23 miles in 2 hours. His rate per hour is miles. 8. $154 was divided among A, B, C, and D, in the proportion of, 1, 1, 1. C got 9. A school contains 50 pupils: dollars. Monday, 3 were absent in the forenoon. Tuesday, 2 were absent all day. Wednesday, 3 absent forenoon and 2 afternoon. Thursday, 4 absent all day. Friday, all present. The per cent of attendance for the week was 10. 64 gal. of wine and 16 gal. of water were mixed. One pint of the mixture contained of a gal. of water. SET IV. COOK COUNTY, ILLINOIS. Applicants for Teachers' Second Grade Certificate. August, 1895. O. T. BRIGHT, Supt. Time, 60 minutes. 1. If a quarter section of land has fenced within it the largest possible circular lot, how many acres of the quarter section will remain outside of the circle? 2. Find the value of the following lumber at $15 per M.: 20 pieces 2 x 4, 18 ft. long. 20 pieces 4 x 4, 12 ft. long. 20 pieces 3 x 10, 16 ft. long. 45 16 ft. stock boards, 15 inches wide. 3. (a) What sum invested in 8% bonds at 33% premium will yield an annual income of $1200? (b) What if the bonds were 331% discount? 4. Find the value of a piece of land 20 ft. x 40 rods at $1000 per acre. 5. What is the ratio of 37 to? Answer in per cent. SET V. Examination Department of the University of the State of New York, January, 1898. 100 credits. Necessary to pass, 75. Time, 9:15 a. m. to 12:15 p. m. Answer the first five questions and five of the others, but no more. If more than five of the others are answered only the first five answers will be considered. Give all operations (except mental ones) necessary to find results. Reduce each result to its simplest form and mark it Ans. Each complete answer will receive 10 credits. 1. Define numerator, denominator, divisor, factor, proportion. 2. Find the weight in kilograms of a stone 1 meter square and .4 of a meter thick, assuming that the stone is 2 times as heavy as water. 4. Find the interest on $375 at 41% from July 1, last year, to the present time. 5. Multiply 65.15 by 3.14159 and divide the result by 57.296, finding a result correct to three decimal places. 6. Find the cost at $50 an acre of a rectangular field 1650 feet long and 825 feet wide. 7. Find the time required to fill a cistern 8 feet square and 5 feet deep by a pipe which admits water at the rate of 1 quart a second. 8. Make a receipted bill of the following: J. L. Robbins & Co. sold this day to Samuel Jones 8 yards of cloth at 37 cents, 24 yards of calico at 81 cents, 1 dozen handkerchiefs at 12 cents each, and 3 dozen towels at $2.50 a dozen. 9. Find the cost of four sticks of timber, each 8 inches by 10 inches and 30 feet long, at $15 a 1000 feet board measure. 10. Find the least common multiple of 153,204, and 510. 11. If 4% bonds to the amount of $8000 face value are bought at 92 %, find the cost of the bonds, and the rate of income on the investment. 12. If 3 men can do a piece of work in 8 days of 10 hours each, how many men will be required to do the same work in 6 days of 8 hours each? (Solve by proportion.) 13. By selling a horse for $144, a profit of 60 per cent is made; find the cost of the horse. 14. The diameter of a bicycle wheel is 28 inches; find the number of revolutions it makes in going 1 mile. 15. Find the square root of 7, correct to three decimal places. |