SET IV. COOK COUNTY, ILLINOIS. 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 2x4, 18 ft. long. 45 16 ft. stock boards, 15 inches wide. 3. (a) What sum invested in 8% bonds at 331% 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 33 to ? Answer in per cent. SET V. Examination Department of the University of the State of New York, January, 1898. 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 24 times as heavy as water. 3x4x 4.2 3. Simplify 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 377 cents, 24 yards of calico at 8} cents, 1 dozen handkerchiefs at 124 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 921%, 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. SET VI. Examination for Admission to State High Schools, Minnesota, 1898. Time, 2 hours. Answer any six-no more. If more are attempted and the student does not designate which six he wishes to be graded upon, the first six answers will be taken. 1. a (2) What is the ratio of 2 to .90 ? b (2) What is the ratio of 4 to ? e (2) What is the ratio of 70% to 50%? 2. a (5) What is the cubical content of a cellar 15 ft. wide, 20 ft. long, and 10 ft. deep? (In the solution express all operations in the form of equations.) b (1) What unit (or units) of measure did you use in the example? c (4) Describe the unit of measure used in measuring boards. 3. (10) A merchant sells an overcoat for $22; a suit of clothes for $23; a hat for $5. On the overcoat he makes 10% of the cost; on the suit 15%, and on the hat 25 %. What per cent of the cost of the goods does he make on the entire sale ? 4. a (5) A man bought a watch and a chain for $70. One-half of the cost of the watch equals f of the cost of the chain. What was the cost of each? b (5) Analyze. 5. (10) The rates at which A, B, and C work are to each other as 2, 3, and 4. What integers will indicate the time it will take each to do a certain piece of work? 6. (10) How long a rope must a horse have in order that he may graze over an acre of land, if he be tied to a stake in the center of a field ? 7. (10) B buys bank stock at 78. and sells it at 84. C buys railroad stock at 70 and sells at 75. Each buys the same number of shares, and B makes $1000 more than C. How much money did B invest? 8. (10) Make (5) and solve (5) a problem in the solution of which it will be necessary to extract the square root. 9. a (5) What is the interest on $700 for 1 yr. 5 mo. and 10 da. at 7% per annum. b (5) Analyze. 10. (10) A servant is engaged for a year for $280 and a suit of clothes. He leaves at the end of six months and receives $130 and the suit. What is the value of the suit? (An algebraic solution is allowed for this problem.) 11. a (5) How long will it take $1560 at 5% simple interest to gain $426.831? b (5) Analyze. SET VII. Examination for State Certificates. Illinois, 1898. 1. (a). Every fraction is a ratio. Explain. (b) Every integral number is a ratio. Explain. 2. In the report of the Committee of Ten it is recom. mended that “the course in arithmetic be at the same time abridged and enriched.” (a) Tell what abridgment you regard as important. (b) Tell what enrichment you consider essential. 3. (a) Tell what sense-magnitudes you prefer to use in presenting to third grade pupils the subject of fractions. (b) At what stage of the work do you think sense-magnitudes should give place to imaginative magnitudes ? 4. (a) When and to what extent should pupils in the grades be required to memorize definitions of mathematical terms? (b) When and to what extent should pupils be required to memorize directions for performing operations ? 5. Mention all the standard linear units with which you are familiar, and give the ratio of each (either exact or approximate) to some other linear unit. 6. What is the weight of 1000 feet of white pine boards (1 inch in thickness) if the specific gravity of the boards is .6? 7. The foundation of my house is 32 feet square on the outside. The house is 20 feet high to the plates and the roof has the usual eave-projections. Give approximately the number of barrels (31) gal.) of water that will fall upon this roof in one year, if the rain-fall is 344 inches. 8. Give approximately the following ratios: (a) Of the circumference to the diameter of a circle. (b) Of the diagonal to the side of a square. (c) Of the area of a circle to the area of its circumscribed square. (d) Of the area of a circle to the area of its inscribed square. 9. What single discount is equal to a discount of 45 per cent. and “5 10's”, i.e., to “45 and 10 and 10 and 10 and 10 and 10 off”, from the list price? 10. If money is worth 6 per cent. annual interest now and prospectively, what is the actual cash value of a note of $1000 running two years and drawing 5 per cent., interest payable annually? |