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4. In 80,937,864 sq. in. how many acres?
5. Q and Y barter. Q makes of 10 cts. 121 cts., Y makes of 15 cts. 19 cts.; which makes the most per cent, and how much?
6. Three men harvested and thrashed a field of grain on shares, A furnishing 4 hands 5 dys., B 6 hands 4 dys., and C 5 hands 8 dys. The whole crop was 630 bu., of which they had one-fifth; how much did each receive?
7. Extract the cube root of 81 to three decimal places.
8. Bought 30m of cloth at $2.50 per metre; at what price per yard must it be sold to gain $25?
1. Find the greatest common divisor of 36,864 and 20,736.
2. Multiply of by of 63/
3. (a) Give the table of metric weights.
(b) A cubical cistern holds 1331kg of water; what is the length of an inner edge?
4. Divide 67.56785 by 0.035, and multiply the result by . Explain the position of the decimal point after division.
5. How much money should be received on a note of $1000, payable in 4 months, discounting at a bank where the interest is 6 per cent?
6. If a man travel 117 miles in 15 days, employing only 9 hours a day, how far would he go in 20 days, travelling 12 hours a day?
7. Extract the square root of 10 to five places.
1. (a) Select the prime numbers between 50 and 100.
(b) What is the least number that can be exactly divided by by, 21, 5, 6, and ?
2. Reduce 0.00096 to its simplest equivalent common fraction.
3. 7465 is 33 per cent of what number?
4. A broker bought 84 shares of railroad stock at 19 per cent discount. He sold 35 shares at 27 per cent discount, and the balance at 8 per cent discount. Did he gain or lose,
and how much?
5. Calculate the cube root of 3.7 to five decimal places.
6. Give the approximate value of the meter in feet; of the kilogram in pounds avoirdupois.
7. Find the weight in kilos of 15 gallons of water.
NOTE 1. Candidates who present themselves for the whole examination may omit questions 2, 3, and 5. Candidates who present themselves for the partial examination will confine themselves to the questions in Plane Geometry.
NOTE 2. State what text-book you have studied, and to what extent.
I. PLANE GEOMETRY.
1. (a) Define the symmetry of a figure with respect to an axis and with respect to a point.
(b) Prove that if a figure is symmetrical with respect to two axes perpendicular to each other, it is also symmetrical with respect to the intersection of these axes.
2. An angle formed by a tangent and a chord is measured by one-half the intercepted arc.
3. To bisect a given arc or angle.
4. (a) If a perpendicular be drawn from the vertex of the right angle to the hypothenuse of a right triangle, the two triangles thus formed are similar to each other and to the whole triangle.
(b) What can you say of the perpendicular as compared with the segments of the hypothenuse? Why?
(c) What of either side about the right angle? Why?
5. On a given straight line to construct a polygon similar to a given polygon?
6. The circumferences of two circles are to each other as their radii, and their areas are to each other as the squares of their radii.
II. - SOLID AND SPHERICAL GEOMETRY.
7. If a straight line and a plane are parallel, the intersection of the plane with planes passed through the line are parallel to that line and to each other.
8. Define a prism. Two prisms are equal, if three faces including a triedral angle of the one are respectively equal to three faces similarly placed including a triedral angle of the other.
9. Every section of a sphere made by a plane is a circle.
10. Between what two limits does the sum of the angles of a spherical triangle lie? Write expressions for the surface and volume of the cylinder, cone, and sphere.
[State what text-book you have studied and to what extent.] 1. To draw a common tangent to two given circles.
2. The bisector of an angle of a triangle divides the opposite side into segments which are proportional to the adjacent sides.
3. The area of a parallelogram is equal to the product of its base and altitude.
4. How do you find the area of a trapezoid? The areas of similar polygons are to each other in what ratio? Of all plane figures having the same area what one has the least perimeter?
5. If a straight line is perpendicular to each of tv straight lines at their point of intersection, it is perpendicula. to the plane of those lines.
6. A triangular pyramid is one-third of a triangular prism of the same base and altitude.
7. Define the terms, spherical excess and tri-rectangular triangle. The area of a spherical triangle is equal to its spherical excess (the right angle being the unit of angles, and the tri-rectangular triangle the unit of areas).
NOTE 1. Candidates for examination on the whole of this subject should take the whole of this paper. Candidates for the first year's partial examination should take the first part; those for the second year's partial examination, the second part.
NOTE 2. State what text-book you have studied on the subject, and to what extent.
1. Of two oblique lines drawn from the same point to the same straight line, that is the greater which cuts off upon the line the greater distance from the foot of the perpendicular. Corollaries.
2. In any triangle the product of two sides is equal to the product of the diameter of the circumscribed circle by the perpendicular let fall upon the third side from the vertex of the opposite angle.
3. Two sides of a triangle and the angle opposite to one of them being given, to construct the triangle.
4. The area of a circle is equal to half the product of its circumference by its radius.
5. Calculate the area of a circle whose radius is 10 ft.
II. SOLID AND SPHERICAL GEOMETRY.
6. The sum of any two face angles of a triedral angle is greater than the third.
7. If the base of a cone is a circle, every section of the cone made by a plane parallel to the base is a circle.