COLLEGE OF PRECEPTORS. (Incorporated by Royal Charter.) 6 4. Solve the quadratic equations : (i.) 3x8 –24—1= 0; (ii.) DET = +1 +42072** 5. If æ+ 8 = 4, prove that «– 3 =+2. 6. The difference of two numbers is 4, and the difference of their squares exceeds their difference by 60; find them. 7. The length of a rectangular field exceeds its breadth by 28 poles, and the square of its diagonal is 2704 square poles; find its area in acres. COLLEGE OF PRECEPTORS. (Incorporated by Royal Charter.) PROFESSIONAL PRELIMINARY EXAMINATION.-SEPTEMBER, 1882. WEDNESDAY, September 6th-Morning, 9.30 to 11,30. ALGEBRA. 1. Find the numerical value of (a +26) (a–26)-(08—28) +(a?–462) d?, when a=10, b=5, c=1, d=3. 2. Find the quotient and remainder, when (22— 2x+4)(a* + 2x+4) is divided by ai — x + 2. 3. Find the G. C. M. of 4x*—124*+192–15 and 6x8 – 13x2 +21a-10. 4. Express in its simplest form 5. Reduce to its simplest form _nini _Sn119 6. Extract the square root of 9x*—12x8 + 7x* —2x+. 7. Solve the simple equation(5x-2)(1 – 3x) – (2-x) (3—2x) = 9 (2x-3) - (4x-1)-2*. 8. Solve the simultaneous simple equations **} = 3, + 0. X-Y 9. Divide the number 45 into two parts such that one-third of the less shall exceed one-fourth of the greater by unity. COLLEGE OF PRECEPTORS. (Incorporated by Royal Charter.) PROFESSIONAL PRELIMINARY EXAMINATION.-SEPTEMBER, 1882. WEDNESDAY, September 6th-Morning, 11.30 to 1. EUCLID. Books I.-IV. 1. Define the terms-plane surface, plane angle, parallelogram, angle in segment of a circle, circle inscribed in rectilineal figure. 2. If two triangles have two sides of the one equal to two sides of the other, each to each ; but have the angle contained by the two sides of the one greater than the angle contained by the two sides, equal to them, of the other; then shall the base of the one that has the greater angle be greater than the base of the other. Having proved this proposition, enunciate (without proof) any one subsequent proposition in the course of the proof of which reference is made to it. 3. Equal triangles on the same base, and on the same side of it, are between the same parallels. Prove that diameters (produced, if necessary) of any pair of parallelograms about the diameter of a given parallelogram will form a parallelogram by meeting diameters (produced, if necessary) of any pair of parallelograms about the other diameter of the said given parallelogram. 4. If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together with the square on half the line bisected, shall be equal to the square on the straight line made up of the half and the part produced. 5. To describe a square that shall be equal to a given rectilineal figure. 6. The angle at the centre is double the angle at the circumference on the same base, that is, on the same part of the circumference. 7. In equal circles, if angles, whether at the centres or circumferences, be equal, the circumferences on which they stand shall be equal. 8. To inscribe an equilateral and equiangular pentagon in a given circle. COLLEGE OF PRECEPTORS. (Incorporated by Royal Charter.) PROFESSIONAL PRELIMINARY EXAMINATION.-SEPTEMBER, 1882. WEDNESDAY, September 6th - Morning, 11.30 to 1. EUCLID. Book I. 1. Define the terms-circle, parallel straight lines, parallelogram. 2. If two angles of a triangle be equal, the sides which are opposite to those equal angles shall be equal. [Note.—You may omit the proof of the first case of the proposition which is set in the next (the 3rd) question.] 3. If two triangles have two angles of the one equal to two angles of the other, each to each ; and have one side of the one equal to one side of the other—namely, sides which are adjacent to the equal angles, or sides opposite to equal angles, in each : then shall the other sides be equal, each to each; and the third angle of the one shall be equal to the third angle of the other. 4. If a straight line fall on two parallel straight lines, it shall make the alternate angles equal to one another. 5. If a parallelogram and a triangle be on the same base and between the same parallels, the parallelogram shall be double of the triangle. Enunciate (without proof) subsequent propositions, of which the proof is partly based on this one. 6. Parallelograms on equal bases, and between the same parallels, are equal. 7. If the square described on one of the sides of a triangle be equal to the squares described on the other two sides, the angle contained by those sides shall be a right angle. 8. AC, one of the equal sides AB, AC of an isosceles triangle, is produced to F, and points, D and E, are taken in BA and BC, such that BD = BE. Join DE, and prove that the angle ECF is double the angle BDE. (Incorporated by Royal Charter.) PROFESSIONAL PRELIMINARY EXAMINATION.-SEPTEMBER, 1882. THURSDAY, September 7th-Afternoon, 2 to 3.30. MECHANICS. 1. Explain the following terms:-resultant, horizontal compo. nent, tension, reaction, energy, horse-power. 2. Describe an experiment which will illustrate and test the truth of the proposition known as the Parallelogram of Forces. Prove that, the greater the angle between two forces, the less will be their resultant. 3. Three cords are tied together at the same point; one of the three hangs vertical and supports a weight of 60 lbs., another is horizontal being attached to a hook in a wall, and the third is tied to a hook in the ceiling. The angle between the third cord and the horizontal cord is 120°. Find the tension in each cord. 4. What is meant by the Moment of a Force about a Point ? Use the Principle of Moments to find the relation between the power and weight with a lover having arms of given lengths. 5. The length, base, and height of an inclined plane are 25 feet, 24 feet, and 7 feet; if a body weighing 100 lbs. is placed on the plane, what force acting along the plane will support it, supposing the plane smooth? What will be the pressure on the plane ? 6. Explain fully the statement that the weight of a body in pounds divided by 32.2 is the mass of the body. A horizontal force equal to the weight of 11 lbs. acts on a body of 100 lbs. which lies on a rough horizontal surface, the friction being one-tenth of the pressure on the surface. What velocity will be given to the body in four seconds ? 7. A body is projected from the earth vertically upwards with a velocity of 80 feet a second, how high will it rise, and how long will it be before it strikes the ground ? Prove, or reason out, each step of your solution. [See next page. |