3 NOTE.-The instructions below apply generally to the examinations, and were printed at the head of each examination paper. In the reprint of the papers of questions which follows, only the instructions special to each subject have been retained. GENERAL INSTRUCTIONS. If the regulations are not attended to, your paper will be cancelled. Immediately before the Examination commences, the following REGULATIONS ARE TO BE READ TO THE CANDIDATES. Before commencing your work, you are required to fill up the numbered slip which is attached to the blank examination paper. *You may not have with you any books, notes, or paper other than that supplied to you for use at this examination. You are not allowed to write, draw, or calculate on your paper of questions. Put the number of the question before your answer. You are to confine your answers strictly to the questions proposed. The value attached to each question is shown in brackets after the question. A full and correct answer to an easy question will in all cases secure a larger number of marks than an incomplete or inexact answer to a more difficult one. You must not, under any circumstances whatever, speak to or communicate with another candidate. Those superintending the examination are not at liberty to give any explanation bearing upon the paper. You must remain seated until your papers have been collected, and then quietly leave the examination room. No candidate will be allowed to leave before the expiration of one hour from the commencement of the examination, and none can be re-admitted after having once left the room. All papers, not previously given up, will be collected at If any of you break any of these regulations, or use any unfair means, you will be expelled, and your paper cancelled. * In certain practical examinations, candidates were allowed the use of books, notes, &c.-see special instructions preceding the papers of questions in those subjects. EVENING EXAMINATION PAPERS. SUBJECT I. PRACTICAL PLANE AND SOLID GEOMETRY. INSTRUCTIONS. Read the General Instructions on page 3. The tracing paper may be detached for use in working the problems, but must be carefully re-attached. The constructions should be very accurate, and distinctly and neatly finished in pencil. The construction lines must be shown. Careless work or work done with soft or blunt pencils will receive little credit. Lines parallel or perpendicular to others may be drawn mechanically without showing any construction. Lines may be bisected by trial. In obtaining numerical answers, graphical constructions may be supplemented by arithmetic. A table of logarithms and functions of angles and useful constants (see pages 286 to 291) is supplied to each candidate. Questions marked (*) have accompanying diagrams. Stage 1. The examination in this subject lasts for four hours. All figures must be drawn on the single sheet of drawing paper supplied. A second sheet is not allowed in this stage. You must not attempt more than eight questions in all, and of these Questions No. 1, No. 7, and No. 9 must be three; that is to say, you are allowed to take not more than five questions in addition to Nos. 1, 7, and 9. 1. By the aid of your protractor, and without using the tables, find the value of sin 23°+tan 23°. Now take out the true values of the sine and tangent from the tables, add them, and calculate the percentage error in your first answer. (9) *2. The diagram shows a rampant arch ring, 18 inches deep, made up of eleven voussoirs or arch stones S, S, S, . . having equal lengths of arc aa, aa, . . . . along the soffit ACB, the joints ab, ab, . . . . being perpendicular to the curve of the soffit. The soffit is made up of two circular arcs AC, CB, each of 90 degrees, and of 6 feet and 3 feet radius. Draw the figure to a scale of inch to 1 foot. N.B.-Do not copy the diagram. (13) *3. The diagram shows a geometrical pattern made up of interlacing equilateral triangles. Draw this figure when aa = 8 cm. N.B. Do not copy the diagram. (13) *4.. Test pieces are made of Portland cement and of cement mortar (1 of cement to 1 of sand), and after an interval of n weeks they are put in a testing machine and their tensile strengths are found to be ƒ and f' pounds per square inch. The curves show the relation between n and f, and between n and f', the scales being such that for the point P, OA represents 52 weeks and OB represents 560 pounds per square inch. What is the strength of cement mortar after 52 weeks interval? Find a length OA, which shall represent, to scale, 20 weeks, and measure f and f" for this value of n. (13) *5. A sliding piece has its end A resting on a cam C which rotates uniformly about O. During half a turn of the cam the slider is lifted from A to B at a uniform speed, and during the next half turn it falls from B to A in like manner. The shape of the cam is shown, incorrectly, and you are required to set out the true shape. (13) Take OA = 3", AB = 1", and do not copy the diagram. *6. The diagram shows a method of measuring approximately the area of a curved figure. A piece of ruled tracing paper (or sheet celluloid) is laid over the figure, and the six ordinates are measured and their mean calculated, viz. : 1 y = (Y1 + Y2 + Y3 + Y1 + Y5 + Y6) › m 6 This gives the height of an equivalent rectangle on AA as base. What is y for the given figure? What is the m area of the figure in square inches? Construct a rectangle of equal area on the base BB. 7. The following are the field notes of the survey of a triangular plot of ground ABC. Bearing means the direction from one station to the next succeeding station, and N. 311° W. indicates the direction 31° West of North : Plot the survey to a scale of 1 cm. to 1 chain. Find and measure the bearing and distance from C to A. What is the enclosed area in square chains? (13) *8. A disc rotating about O has two masses m1 and m, fixed to it as shown, which exert centrifugal forces on the bearing of 5 pounds and 8 pounds along the radii OA and OB. Find the resultant centrifugal force. Measure its magnitude and the angle which its line makes with OA. (13) #9. A geometrical model is made by fixing a piece of bent wire ABC in a board as shown. (a) What are the true lengths of the two parts (b) What angle does AB make with the board? (13) *10. Represent the geometrical model of Question 9, consisting of the board and bent wire, in pictorial projection in a manner similar to that used for the cube, where lines parallel to oy and oz are drawn horizontally and vertically, to a scale of full size, and lines parallel to or are drawn by using the 45° set-square, and to a scale of half size. Let the directions OX, OY of the board correspond with the directions ox, oy of the cube. N.B.-The figure need not be copied, dimensions being taken directly from the diagram. (13) *11. Writing desk. The plan and an elevation are shown with the desk closed. Draw the plan when the lid is opened by turning about the hinge HH through an angle of 135°. From your plan project an elevation on xy. (13) *12. The rectangle P shows a horizontal plot of ground, raised above the surrounding level, with embankments A, B, C, and D on its four sides. The embankment A has a slope of 40° to the horizontal; find the slopes of the embankments B and C. The embankment D has a slope of 23°, show its boundary. (13) *13. You are given the plan and elevation of the frustum of a square pyramid. Set out the true shape of one of the sloping faces of the solid. Draw the plan of the mid section SS, and find its area a, and the areas a1 and a of the ends of the solid. Measure the height and calculate the volume of the frustum by using the prismoidal formula |