SENIOR MATHEMATICS. (Candidates may select (a) or (b) of each question in A, three questions from B, two from C, and two from D). A. 1. (a) The sides of a parallelogram are 4 in. and 6 in. and the angle between them is 36° 52'. Find its area and the length of the diagonals. (b) Prove (1) sin 70° sin 10°-cos 140°. (2) cos-12/V5+tan-11/+tan-1 //4. (b) Use the formula in (a) to find the angles B and C of the triangle ABC given A=39° 27' 24", b=22.87, c=29.42 (Use logarithms throughout.) B. 3. Find the sum of n terms of the series, 4. Two wheels are to be geared so that one will make as nearly as possible 1900 revolutions while the other makes 2727 and neither wheel is to have more than 525 teeth. After 190 revolutions of the larger wheel, what part of a revolution is the smaller wheel out? 5. Given r-y-2y2+3y3+y*, assume y=ax+bx2+cx2+dx++ and compute the values of a, b, c and d. 6. Employ the binomial theorem to evaluate (1036) correct to two places of decimals, and verify your result by using logarithms. C. 7. The coordinates of the vertices of a triangle are (-4, 2), (-1, -6) and (8, 1). Plot the triangle and find (a) its area, (b) the coordinates of its centroid. 8. Find the equation of the line through the centre of the circle 2+y2+6x-8y+3=0, and perpendicular to the line -6y+3=0. 9. (a) What is the general equation of the conic sections? (b) What conic section is represented by each of the following equations: (1) 7x2+7y2-2y=4, (2) y2+2x=3y+2, (3) 3x2+6y2=8, (4) x2-9y2=10, (5) x2+4y2—3x+2y—8—0. (c) Graph any one of (2), (3) or (4). D. 10. (a) How many lines are determined by six planes, no three of which have a common line of intersection. (b) What is the relation between the face and dihedral angles of reciprocal corners? (c) Employ Euler's theorem to find the number of corners on a polyhedron composed of 8 rectangles and 16 triangles. (d) Write out the prismoidal formula. (e) How many pounds of sand are contained in a pail, level full, 12 in. high, diameter of top 10 in., diameter of bottom 8 in., if a cubic foot of sand weighs 100 lbs.? terms of its edges, prove that cos'a+cos2B+cos2y= 1 where a, ẞ and y are the angles the diagonal makes with its edges. 13. Find an expression for the volume of a truncated prism. |