Tiêu đề Copy of T980 - MATHEMATICS N6 QP APRIL 2016.pdf ✅

Copyright reserved Please turn over T980(E)(A6)T APRIL EXAMINATION NATIONAL CERTIFICATE MATHEMATICS N6 (16030186) 6 April 2016 (X-Paper) 09:00–12:00 Calculators may be used. This question paper consists of 5 pages and 1 formula sheet of 7 pages.
(16030186) -2- T980(E)(A6)T Copyright reserved Please turn over DEPARTMENT OF HIGHER EDUCATION AND TRAINING REPUBLIC OF SOUTH AFRICA NATIONAL CERTIFICATE MATHEMATICS N6 TIME: 3 HOURS MARKS: 100 INSTRUCTIONS AND INFORMATION 1. 2. 3. 4. 5. 6. 7. 8. Answer ALL the questions. Read ALL the questions carefully. Number the answers according to the numbering system used in this question paper. Questions may be answered in any order, but subsections of questions must be kept together. Show ALL the intermediate steps. ALL the formulae used must be written down. Questions must be answered in BLUE or BLACK ink. Write neatly and legibly.

(16030186) -4- T980(E)(A6)T Copyright reserved Please turn over QUESTION 4 4.1 Calculate the particular solution of: x x y x dx dy x sec 2sin 2sin  (sin 2 )  at (0;1) (5) 4.2 Calculate the particular solution of: 2 2 dx d y dx dy  7 + 6 y = 2x  3 , if 1 y  when x  0 and  2 dx dy when x  0 . (7) [12] QUESTION 5 5.1 5.1.1 Calculate the points of intersection of the two curves x y 3  and y  x  4  0. Make a neat sketch of the curves and show the area, in the first quadrant, bounded by the curves. Show the representative strip/element that you will use to calculate the volume (use the SHELL method only) generated if the area bounded by the curves rotates about the y -axis. (3) 5.1.2 Use the SHELL method to calculate the volume generated if the area, described in QUESTION 5.1.1, bounded by the two curves x y 3  and y  x  4  0, rotates about the y-axis. (5) 5.2 5.2.1 Make a neat sketch of the graph y  tan x . Show the representative strip/element that you will use to calculate the volume generated if the area bounded by the graph, the ordinates 0 y  and 3  x  rotates about the x-axis. (2) 5.2.2 Calculate the volume generated if the area, described in QUESTION 5.1.1, rotates about the x -axis. (3) 5.2.3 Calculate the volume moment about the y -axis as well as the distance of the centre of gravity from the y -axis. (6) 5.3 5.3.1 Calculate the points of intersection of the two curves y = 2 2x and 3 y x  . Make a neat sketch of the curves and show the area bounded by the curves. Show the representative strip/element, PERPENDICULAR to the x -axis, that you will use to calculate the area bounded by the curves. (3)