Tiêu đề Copy of T900 - MATHEMATICS N6 QP NOV 2016.pdf ✅

(16030186) -2- T900(E)(N24)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. Use only BLUE or BLACK ink. Write neatly and legibly.
(16030186) -3- T900(E)(N24)T Copyright reserved Please turn over QUESTION 1 1.1 If z = ) tan( ) cosec( 3 2 2 x y  xy calculate the following: 1.1.1 x z   (2) 1.1.2 y z   (1) 1.2 The parametric equations of a function are given as 2 x  t and 5 y  2t . Calculate the value of 2 2 dx d y (3) [6] QUESTION 2 Determine  y dx if: 2.1 y = arcsin 3x (2) 2.2 y = sec 2x 2 4 (4) 2.3 y = 4 12 24 1 2 x  x  (4) 2.4 y = cosec 4x.cos 4x 5 3 (4) 2.5 y = x .sin 2x 3 (4) [18] QUESTION 3 Use partial fractions to calculate the following integrals: 3.1      (2 1) ( 1) 3 3 1 2 2 x x x x dx (6) 3.2     x x x x 3 4 2 2 dx (6) [12]
(16030186) -4- T900(E)(N24)T Copyright reserved Please turn over QUESTION 4 4.1 Calculate the particular solution of 2 1 2  y  t  t  dt dy t , if t  1 when 2 1 y   . (5) 4.2 Calculate the particular solution of 2 2 dx d y dx dy  2 + 2 y = 2 6 x e , if 1 y  when x  0 and  1 dx dy when x  0 . (7) [12] QUESTION 5 5.1 5.1.1 Make a neat sketch of the graph y  2ln x . Show the representative strip/element that you will use to calculate the volume generated if the area bounded by the graph, the line y  2 , the x -axis and the y-axis rotates about the x-axis. (2) 5.1.2 Calculate the volume generated if the area described in QUESTION 5.1.1 rotates about the x -axis. (5) 5.2 5.2.1 Calculate the points of intersection of the two curves y = x  6 and xy  8 . Make a neat sketch of the two curves and show the area bounded by the curves in the second quadrant. Show the representative strip/element PARALLEL to the x-axis that you will use to calculate the area bounded by the curves. (3) 5.2.2 Calculate the area bounded by the two curves in the second quadrant described in QUESTION 5.2.1. (3) 5.2.3 Calculate the second moment of area when the area bounded by the two curves in the second quadrant described in QUESTION 5.2.1 is rotated about the x-axis. (4) 5.2.4 Express the answer in QUESTION 5.2.3 in terms of the area. (1) 5.3 5.3.1 Make a neat sketch of the graph 36 9 4 2 2 x  y  and show the representative strip/element PERPENDICULAR to the x-axis that you will use to calculate the volume of the solid generated when the area bounded by the curve for 0  x  2 rotates about the x-axis. (2) 5.3.2 Calculate the volume described in QUESTION 5.3.1. (3) 5.3.3 Calculate the moment of inertia of the solid obtained when the area described in QUESTION 5.3.1 rotates about the x-axis. (5)