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2014

This document is an examination paper for Advanced Programme Mathematics, dated November 3, 2014, consisting of various mathematical problems across multiple topics including algebra, calculus, and trigonometry. It includes instructions for the exam, a total of 10 questions, and an information sheet with general formulae. The exam is designed to assess students' understanding and application of advanced mathematical concepts.

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24 views26 pages

2014

This document is an examination paper for Advanced Programme Mathematics, dated November 3, 2014, consisting of various mathematical problems across multiple topics including algebra, calculus, and trigonometry. It includes instructions for the exam, a total of 10 questions, and an information sheet with general formulae. The exam is designed to assess students' understanding and application of advanced mathematical concepts.

Uploaded by

chive.tablas.1k
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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CORNWALL HILL COLLEGE DEPARTMENT OF MATHEMATICS, Advanced Programme Mathematics 1 Time: 2,5 Hours Date: 3 November 2014 Marks: 200 Examiner: Mrs M van Niekerk Moderato! Mrs S Hickling, Mr P van Schalkwyk INSTRUCTIONS: 1. The question paper consists of 10 pages. The Information Sheet (formulae) is on page 9 and 10. Please check that your paper is complete. 2. Answer all the questions. 3. Read the questions carefully. 4. _ Itis in your own interest to write legibly and to present your work neatly. 5. All the necessary working details must be clearly shown. 6. Approved calculators may be used except where otherwise stated. 7. Where necessary write correct to two decimal places, unless otherwise stated. 8. GOOD LUCK! ADVANCED PROGRAMME MATHEMATICS GRADE 12, 3 November 2014 PAGE 2.0F 10 QUESTION 1 a) Solve for x: (1) eS +x=5 (4) (2) 3*243-*-4=0 (8) (3) 6) (4) 3x45) =1 (4) : Sxt7 6) Resolve into partial fractions: 5 > (7) ©) _Iftwo electrical resistors with resistances R, and Rp are connected in parallel (see the diagram), then the total resistance is given by: R Wes Rp (1) Simplify the expression for R. (3) (2) If the total resistance is 2 ohms and R, has a resistance of 10 ohms, determine the resistance of Ry. (6) [38] ADVANCED PROGRAMIME MATHEMATICS GRADE 11 3 November 2014 PAGE 3 OF 10 QUESTION 2 a) Given f(x) = x* + kx? + px — 8 with roots ¥2 and —2i. Determine the value of k and ” b) Find a polynomial g(x) of degree 3 with a constant value of 10 and zeros and3—i. (8) (15) QUESTION 3 a) Sketch the functions of f(x) = 7x —4 and g(x) = | 4 — 4], clearly indicating all the cuts with the axes, points of intersection and any asymptotes. (8) b) Hence, determine f(x) > g(x) (2) [29] ‘QUESTION 4 a) Determine the value of the following limits, if they exist, () (5) (2) (3) (@) (3) (4) (5) b) Write y +q (5) (24) ADVANCED PROGRAMME MATHEMATICS GRADE 11 3 November 2014 PAGE 4 OF 10 QUESTION 5 a) Wf f(x) = x? —4x +3 and g(x) = —5x — 2, determine: M feg (3) (2) gf@)) (3) 8) gegeg (4) (4) g*@) (2) b) The sketch is of the function ie x-3| for x>I ‘x)= Ux for x5 5 Determine the values of a, b,c, d,e, f,g, and h. (8) af{i-x* ixs0 4) ter = (357, jx>0 (1) Sketch p(x) (a) (2) State the x — value(s) for which p'(x) > 0. a (3) State the x — value(s) for which p'(x) = 0. ( 124) [ADVANCED PROGRAMME MATHEMATICS GRADE 12, 3 November 2014 PAGE 6 OF 10 QUESTION 7 Use a Riemann Sum to determine the area between the curve f(x) = 4x? + 1 and the x — axis if 0 Bs we @ Question = a) (eH 2c AM x+22)(x-22) = (- 2) (x*-4d*) or = (YOM) & Se Ie taext-zy > — = * tent -3 We 2% =o” x oe bE) 3K) =-@x ~) (0-3), = é) -(2x-1) r= 6X49 +1 3a ) 2X3 = 1ext + 26x -%* + 6K -y0) 3 -Qx° -13x% +26x ~j9 =-2)\3 ee aye guts atte ! hin 1s @) a) Question 3 a) 6 b) xe I @ xe (@x-3) = 4 arr +oxt9 a 1252 3 FB aa et = ax +9+9 = ao ma Ca a be PEt) x70 = GC ee @) : 5 x 3) xe = are yet i 2 ta x x = le ee x> = Kata iis tee eae - @) 4) Lu Sih 7X ro Gx Le, * yee —}-— 6 Berne ~*~ T iO Su0 = et 7

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