امتحان شهادة دبلوم التعليم العام للمدارس الخاصة )ثنائية اللغة( الدور األول - الفصل الدرايس األول
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1 رقم الورقة رقم املغلف تنبيه: الرياضيات. األسئلة يف ( 16 ) صفحات. امتحان شهادة دبلوم التعليم العام للمدارس الخاصة )ثنائية اللغة( للعام الدرايس 144/14 ه / م الدور األول - الفصل الدرايس األول تعليامت وضوابط التقدم للامتحان: الحضور إلى اللجنة قبل عشر دقاي ق من بدء الامتحان للا همية. إبراز البطاقة الشخصية لمراقب اللجنة. مينع كتابة رقم الجلوس أو الاسم أو أي بيانات أخرى تدل على شخصية الممتحن في دفتر الامتحان وإلا ألغي امتحانه. يحظر على الممتحنني أن يصطحبوا معهم مبركز الامتحان كتبا دراسية أو كراسات أو مذكرات أو هواتف محمولة أو أجهزة النداء الا لي أو أي شيء له علاقة بالامتحان كام لا يجوز إدخال آلات حادة أو أسلحة من أي نوع كانت أو حقاي ب يدوية أو آلات حاسبة ذات صفة تخزينية. يجب أن يتقيد المتقدمون بالزي الرسمي (الدشداشة البيضاء والمصر أو الكمة للطلاب والدارسني والزي المدرسي للطالبات واللباس العامين للدارسات ( ومينع النقاب داخل المركز ولجان الامتحان. لا يسمح للمتقدم المتا خر عن موعد بداية الامتحان بالدخول إلا إذا كان التا خري بعذر قاهر يقبله ري يس المركز وفي حدود عشر دقاي ق فقط. يتم الالتزام بالا جراءات الواردة في دليل الطالب لا داء امتحان شهادة دبلوم التعليم العام. يقوم المتقدم بالا جابة عن أسي لة الامتحان المقالية بقلم الحبر (الا زرق أو الا سود). يقوم المتقدم بالا جابة عن أسي لة الاختيار من متعدد بتظليل الشكل ) ( وفق النموذج الا يت: عاصمة سلطنة عمان هي: س الدوحة القاهرة أبوظبي مسقط ملاحظة: يتم تظليل الشكل ) ( باستخدام القلم الرصاص وعند الخطا امسح بعناية لا جراء التغيري. صحيح غري صحيح زمن اإلجابة: ثالث ساعات. اإلجابة يف الورقة نفسها.
2 Question One There are 14 multiple choice items worth two marks each. Shade the correct answer for each of the following items. 1. lim h"0 ƒ (2) ƒ ( 2) ƒ( 2) ƒ( 2+h) h = ƒ (2) ƒ ( 2) (28 marks) 2. If y = a x 2 +5 and d2 y = 6 at x = 1, then a= dx The coordinates of the stationary point of the curve y = 2x x 2 is: (1, 2) (0, 0) (1, 1) (2, 0) 4. If 6x (x 1)(x + 2) = A (x 1) + B (x + 2), then the value of 2A B is:
3 5. Which of trigonometric functions are both odd? cosθ, cosecθ secθ, cotθ 6. If cotθ = 4 and θ is reflex, then secθ= cosecθ, cotθ cosθ, secθ If cot(θ 0 ) = 1, 0 < θ < 90, then θ= If t = cosθ, then t = cos2θ cos θ cos2θ 1 2 cos θ 2 9. (π 2 ) dt = π t πt + c π π + c π 2 t t + c π π + c 2
4 10. x 8 dx = x 2 x + x 2 + 4x + c x x 2 + 4x + c x + 2x 2 + 4x + c x 2x 2 + 4x + c 11. Consider the sketch, b If A 1,A 2 are two areas, then f (x)dx = a a A 1 =6.7 y A 2 =1. b x f(x)
5 12. Consider the sketch. It's symmetric around y-axis. If the sum of ordinates's values ( y 1, y 2,..., y n-1 ) is 5 and f(x)dx=, then the width of each interval for the shaded area is: y f(x) (,4) x 1. If E 1 and E 2 are two mutually exclusive events, P(E 1 ) = 0.05, P(E 2 ')= 0.07, then P(E 1 E 2 ) = On an experiment of throwing a fair die (has each face number 1 to 6) and tossing a coin, the results were recorded on each of them. If A is "the event of observing tail", B is "the event of observing ", then P(A B) =
6 Extended Questions Write your answer for each of the three questions in the constructed response section in the space provided. Be sure to show all your work and correct units where applicable. Question Two: [14 marks] a) i. If 5x+7 (x 5)(x 2 + 7) = A(x2 +7) + Bx(x 5) + c (x 5) (x 5)(x 2 + 7), find A. ( marks) 5
7 ii. Express x + 4x 2 (x + 1)(x + ) in partial fractions (marks) 6
8 b) Find the equation of the tangent to y = x 2 + x at x = 1 (marks) 7
9 c) Without using a calculator: Find the value of sin120 + tan75 (5marks) 8
10 Question Three: [14 marks] 1 4 a) i. If f(x) = x, find f "(x) (2 marks) ii. Given that y = 2x + x has gradient equal 7 at the point (a, b), find possible values for a and b. (2 marks) 9
11 b) i. Find the range of values of x for which y is decreasing, given that y = 4 x 16x + 9. ( marks) 10
12 ii. A container in the shape of a right circular cylinder with no top. It has surface area π square metres. What height (h) and base radius (r) which makes the volume of the container as maximum as possible? ( marks). 11
13 c) i. Find ( y 5 8 )dy (2 marks) ii. Find the equation of the curve which its gradient is given by x 2 2x and f(2) = 7 (2 marks) 12
14 Question Four: [14 marks] a) i. Find the value of R and tan α in this identity: 4sin θ + 2cos θ= R cos (θ α) ( marks) ii. Prove the identity 2cot 2 (90 θ) sec 2 θ 2 + 2cosec 2 θ = ± 2 tan 2 θ. ( marks) 1
15 b) i. If f(6) = 1 and f(9) = 17, find 9 6 f ' (x) dx (2 marks) 14
16 ii. Consider the sketch. Find the shaded area. (2 marks) f 1 (x) = x 2 8 y x ( 2, 4) (2, 4) f 2 (x) = x 2 15
17 c) If A and B are defined in the sample space, P(A B) = 4, P(A) = 2 find: and P(A B) = 1 4, i. P(A'). (1 mark) ii. P(A B). ( marks) [ End of Examination ] 16
18 Diploma, Semester First First Session, Bilingual Private Schools, Mathematics 2012/201 17
19 18
20 م س و د ة ال يتم تصحيحها 19
س الدوحة القاهرة أبوظبي
رقم الورقة رقم المغلف تنبيه: المادة: رياضيات. الا سي لة في ) ١٤ ( صفحة. امتحان دبلوم التعليم العام للمدارس الخاصة (ثناي ية اللغة) للعام الدراسي ١٤٣٥/١٤٣٤ ه - ٢٠١٣ ٢٠١٤ / م الدور الثاين - الفصل الدراسي
More informationامتحان شهادة دبلوم التعليم العام - المدارس الخاصة - ثناي ية اللغة للعام الدراسي ١٤٣٣/١٤٣٢ ه - ٢٠١١ ٢٠١٢ / م الدور الا ول - الفصل الدراسي الا ول
رقم الورقة رقم المغلف تنبيه: المادة: الرياضيات - ثناي ية اللغة. الا سي لة في ) ١٤ ( صفحة. امتحان شهادة دبلوم التعليم العام - المدارس الخاصة - ثناي ية اللغة للعام الدراسي ١٤٣٣/١٤٣٢ ه - ٢٠١١ ٢٠١٢ / م الدور
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