mathematics extended part 2 (algebra calculus ......mathematics extended part 2 (algebra calculus)...

2016-DSE MATH EP M2

HONG KONG EXAMINATIONS AND ASSESSMENT AUTHORITY

HONG KONG DIPLOMA OF SECONDARY EDUCATION EXAIVIIN.I\TION 2016

MATHEMATICS Extended Part

Module 2 (Algebra and Calculus)

Question-Answer Book

8.30 am - 11. 00 am (2½hours)

This paper must be answered in English

INSTRUCTIONS

(1) After the announcement of the start of theexammat,on, you should first write yourCandidate Number in the space provided on and stick barcode labels in the spacesprovided on Pages 1, 3, 5, 7, 9 and 11.

(2) This paper consists of TWO sections, A and B.

(3) Attempt ALL questions in this paper. Write youranswers in the spaces provided in this QuestionAnswer Book. Do not write in the margins.Answers written in the margins will not bemarked.

(4) Graph paper and supplementary answer sheetswill be supplied on request. Write yourCandidate Number, mark the question numberbox and stick a barcode label on each sheet,and fasten them with string INSIDE this book.

(5) Unless otherwise specified, all working must beclearly shown.

(6) Unless otherwise specified, numerical answersmust be exact.

(7) No extra time will be given to candidates forsticking on the barcode labels or filling in thequestion number boxes after the'Time is up'announcement.

2016心SE-MATH-EP(M2)-J 28

Please stick the barcode label here.

三

更多試卷歡迎瀏覽 http://dsepp.com

FORMULAS FOR REFERENCE

sin(A士B)= sin A cos B土cosAsinB

cos(A士B) = cos A cos B干sinA sin B

tan(A土B)= tan A士tanB1千tanAtanB

2sin A cos B = sin(A+B)+sin(A-B)

2cos AcosB = cos(A+ B)+cos(A-B)

2sin A sin B = cos(A-B)-cos(A+ B)

A+B A-Bsin A + sin B = 2 sin cos

2 2 A+B A-B

sin A -sin B = 2 cos sin2 2

A+B A-Bcos A+ cos B = 2 cos cos

2 2 A+B A-B

cosA-cosB=-2sin sin 2 2

*******************************************************************•�************************

SECTION A (50 marks)

1

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20 I 6-DSE-MATH-EP(M2}-2 29 更多試卷歡迎瀏覽 http://dsepp.com

3. Consider the curve C: y = 2ex , where x > 0 . It is given that P is a point lying on C . Thehorizontal line which passes through P cuts the y-axis at the point Q . Let O be the origin. Denotethe x-coordinate of P by u .

(a) Express the area of AOPQ in terms of u.

(b) If P moves along C such that OQ increases at a constant rate of 6 units per second, fmd therate of change of the area of AOPQ when u = 4 .

(5 marks)

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2016-DSE-MATH-EP(M2)--4 31


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6. (a) Prove that x + 1 is a factor of 4x3 + 2x2一 3x 一 I .

(b)

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3冗 1-Using the results of(a) and (b), prove that cos 一～＝一一一－．✓5

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(b) Evaluate

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mathematics extended part 2 (algebra calculus ......mathematics extended part 2 (algebra calculus)...

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