2016 DSE 数学延伸部分-M2 真题 答案 详解

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真题(英文)

2016-DSE MATH EP M2

HONG KONG EXAMINATIONS AND ASSESSMENT AUTHORITY HONG KONG DIPLOMA OF SECONDARY EDUCATION EXAMINATION 2016

MATHEMATICS Extended Part Module 2 (Algebra and Calculus) Question-Answer Book

8:30 am - 11:00 am (2½ hours)

This paper must be answered in English

INSTRUCTIONS

(1) After the announcement of the start of the examination, you should first write your Candidate Number in the space provided on Page 1 and stick barcode labels in the spaces provided 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 your answers in the spaces provided in this Question-Answer Book. Do not write in the margins. Answers written in the margins will not be marked.

(4) Graph paper and supplementary answer sheets will be supplied on request. Write your Candidate Number, mark the question number box and stick a barcode label on each sheet, and fasten them with string INSIDE this book.

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

(6) Unless otherwise specified, numerical answers must be exact.

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

2016-DSE-MATH-EP(M2)-1 28

• A032E001*

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真题(中文)

2016-DSE 數學 延伸部分 單元二

香港考試及評核局 2016年香港中學文憑考試

數學 延伸部分 單元二（代數與微積分） 試題答題薄

本試卷必須用中文作答 兩小時三十分鐘完卷 (上午八時三十分至上午十一時)

考生須知 (一) 宣布開考後，考生須首先在第1頁之適當位置填寫考生編號，並在第1、3、5、7、9及11頁之適當位置貼上電腦條碼。 (二) 本試卷分兩部，即甲部和乙部。 (三) 本試卷各題均須作答，答案須寫在本試題答題簿中预留的空位內。不可在各頁邊界以外位置書寫。寫於邊界以外的答案，將不予評閱。 (四) 如有需要，可要求派發方格紙及補充答题紙。每張紙均須填寫考生編號、填畫試題編號方格、貼上電腦條碼，並用繩綁於簿內。 (五) 除特別指明外，須詳細列出所有算式。 (六) 除特別指明外，數值答案須用真確值表示。 (七) 試場主任宣布停筆後，考生不會獲得額外時間貼上電腦條碼及填畫試題編號方格。

請在此貼上電腦條碼 考生編號

2016-DSE-MATH-EP(M2)-1 28

答案(中文)

評卷參考

單元二（代數與微積分）

本文件供閱卷員參考而設，並不應被視為標準答案。考生以及沒有參與評卷工作的教師在詳釋文件內容時應小心謹慎。

一般閱卷原則

1. 評卷時，閱卷員須跟循評卷參考的部分標準給分，這是十分重要的。很多時考生會運用評卷參考以外的方 法而得到正確答案，一來說，只要運用合理的方法而取得正確答案，該考生應可獲得該部分的所有分数（除題目特別指明特定方法外）。閱卷員應有耐性地評閱評卷參考以外的解題方法。

2. 在評卷參考中，分数會分為下列三類： 「M」分 使用正確方法的得分； 「A」分 正確答案的得分； 沒有「M」或「A」的分 正確地完成證題或推演得題目所給的答案的得分。 某些題目由數部分組成，而後部分的答案卻需依賴較前部分所得的結果。在此情况下， 若考生因為前部分錯誤的結果而導致後部分的答案錯誤，但卻能運用正確的方法去解题， 則方法正確的步驟可給「M」分，而相應的答案將沒有「A」分（除特别指明外）。

3. 為方便閱卷員評卷，評卷參考已盡量詳盡。當然，考生的答案多不會如評卷參考般清楚列 寫出來，諸如欠缺某幾個步驟或將步驟隱含於字裏行間。如遇到類似情況，閱卷員應運用他們的專業知識去判断是否給分。一來說，如考生的答案顯示他已運用相關的概念或技巧，則該部分應予給分。

4. 評卷時遇有不清楚的地方，應以考生的利益為依歸。

5. 評卷參考中，塗上除影的部分代表可省略的步骤，有外框的部分代表運用不同方法的答案。所有分数答案必须化简。

6. 除在题目中特别指明外，不以真確值表示的数值答案均不被接受。

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答案(英文)

Marking Scheme
Module 2 (Algebra and Calculus)

This document was prepared for markers’ reference. It should not be regarded as a set of model answers. Candidates and teachers who were not involved in the marking process are advised to interpret its contents with care.

General Marking Instructions

1. It is very important that all markers should adhere as closely as possible to the marking scheme. In many cases, however, candidates will have obtained a correct answer by an alternative method not specified in the marking scheme. In general, a correct answer merits all the marks allocated to that part, unless a particular method has been specified in the question. Markers should be patient in marking alternative solutions not specified in the marking scheme.
2. In the marking scheme, marks are classified into the following three categories:
3. 'M' marks awarded for correct methods being used;
4. 'A' marks awarded for the accuracy of the answers;
5. Marks without ‘M’ or ‘A’ awarded for correctly completing a proof or arriving at an answer given in a question. In a question consisting of several parts each depending on the previous parts, ‘M’ marks should be awarded to steps or methods correctly deduced from previous answers, even if these answers are erroneous. However, ‘A’ marks for the corresponding answers should NOT be awarded (unless otherwise specified).
6. For the convenience of markers, the marking scheme was written as detailed as possible. However, it is still likely that candidates would not present their solution in the same explicit manner, e.g., some steps would either be omitted or stated implicitly. In such cases, markers should exercise their discretion in marking candidates’ work. In general, marks for a certain step should be awarded if candidates’ solution indicated that the relevant concept/technique had been used.
7. In marking candidates’ work, the benefit of doubt should be given in the candidates’ favour.
8. In the marking scheme, ‘r.t.’ stands for ‘accepting answers which can be rounded off to’ and ‘f.t.’ stands for ‘follow through’. Steps which can be skipped are shaded whereas alternative answers are enclosed with rectangles. All fractional answers must be simplified.
9. Unless otherwise specified in the question, numerical answers not given in exact values should not be accepted.

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