2019 DSE 数学-Mathematics 真题 答案 详解

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答案(中文)

評卷參考

本文件供閱卷員参考而設，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釆釋文件內容時應小心謹慎。

一般閱卷原则

1. 評卷時，閱卷員須跟隨評卷參考的评分標準給分，這是十分重要的。很多時考生會運用評卷參考以外的方怯而得到正確答案，一般來說，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（除題目特别指明特定方法外）。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，分数會分为下列三類： 「M」分 使用正确方法的得分； 「A」分 正确答案的得分； 没有「M」或「A」的分 正确地完成题目或推演题目所给的答案的得分。 某些题目由数部分组成，而较後部分的答案却需依赖前部分所得的结果。在这种情况下，若考生因為前部分錯誤的结果而导致後部分的答案错误，但卻能運用正确的方法去解题，则方法正确的步骤可给「M」分，而相應的答案將沒有「A」分（除特别指明外）。

3. 為方便阅卷员评卷，评卷参考已尽量详尽。当然，考生的答案多不会如评卷参考般清楚列出来，诸如欠缺某個步驟或将步骤隐含於字裏行間。如遇到類似情况，阅卷员應運用他們的专业知識去判断是否给分。一般來說，如考生的答案顯示他已運用相關的概念或技巧，則该部分应予给分。

4. 评卷時遇有不清楚的地方，應以考生的利益為依歸。

5. 评卷参考中，密密麻麻的部分代表可省略的步骤，有外框的部分代表运用不同方法的答案。所有分数答案必须化简。

答案(英文)

Marking Scheme

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:

   • 'M' marks awarded for correct methods being used;
   • 'A' marks awarded for the accuracy of the answers;
   • 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).

3. 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.

4. In marking candidates’ work, the benefit of doubt should be given in the candidates’ favour.

5. 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 whereas alternative answers are enclosed with [rectangles]. All fractional answers must be simplified.

43

真题 Paper 1(中文)

2019-DSE 數學 必修部分 卷一

香港考試及評核局 2019年香港中學文憑考試

數學 必修部分 試卷一 試題答題簿

本試卷必須用中文作答 兩小時十五分鐘完卷 (上午八時三十分至上午十時四十五分)

考生须知 (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) 本試卷分三部，即甲部(1)、甲部(2)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預留的空位內。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) 如有必要，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，並用纏綁於薄內。 (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，或準確至三位有效數字的近似值表示。 (七) 本試卷的附圖不一定依比例繪成。 (八) 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

2019-DSE-MATH-CP 1-1 4 * A030C001 *

真题 Paper 2(中文)

2019-DSE數學必修部分卷二

香港考試及評核局 2019年香港中學文憑考試

數學 必修部分 試卷二

一小時十五分鐘完卷 (上午十一時三十分至下午十二時四十五分)

考生須知 (一)細讀答题紙上的指示。宣布開考後，考生须首先於適當位置貼上電腦條碼及填上各项所需资料。宣布停筆後，考生不會獲得額外時間貼上電腦條碼。

(二)試場主任宣布開卷後，考生须检查试题有否缺漏，最后一题之后愿有「试卷完」字樣。

(三)本试卷各题估分相等。

(四)本试卷全部试题均须回答。為便於修正答案，考生宜用 HB 铅笔把答案填在答题纸上。錯誤答案可用潔淨膠擦將筆痕徹底擦去。考生须清楚填答答案，否则會因答案未能被辨認而失分。

(五)每题只可填一个答案，若填多个答案，則该题不给分。

(六)答案错误，不另扣分。

考试结束前不可将试卷带离考场

2019-DSE-MATH-CP 2-1

28

真题 Paper 1(英文)

2019-DSE MATH CP PAPER 1

HONG KONG EXAMINATIONS AND ASSESSMENT AUTHORITY HONG KONG DIPLOMA OF SECONDARY EDUCATION EXAMINATION 2019

MATHEMATICS Compulsory Part PAPER 1 Question-Answer Book 8:30 am - 10:45 am (2¼ 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 THREE sections, A(1), A(2) 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 should be either exact or correct to 3 significant figures.

(7) The diagrams in this paper are not necessarily drawn to scale.

(8) 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.

© Hong Kong Examinations and Assessment Authority All Rights Reserved 2019

2019-DSE-MATH-CP 1-1

• A O 3 O E O O 1 *

真题 Paper 2(英文)

2019-DSE MATH CP PAPER 2 HONG KONG EXAMINATIONS AND ASSESSMENT AUTHORITY HONG KONG DIPLOMA OF SECONDARY EDUCATION EXAMINATION 2019 MATHEMATICS Compulsory Part PAPER 2 11:30 am - 12:45 pm (1¼ hours)

INSTRUCTIONS 1. Read carefully the instructions on the Answer Sheet. After the announcement of the start of the examination, you should first stick a barcode label and insert the information required in the spaces provided. No extra time will be given for sticking on the barcode label after the 'Time is up' announcement. 2. When told to open this book, you should check that all the questions are there. Look for the words ‘END OF PAPER’ after the last question. 3. All questions carry equal marks. 4. ANSWER ALL QUESTIONS. You are advised to use an HB pencil to mark all the answers on the Answer Sheet, so that wrong marks can be completely erased with a clean rubber. You must mark the answers clearly; otherwise you will lose marks if the answers cannot be captured. 5. You should mark only ONE answer for each question. If you mark more than one answer, you will receive NO MARKS for that question. 6. No marks will be deducted for wrong answers.

香港考試及評核局保留版權 Hong Kong Examinations and Assessment Authority All Rights Reserved 2019 2019-DSE-MATH-CP 2-1 Not to be taken away before the end of the examination session