2015 DSE 数学-Mathematics 真题 答案 详解

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答案(中文)

Paper 1

Solution | Marks | Remarks |---|---|--- 1. (\frac{m^9}{(m^3 n^{-7})^5} = \frac{m^9}{m^{15} n^{-35}} = \frac{n^{35}}{m^{15-9}} = \frac{n^{35}}{m^6}) | 1M 1M 1A | for ((a^h)^k = a^{hk}) or ((ab)^e = a^l b^\ell) for (\frac{c^p}{c^q} = c^{p-q}) or (a^{-r} = \frac{1}{d^r}) 2. (\frac{4a + 5b - 7}{b} = 8) (4a + 5b - 7 = 8b) (4a - 7 = 8b - 5b) (4a - 7 = 3b) (b = \frac{4a - 7}{3}) | 1M 1M 1A | for putting (b) on one side or equivalent 3. The required probability (\frac{1+2+3}{(4)(5)} = \frac{6}{20} = \frac{3}{10}) | 1M+1M 1A | 0.3

答案(英文)

Solution Marks Remarks

1. (\frac{m^9}{(m^3n^{-7})^5} = \frac{m^9}{m^{15}n^{-35}} = \frac{n^{35}}{m^{15}m^{-9}} = \frac{n^{35}}{m^6}). 1M for ((a^pb^q)^r=a^{pr}b^{qr})
   1M for (a^{-p}=\frac{1}{a^p})
   1A
   ……(3)

2. (\frac{4a+5b-7}{b}=8)
   (4a+5b-7=8b)
   (-3b=7-4a)
   (b=\frac{4a-7}{3}).
   1M for putting (b) on one side or equivalent
   1M
   1A
   ……(3)

3. The required probability (\frac{3+2+1}{4\times5}=\frac{3}{10}). 1M + 1M for the nominator 1M for the denominator
   1A or 0.3
   ……(3)

4.(a) (x^3+x^2y-7x^2=x^2(x+y-7)).
1A

4.(b) (x^3+x^2y-7x^2-x-y+7=x^2(x+y-7)-x-y+7=(x+y-7)[x^2-(x+y-7)]=(x-1)(x+1)(x+y-7)).
1M for using (a)
1M for factorization or equivalent
1A
……(4)

5.(a) (\frac{7-3x}{5}\leq2(x+2), 7-3x\leq10x+20, x\geq-1, 4x-13>0, x>\frac{13}{4}). Thus, the required solution is (x>\frac{13}{4}).
1A
1A
1A
……(4)

5.(b) 4
1A

6.(a) Let $x$ be the selling price of the book. (\frac{x-250}{250}=20\%), (x=300). Thus, the selling price of the book is $300. 1M for percentage profit
1A u-1 for missing unit

真题 Paper 1(中文)

2015-DSE 數學 必修部分 卷一

香港考試及評核局 2015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)

考生須知 1. 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。 2. 本試卷分三部份，即甲部(1)、甲部(2)和乙部。 3. 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。 4. 如有需要，可要求派發方格紙及補充答题纸。每張紙均須填寫考生編號、填寫試題编號方格、貼上電腦條碼，並用繩縛於簿內。 5. 除特别指明外，须詳細列出所有算式。 6. 除特别指明外，數值答案須用真確值，或準確至三位有效数字的近似值表示。 7. 本试卷的附圖不一定依比例繪成。 8. 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寫試題编號方格。

請在此貼上電腦條碼 考生编號

2015-DSE-MATH-CP 1-1 4 A030C001

真题 Paper 2(中文)

2015-DSE 數學 必修部分 卷二 MC

香港考試及評核局 2015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，考生須首先於適當位置貼上電腦條碼及填上各項所需資料。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，考生須檢查試題有否缺漏，最後一題之後應有「試卷完」字樣。

(三) 本試卷各題估分相等。

(四) 本試卷全部試題均須回答。為便於修正答案，考生宜用 HB 鉛筆把答案填在答題紙上。錯誤答案可用潔淨膠擦將筆痕徹底擦去。考生須清楚填寫答案，否則會因答案未能被辨認而失分。

(五) 每題只可填一個答案，若填多個答案，則該題不給分。

(六) 答案錯誤，不另扣分。

考試結束前不可將試卷攜離試場

2015-DSE-MATH-CP 2-1

28

真题 Paper 1(英文)

2015-DSE MATH CP PAPER 1

HONG KONG EXAMINATIONS AND ASSESSMENT AUTHORITY HONG KONG DIPLOMA OF SECONDARY EDUCATION EXAMINATION 2015

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 2015

2015-DSE-MATH-CP 1-1

• A O 3 O E O O 1 *

真题 Paper 2(英文)

2015-DSE MATH CP PAPER 2 MC HONG KONG EXAMINATIONS AND ASSESSMENT AUTHORITY HONG KONG DIPLOMA OF SECONDARY EDUCATION EXAMINATION 2015 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 2015 Not to be taken away before the end of the examination session 2015-DSE-MATH-CP 2-1 1