2021 DSE 数学-Mathematics 真题 答案 详解

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答案(中文)

试卷一

解	分	備註
1. $(a\beta^3)(\alpha^{-2}\beta^4)^5$
$(a\beta^3)(\alpha^{-10}\beta^{20})$
$\frac{\beta^{23}}{\alpha^9}$
1M	给 $(a^h)^k = a^{hk}$ 或 $(ab)' = d'b'$
1M	给 $c^pc^q = c^{p+q}$ 或 $d^rd' = \frac{1}{d'^r}$
1A	——(3)

1. $\frac{4-3a}{b} = 5$
   $4 - 3a = 5b$
   $3a = 5b$
   $a = \frac{4-5b}{3}$
   | 1M | 或等价 | | 1M | 或等价 | | 1A | ——(3) |

$\frac{4-3a}{b} = 5$
$4 - 3a = 5b$
$b$
$b$
$3a = b$
$5 - b$
$a = \frac{-b}{3}(\frac{5-b}{b})$
$a = \frac{4}{3} - \frac{5b}{3}$
| 1M + 1M | 或等价 | | 1A | ——(3) |

1. (a) $6x^2 + xy - 2y^2$
   $= (2x-y)(3x+2y)$
   (b) $8x - 4y - 6x^2 - xy + 2y^2$
   $= 4(2x-y) - (2x-y)(3x+2y)$
   $= (2x-y)(4-3x-2y)$
   | 1A | 或等价 | | 1M | 给利用(a)的结果 | | 1A | 或等价 | | ——(3) |

2. (a) $\frac{7(x-2)}{5} + 11 > 3(x-1)$
   $7x - 14 > 15x - 70$
   $-8x > -56$
   $x < 7$
   $x + 4 \geq 0$
   $x \geq -4$
   因此，所求的范围為 $-4 \leq x < 7$
   (b) 6
   | 1M | 给将 x 放在一邊 | | 1A | ——(3) | | 1A | ——(4) |

答案(英文)

香港考試及評核局
HONG KONG EXAMINATIONS AND ASSESSMENT AUTHORITY
2021年香港中學文憑考試
HONG KONG DIPLOMA OF SECONDARY EDUCATION EXAMINATION 2021

數學 必修部分 試卷一
MATHEMATICS COMPULSORY PART PAPER 1

評卷參考
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2021-DSE-MATH-CP 1-1

真题 Paper 1(中文)

2021-DSE 數學 必修部分 卷一

香港考試及評核局

2021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。

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Hong Kong Examinations and Assessment Authority

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2021-DSE-MATH-CP 1-1

請在此貼上電腦條碼

考生編號

• A030C001 *

真题 Paper 2(中文)

2021-DSE 數學 必修部分 卷二

香港考試及評核局 2021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，最後一题之后應有「試卷完」字樣。

(三)本试卷各题占分相等。

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

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2021-DSE-MATH-CP 2-1

考试结束前不可将试卷带离考场

真题 Paper 1(英文)

2021-DSE MATH CP PAPER 1

HONG KONG EXAMINATIONS AND ASSESSMENT AUTHORITY HONG KONG DIPLOMA OF SECONDARY EDUCATION EXAMINATION 2021

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 2021

2021-DSE-MATH-CP 1-1

Please stick the barcode label here.

Candidate Number

A O 3 0 E 0 0 1

真题 Paper 2(英文)

2021-DSE MATH CP PAPER 2 HONG KONG EXAMINATIONS AND ASSESSMENT AUTHORITY HONG KONG DIPLOMA OF SECONDARY EDUCATION EXAMINATION 2021 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 2021 Not to be taken away before the end of the examination session 2021-DSE-MATH-CP 2-1