2024 DSE 数学-Mathematics 真题 答案 详解

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答案(中文)

试卷一

解	分	附注
1. (\frac{2}{4h-7} - \frac{3}{6h-5})
=(\frac{2(6h-5)-3(4h-7)}{(4h-7)(6h-5)})
=(\frac{12h-10-12h+21}{(4h-7)(6h-5)})
=(\frac{11}{(4h-7)(6h-5)})	1M	或等价
	1M
	1A	(3)
2. (\frac{Ax+C}{B}=3x)
(Ax+C=3Bx)
(Ax-3Bx=-C)
(x=\frac{C}{3B-A})	1M	给将 x 放在一邊
	1M	或等價
	1A

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:
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.
6. 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).
7. 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.
8. In marking candidates' work, the benefit of doubt should be given in the candidates' favour.
9. 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.

Paper 1

Solution	Marks	Remarks
1. (\frac{2}{4h-7} - \frac{3}{6h-5})
= (\frac{2(6h-5)-3(4h-7)}{(4h-7)(6h-5)})
= (\frac{12h-10-12h+21}{(4h-7)(6h-5)})
= (\frac{11}{(4h-7)(6h-5)})	IM	or equivalent
2. (\frac{Ax+C}{B}=3x)
(Ax+C=3Bx)
(Ax-3Bx=-C)
(x=\frac{C}{3B-A})	1M	for putting (x) on one side
	1M	or equivalent
3. (\frac{Ax+C}{B}=3x)
(\frac{Ax}{B}+\frac{C}{B}=3x)
(Ax-3x=\frac{-C}{B})
(x=\frac{C}{3B-A})	1M	for putting (x) on one side
	1M	or equivalent
4. (a) (6r^2-13rs-28s^2=(2r-7s)(3r+4s))	1A	or equivalent
(b) (4r-14s+6r^2-13rs-28s^2=4r-14s+(2r-7s)(3r+4s)=2(2r-7s)+(2r-7s)(3r+4s)=(2r-7s)(2+3r+4s))	1M	for using the result of (a)
	1A	or equivalent
5. (a) (\frac{5x+7}{4}-1<2x)
(5x+7-4<8x)
(-3x<-3)
(x>1)
(3x+9\geq0)
(x\geq-3)
Thus, the required range is (x>1) .	1M	for putting (x) on one side
	1A
(b) 2	1A

真题 Paper 1(中文)

真题 Paper 2(中文)

2024-DSE 數學 必修部分 卷二

香港考試及評核局 2024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·考生須首先於邊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·考生須檢查试题有否缺漏·最後一題之後應有「試卷完」字樣。

（三）本試卷各題估分相等。

（四）本试卷全部试题均须回答·为便於修正答案·考生宜用HB鉛筆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·考生須清楚填寫答案·否则會因答案未能被辨認而失分。

（五）每题只可填一个答案·若填多個答案·則該題不给分。

（六）答案錯誤·不另扣分。

2024-DSE-MATH-CP 2-1

真题 Paper 1(英文)

2024-DSE MATH CP PAPER 1

HONG KONG EXAMINATIONS AND ASSESSMENT AUTHORITY HONG KONG DIPLOMA OF SECONDARY EDUCATION EXAMINATION 2024

MATHEMATICS Compulsory Part PAPER 1 Question-Answer Book

8:30 am – 10:45 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 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.

2024-DSE-MATH-CP 1–1

真题 Paper 2(英文)

2024-DSE MATH CP PAPER 2 HONG KONG EXAMINATIONS AND ASSESSMENT AUTHORITY HONG KONG DIPLOMA OF SECONDARY EDUCATION EXAMINATION 2024 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.

2024-DSE-MATH-CP 2-1 1