2023 DSE 数学延伸部分-M1 真题 答案 详解

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真题(英文)

2023-DSE MATH EP M1
HONG KONG EXAMINATIONS AND ASSESSMENT AUTHORITY
HONG KONG DIPLOMA OF SECONDARY EDUCATION EXAMINATION 2023

MATHEMATICS Extended Part
Module 1 (Calculus and Statistics)
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 should be either exact or given to 4 decimal places.
(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.

© Hong Kong Examinations and Assessment Authority All Rights Reserved 2023
2023-DSE-MATH-EP(M1)-1
1
* A O 3 1 E 0 0 1 *

真题(中文)

香港考試及評核局 2023年香港中學文憑考試 數學延伸部分 單元一（微積分與統計） 試題答題簿

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) 本試卷分兩部份，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，並用繩帶於簿內。 (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或四位小數表示。 (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。

©香港考試及評核局保留版權 Hong Kong Examinations and Assessment Authority All Rights Reserved 2023

2023-DSE-MATH-EP(M1)-1

答案(英文)

1a 0.1 + 0.3 + k + 0.2 = 1 k = 0.4 E(X) = -1 × 0.1 + n × 0.3 + 3 × 0.4 + 6 × 0.2 = 0.3n - 2.3 E(X^2) = (-1)^2 × 0.1 + n^2 × 0.3 + 3^2 × 0.4 + 6^2 × 0.2 = 0.3n^2 + 10.9 Var(X) = E(X^2) - [E(X)]^2 = (0.3n^2 + 10.9) - (0.3n - 2.3)^2 = 0.21n^2 + 1.38n + 5.61 Var(X) = 3.69 0.21n^2 + 1.38n + 5.61 = 3.69 7n^2 + 46n + 64 = 0 (7n + 32)(n + 2) = 0 n = -32/7 (rej.) or -2 n = -2 E(X^4) = (-1)^4 × 0.1 + (-2)^4 × 0.3 + 3^4 × 0.4 + 6^4 × 0.2 = 296.5 Var(X^2) = E((X^2)^2) - [E(X^2)]^2 = E(X^4) - [E(X^2)]^2 = 296.5 - [0.3(-2)^2 + 10.9]^2 = 150.09