2019 DSE 数学延伸部分-M1 真题 答案 详解

---

真题(英文)

SECTION A (50 marks)

1. The table below shows the probability distribution of a discrete random variable X, where k is a constant:

x	8	11	k	27	32
P(X = x)	0.2	0.1	0.3	0.3	0.1

It is given that Var(X) = 66. Find k, E(3X + 5) and Var(3X + 5). (6 marks)

Answers written in the margins will not be marked.

2019-DSE-MATH-EP(MI)-2

Provided by dse.life

真题(中文)

第三级单元一 附评语之示例 2019-DSE 数学 延伸部分 单元一

香港考试及評核局 2019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，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纸。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，並用繩帶於薄內。 (五) 除特别指明外，须详细列出所有算式。 (六) 除特别指明外，数值答案须用真確值或四位小数表示。 (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编號方格。

©香港考试及評核局保留版權 Hong Kong Examinations and Assessment Authority All Rights Reserved 2019

2019-DSE-MATH-EP(M1)-1 1 * A031C001 *

答案(英文)

Marking Scheme
Module 1 (Calculus and Statistics)

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 ‘ft.’ stands for ‘follow through’. Steps which can be skipped are shaded whereas alternative answers are enclosed with rectangles. All fractional answers must be simplified. 6. Unless otherwise specified in the question, numerical answers should either be exact or given to 4 decimal places. Answers not accurate up to the required degree of accuracy should not be accepted.