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機密(只限關卷員使用)CONFIDENTIAL (FOR MARKER'S USE ONLY)
香港考試及評核局HONG KONG EXAMINATIONS AND ASSESSMENT AUTHORITY
2014年香港中擧文憑考試
HONG KONG DIPLOMA OF SECONDARY EDUCATION EXAMINATION 2014
This marking scheme has been prepared by the Hong Kong Examinations and Assessment Authority for the reference of markers. The use of this marking scheme is subject to the relevant appointment terms and Instructions to Markers. In particular:
The Authority retains all proprietary rights (including intellectual property rights) in this marking scheme. This marking scheme, whether in whole or in part, must not be copied, published, disclosed, made available, used or dealt in without the prior written approval of the Authority. Subject to compliance with the foregoing, a limited permission is granted to markers to share this marking scheme, after release of examination results of the cWTent HKDSE examination, with teachers who are teaching the same subject.
Under no circumstances should students be given access to this marking scheme or any part ofit. The Authority is counting on the co-operation of markers/teachers in this regard.
Hong Kong Diploma of Secondary Education Examination Mathematics Compulsory Part Paper 1
General Marking Instructions
I. It is very important that all markers should adhere as closely as possible to the marking scheme. In manycases, however, candidates will have obtained a correct answer by an alternative method not specified in themarking scheme. In general, a correct answer merits all the marks allocated to that part, unless a particularmethod has been specified in the question. Markers should be patient in marking alternative solutions notspecified 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 amvmg
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 stilllikely that candidates would not present their solution in the same explicit manner, e.g. some steps wouldeither be omitted or stated implicitly. In such cases, markers should exercise their discretion in markingcandidates'work. In general, marks for a certain step should be awarded if candidates'solution indicated thatthe 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'f.t.'stands for'follow through'. Steps which can be skipped are噩噩噩whereas alternative answers are enclosed with転tangles! . All fractional answers must be simplified.
8. (a) The coordinates of P ' are (5,3). The coordinates of Q ' are (-19, 刁).
(b) The slope of PQ5+7
-3-2-12
5
The slope of P'Q' 3+7 5 + 19 5
12
So, the product of the slope of PQ and the slope of P'Q'is -1 . Thus, PQ is perpendicular to P'Q'.
9. (a) In LlABC and LlBDC,乙BAC=乙DBC乙ACB=乙BCD
LlABC - 11BDC
(given ) ( common乙)霉-靄霰罰(AAA)
lA lA
IM
IA
一一一-(5)
----------------:
{------1
/either one
either one
一一一一一一]一一一一一一一]
-------'
[已知][公共角]
(AA) (eqmangular) [等角]
Markini:i; Scheme: 严「 A ny correct proof with correct reasons.Case 2 A ny correct proof without reasons.
2-1
(b) CD BC BC AC CD 20 20 25 CD =16 cm
IM
BD2 +CD2
=122 +162
= 202
=BC 2
Thus, LlBCD is a right-angled triangle.
lM
IA I f.t. ----------(5)
2014-DSE-MATH-CP 1-5
機密(只限關卷員使用)CONFIDENTIAL (FOR MARKER'S USE ONLY)
Solution Marks Remarks
10. (a) The distance ofcar A from town X at 8:15 in the morning 45 =— (80)120
=30km
(b) Suppose that car A and car B first meet at the time t minutes after7:30 in the morning.
t 44 120 80 t =66 Thus, car A and car B frrst meet at 8:36 in the morning.
(c) During the period 8: 15 to 9:30 in the morning, car B travels 36 kmwhile car A travels more than 36 km .So, the average speed of car A is higher than that of car B .Thus, the claim is disagreed.
IM
IA ----------(2)
IM
IA ----------(2)
IM
IA I ft.
The average speed of car A during the period 8: 15 to 9:30 in the morning 80-30
1.2550
1.25=40 km/h en。
IIIlIII.
I
-
e
-
h
-
ti
-
e
80一
2tpeccaM
l
The average speed of car B during the period 8: 15 to 9:30 in the morning 80-44
1.25361.25
= 28.8 km/h
Note that 40 > 28.8 . So, the average speed of car A is higher than that of car B . Thus
,_ the clai!}l is disagreed. IA jf.t.
----------(2)
2014-DSE-MATH-CP 1-6
機密(只限閱卷員使用)
CONFIDENTIAL {FOR MARKER’S USE ONLY) Solution Marks Remarks
11. (a) The range
罐罐蠶= 73 thousand dollars
IM lA
e n nu
「It
--仗,lti
-
-h
-
-
HU
-
-e
- The inter-quartile range 體蠶鹽= 21 thousand dollars lA
...一(3)
(b) The mean of the prices of the remaining paintings in the art gallery (33)(53)一 32-34-58-59 lM
33-4 1566
29 = 54 thousand dollars lA
Note that 32 and 34 are less than 55 . Also note that 58 and 59 are greater than 55 .
The median of the prices of the remaining paintings in the 訂t gallery =55 伽sand dollars I lA
一---(3)
2014-DSE-MATH-CP 1-7
機密(只限關卷員使用)CONFIDENTIAL (FOR MARKER'S USE ONLY)
12. (a) The radius of C=」(6-0)2 +(11-3)2
= 10
Solution Marks
IM
Remarks
2 Thus, the equation of C is x + (y - 3) 2 =10 2 IA I x2 +y2 -6y-9l=O
(b) (i) Let (x, y) be the coordinates of P.
如-0)2 +(y-3)2 =」(x-6)2 +(y-11)2
3x+4y-37=0 Thus, the equation of「is 3x+4y-37=0.
The slope of AG 11-36-04
= -
-3 Note that the slope of「is — .4 Also note that the mid-point of AG is (3, 7) . The equation of 「 is
-3 y-7= 一(x-3)4
3x+4y-37=0
(ii) 「 is the perpendicular bisector of the line segment AG.
(iii) The perimeter of the quadrilateral AQGR= 4(10)=40
2014-DSE-MATH-CP 1-8
一一一-(2)
IM IA
IM
IA
IA
lM lA
----------(5)
機密(只限關卷員使用)CONFIDENTIAL (FOR MARKER'S USE ONLY)
Solution
13. (a) Let f(x) = px 2 +q" --------· , -一,上面
So, we have 4p+q=59 and 49p+q=-121. Solving, we have p = -4 and q = 75 .
Therefore, we have f(x) = 75 - 4x2 .
Thus, we have f(6) = -69 .
(b) By (a), we have a= -69 .
Since f(x) = 75 - 4x2 , we have f(-6) = f(6) .
So, we have b = -69 .
AB = 6-(-6)
=12
The area of llABC (12)(69)
2 =414
2014-DSE-MATH-CP 1-9
Marks
IA IM
IA
IA ----------(4)
IM
IM
IM
IA ----------(4)
Remarks
for either substitution for both correct
--------------,
either one I
______________ !
can be absorbed
2
14. (a)
(b)
機密(只限關巻員使用)CONFIDENTIAL (FOR MARKER'S USE ONLY)
Solution
The slant height of the circular cone = 」722 +962
=120 cm
The area of the wet curved surface of the vessel
=頑(72)(120) (96 -60 + 28)2 - (96 -60)2
962
=冗(72)(120)642 -362
962
=2625冗cm2
Let R cm be the radius of the water surface. R Then, we have 一 = 96-60+2872 96
R 64 Therefore we have 一 = 一 ·, 72 96 So, we have R=48 . Let r cm be the base radius of the lower part of the inverted right circular cone.
「 96-60Then, we have 一- = 96 72 Therefore, we have -r = 一
36一.72 96
So, we have r = 27 . The area of the wet curved surface of the vessel
=冗(48)」482 +642 -冗(27)」272 +362
=冗-(48)(80)-冗·(27)(45)=2 625兀cm2
The volume of the circular cone = 一
I 冗(72)2 (96)
= 165 888冗cm3
The volume of water in the vessel
= 165 888严鬥963
=40404冗cm3
�0.126932909 m 3
>0.l m 3
Thus, the claim is agreed.The volume of water in the vessel