MATHEMATICS. The assessment objectives of the Compulsory Part are to test the candidates :

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1 MATHEMATICS INTRODUCTION The public assessmet of this subject is based o the Curriculum ad Assessmet Guide (Secodary 4 6) Mathematics joitly prepared by the Curriculum Developmet Coucil ad the Hog Kog Examiatios ad Assessmet Authority. Cadidates have to refer to the Guide for the kowledge, uderstadig, skills ad attitudes they are required to demostrate i the assessmet. The curriculum comprises a Compulsory Part ad a Exteded Part. Cadidates takig the HKDSE Mathematics Examiatio may choose to take either the Compulsory Part oly or the Compulsory Part plus oe of the two modules of the Exteded Part. The 05 Assessmet Framework may be subject to chage based o the experiece of the first admiistratio of the HKDSE Examiatio. Schools ad the public will be iformed of ay chages with adequate advace otice. ASSESSMENT OBJECTIVES The assessmet objectives of the Compulsory Part are to test the cadidates :. kowledge of the mathematical facts, cocepts, skills ad priciples preseted i the Curriculum ad Assessmet Guide;. familiarity with ad use of mathematical symbols; 3. ability to use appropriate mathematical techiques for solvig a variety of problems; ad 4. ability to commuicate ideas ad to preset argumets mathematically. The assessmet objectives of Module (Calculus ad Statistics) of the Exteded Part are to test the cadidates :. uderstadig of the cocepts, priciples ad methods i Calculus ad Statistics preseted i the Curriculum ad Assessmet Guide; ad. ability to apply appropriate techiques i Calculus ad Statistics for solvig a variety of problems. The assessmet objectives of Module (Algebra ad Calculus) of the Exteded Part are to test the cadidates :. uderstadig of the cocepts, priciples ad methods i Algebra ad Calculus preseted i the Curriculum ad Assessmet Guide; ad. ability to apply appropriate techiques i Algebra ad Calculus for solvig a variety of problems. 05-HKDSE-MATH

2 MODE OF ASSESSMENT The mode of public assessmet i the Compulsory Part is show below: Compoet Weightig Duratio Public Examiatio Paper Paper Covetioal questios Multiple-choice questios 65% 35% ¼ hours ¼ hours The mode of public assessmet i Module (Calculus ad Statistics) is show below: Compoet Weightig Duratio Public Examiatio Covetioal questios 00% ½ hours The mode of public assessmet i Module (Algebra ad Calculus) is show below: Compoet Weightig Duratio Public Examiatio Covetioal questios 00% ½ hours PUBLIC EXAMINATION Compulsory Part The examiatio will cosist of two papers: Paper ( hours) (65%) 4 This paper will cosist of two sectios i which all the questios are to be attempted. Sectio A will cosist of questios o the Foudatio Topics of the Compulsory Part together with the Foudatio Part of the Secodary -3 Mathematics Curriculum. Sectio B will cosist of questios o the Compulsory Part together with the Foudatio Part ad the No-Foudatio Part of the Secodary -3 Mathematics Curriculum. Sectio A will further be divided ito two parts. Sectio A() (35 marks) will cosist of 8 to elemetary questios. Sectio A() (35 marks) will cosist of 4 to 7 harder questios. Sectio B (35 marks) will cosist of 4 to 7 questios. Paper ( hours) (35%) 4 This paper will cosist of two sectios i which all the questios are to be attempted. Sectio A ( 3 of the paper mark) will cosist of questios o the Foudatio Topics of the Compulsory Part together with the Foudatio Part of the Secodary -3 Mathematics Curriculum. Sectio B ( of the paper 3 mark) will cosist of questios o the Compulsory Part together with the Foudatio Part ad the No-Foudatio Part of the Secodary -3 Mathematics Curriculum. All questios i the paper will be multiple-choice questios. Notes:. Cadidates are ot expected to perform legthy maipulatios.. I calculatios cadidates are expected to give aswers to appropriate degrees of accuracy. 05-HKDSE-MATH

3 3. Electroic calculators ad mathematical drawig istrumets may be used i the examiatio. 4. SI ad metric uits will be used i the examiatio wherever appropriate. 5. Cadidates should ote the commo otatios to be used i mathematics examiatio papers. Module (Calculus ad Statistics) The examiatio will cosist of oe paper of hours duratio. The paper will be divided ito two sectios i which all the questios are to be attempted. Sectio A (50 marks) will cosist of 8- short questios. Sectio B (50 marks) will cosist of 3-5 log questios. Notes:. Kowledge of the subject matter i the Compulsory Part together with the Foudatio Part ad the No-Foudatio Part of Secodary -3 Mathematics Curriculum is assumed.. I calculatios cadidates are expected to give aswers to appropriate degrees of accuracy. 3. Electroic calculators ad mathematical drawig istrumets may be used i the examiatio. 4. Statistical tables will be prited i the questio paper where appropriate. 5. SI ad metric uits will be used i the examiatio wherever appropriate. 6. Cadidates should ote the commo otatios to be used i mathematics examiatio papers. Module (Algebra ad Calculus) The examiatio will cosist of oe paper of hours duratio. The paper will be divided ito two sectios i which all the questios are to be attempted. Sectio A (50 marks) will cosist of 8- short questios. Sectio B (50 marks) will cosist of 3-5 log questios. Notes:. Kowledge of the subject matter i the Compulsory Part together with the Foudatio Part ad the No-Foudatio Part of Secodary -3 Mathematics Curriculum is assumed.. Electroic calculators ad mathematical drawig istrumets may be used i the examiatio. 3. Trigoometric formulas will be provided for cadidates referece i the questio paper. 4. SI ad metric uits will be used i the examiatio wherever appropriate. 5. Cadidates should ote the commo otatios to be used i mathematics examiatio papers. 05-HKDSE-MATH

4 SCHOOL-BASED ASSESSMENT (SBA) I the Compulsory Part, studets will be required to complete two assessmet tasks: oe i Secodary 5 ad the other i Secodary 6. These tasks will be more exteded i ature tha the questios i traditioal tests ad examiatios, ad should provide opportuities for studets to demostrate their competece i the followig skills ad abilities, which are embodied i the curriculum objectives:. applyig mathematical kowledge to solve problems;. reasoig mathematically; 3. hadlig data ad geeratig iformatio; ad 4. usig mathematical laguage to commuicate ideas. The assessmet tasks ca be i the form of writte assigmets or eve practical tasks, ad will be coducted maily i school uder teacher supervisio. A wide variety of types of tasks ca be adopted for assessmet purposes, icludig, for istace, mathematical ivestigatios ad solvig more sophisticated problems i real-life situatios or with mathematics itself. It is proposed that the required assessmet tasks are:. oe task o mathematical ivestigatio or problem-solvig; ad. oe task o data hadlig. The detailed requiremets, regulatios, assessmet criteria ad guidelies are provided i the SBA Hadbook for HKDSE Mathematics (Trial Versio) published by the Hog Kog Examiatios ad Assessmet Authority. There is o time-lie for the implemetatio of SBA i Mathematics ad a review will be coducted i the school year 0/3. Durig the trasitio years, the curriculum for Mathematics will remai itact ad schools will be expected to coduct the SBA activities as itegral parts of learig ad teachig ad iteral assessmet as recommeded i the Curriculum ad Assessmet Guide. 05-HKDSE-MATH

5 The Commo Notatios to be Used i the Hog Kog Diploma of Secodary Educatio Mathematics Examiatio Papers (A asterisk below idicates that the symbol could be used without further defiitio for the papers cocered.) Compulsory Part Module Module a A a is a elemet of the set A ( A ) φ the empty set the umber of elemets i a fiite set A N the set of atural umbers {,, } Z the set of itegers Q the set of ratioal umbers R the set of real umbers A B A is a subset of B R uio itersectio 3 R A the -dimesioal rectagular coordiate system the 3-dimesioal rectagular coordiate system the complemet of the set A i a give uiversal set B \ A the complemet of the set A i B [ a, b ] the closed iterval { x R : a x b} ( a, b ) the ope iterval { x R : a < x < b} f : A B f is a fuctio from the domai A to the rage B a k k = a k k = P r the sum of umbers a, a,, a the product of umbers a, a,, a the umber of permutatios of r objects take from objects C r the biomial coefficiet, the umber of combiatios of r objects take from objects x e, exp(x) the expoetial fuctio with base e l x the logarithmic fuctio to base e H.C.F. the highest commo factor L.C.M. the least commo multiple 05-HKDSE-MATH

6 Compulsory Part Module Module M the iverse of the matrix M T M the traspose of the matrix M det M, M the determiat of the square matrix M AB a the vector represeted i magitude ad directio by the directed lie segmet AB the vector a â a uit vector i the directio of a i, j, k a the magitude of a uit vectors i the directios of the Cartesia coordiate axes a b the scalar product of a ad b a b the vector product of a ad b f ( x ), f ( x) the first derivative ad the secod derivative of f( x ) with respect to x &, & x x P ( A ) P ( A B) the first derivative ad the secod derivative of x with respect to t probability of the evet A probability of the evet A coditioal o the evet B E( X ) expectatio of the radom variable X Var( X ) variace of the radom variable X µ populatio mea σ populatio variace x sample mea s sample variace, = s ( x x) B (, p) biomial distributio with parameters ad p N( µ, σ ) ormal distributio with mea µ ad variace σ Po( λ ) Poisso distributio with mea λ 05-HKDSE-MATH

MATHEMATICS. The assessment objectives of the Compulsory Part are to test the candidates :

MATHEMATICS. The assessment objectives of the Compulsory Part are to test the candidates : MATHEMATICS INTRODUCTION The public assessmet of this subject is based o the Curriculum ad Assessmet Guide (Secodary 4 6) Mathematics joitly prepared by the Curriculum Developmet Coucil ad the Hog Kog