MATHEMATICS SYLLABUS SECONDARY YEARS 4-7

Eurpean Schls Office f the Secretary-General Ref.: 2010-D-441-en-5 Orig.: FR MATHEMATICS SYLLABUS SECONDARY YEARS 4-7 Preamble t the syllabuses FOLLOW-UP ON THE MEETING OF THE JOINT TEACHING COMMITTEE OF 9, 10 AND 11 FEBRUARY 2011 APPROVED BY THE JOINT TEACHING COMMITTEE AT ITS MEETING OF 5 AND 6 OCTOBER 2011 Immediate entry int frce 1/23

PREAMBLE 1. OBJECTIVES 1.1. General bjectives The secndary sectin f the Eurpean Schls needs t perfrm the dual task f prviding frmal, subject-based educatin and f encuraging pupils persnal develpment in a wider scial and cultural cntext. Frmal educatin invlves the acquisitin f knwledge and understanding, cncepts and skills within each subject area. Pupil shuld learn t describe, interpret, judge and apply their knwledge. Persnal develpment f pupils is dne in a range f spiritual, mral, scial and cultural cntexts. It invlves fr pupils an awareness f apprpriate behaviur, and understanding f the envirnment in which they wrk and live and a develpment f individual identity. In practice these tw tasks are inseparable within the schl. These tw majr bjectives are develped in the cntext f a highlighted awareness f Eurpean reality, the characteristic feature f which is the richness f Eurpean cultures. This awareness and the experience acquired as a result f shared Eurpean life shuld lead t the develpment in pupils f behaviur shwing clear respect fr the traditins f each individual cuntry in Eurpe, while at the same time preserving their wn identities. 1.2. Subject-specific bjectives Mathematics instructin must prgress systematically and create a lasting fundatin fr the assimilatin f mathematical cncepts and structures. The aim is t develp pupils mathematical skills, such as creative, lgical and analytical thinking. Pupils shuld develp the skills f frmulating mathematical prblems apprpriately, then finding the slutins t the prblems and finally presenting their methds and cnclusins in a neat and rderly fashin. Prblems that cme up in day-t-day situatins, and that can be reslved with the aid f mathematical thinking r peratins, are t be utilised effectively. This syllabus f mathematics aims t imprve the teaching f mathematics by guaranteeing mre equality, and by updating the syllabus t crrespnd better t the new demands f the sciety. The syllabus preserves the fundatins f mathematics teaching and leaves the cre f the subject unchanged but at the same time it has as a new bjective the systematic implementatin f mdern technlgical tls in the teaching. It als aims t create a cmmn vehicle fr teaching while allwing the teachers the freedm t intrduce the fundamental cncepts f the syllabus accrding t their wn teaching methds. 2/23

Als, this syllabus allws fr differences in pupils level f perfrmance and enables them t excel. It eliminates the need fr the pupil t master simple rutines. This syllabus als places a great deal f emphasis n strategic thinking skills, as well as analysing results btained. It is imprtant t underline that the syllabus is nt based n the use f technlgical tls. On the cntrary, purpseful and efficient use f these tls helps pupils t becme cnfident in the fundamental mathematical cncepts. It is als pssible t differentiate the learning methds accrding t the age, level f studies chsen, and knwledge and skills f each pupil. 1.3. Structure f studies YEARS 1, 2, 3 COMMON SYLLABUS YEARS 4, 5 ELEMENTARY LEVEL 4P YEARS 4, 5 STANDARD LEVEL 6P YEARS 6, 7 ELEMENTARY LEVEL 3P YEARS 6, 7 STANDARD LEVEL 5P YEARS 6, 7 (*) FURTHER LEVEL 3P BACCALAUREATE WRITTEN EXAM (COMPULSORY) BACCALAUREATE WRITTEN EXAM (COMPULSORY) BACCALAURETATE ORAL EXAM (COMPULSORY) 3/23

(*) The further level curse can nly be studied in cnjunctin with the standard level (5p). 1.3.1 Elementary level This curse is intended fr pupils wh d nt cnsider cntinuing with studies where mathematics plays an imprtant rle. Its purpse is t help pupils t understand the scientific and technlgical wrld surrunding them withut putting t much emphasis n theretical aspects f mathematics. In the years 6 and 7 the 3 perid curse is nrmally preceded by the 4 perid curse in years 4 and 5. 1.3.2 Standard level This curse is intended fr pupils wh need mathematics in their higher level studies and because f this can benefit frm a slid fundatin and a gd general knwledge f mathematics. In years 6 and 7 the 5 perid curse is nrmally preceded by the 6 perid curse in years 4 and 5. 1.3.3 Further level This curse is nly intended fr pupils wh have taken the 5 perid curse in years 6 and 7. Its purpse is t prvide pupils with the knwledge sufficient fr higher studies where mathematics has an imprtant and fundamental rle. The curse requires dedicatin and the pupils are trained t slve prblems with mre varied methds. The syllabus cnsists f tw parts ne cmpulsry and the ther ptinal - which allw fr the incrpratin f natinal syllabuses as well as entry requirements t institutins f higher educatin in different member states. In year 6 the teacher shall include ne f the ptins given in the syllabus in the ptinal part. In year 7 the teacher shall include tw f the ptins given in the syllabus in the ptinal part. 4/23

2. CONTENT In this dcument the syllabus is presented in three clumns. The first clumn titled «tpics» gives the cntent f the chapters. The secnd clumn titled «knwledge and skills» states the bjectives t be attained and defines clearly the techniques, cncepts and strategies the pupil must understand and master withut having any technlgical tl as a supprt. The third clumn titled «use f technlgical tl» indicates the knwledge and skills required fr effective use f technlgical tls assciated with this syllabus. Unlike in the syllabus fr years 1, 2 and 3, the third clumn des nt list pssible teaching appraches which culd be adpted when teaching the respective tpics mentined in the tw previus clumns. The third clumn here is an integral part f the syllabus defining the skills the pupil has t acquire t use the technlgical tls in rder t perfrm calculatin techniques, analyse prblems, make cnjectures, link cncepts tgether, develp strategies and test results. This clumn als suggests the use f a technlgical tl in tests, exams and the Baccalaureate. 3. METHODOLOGY 3.1 Use f technlgical tl Many students have difficulty understanding mathematical prblems and apprpriately applying their knwledge. Often they d nt succeed in establishing a cnnectin between their existing knwledge f mathematics and the methd needed t slve a prblem. Therefre, the fundamental aspect f this syllabus is the systematic use f a technlgical tl at all levels which: is the same in all Eurpean schls fr all students and all levels f mathematics educatin frm the 4th year; is sustainable ver time because the sftware can be updated; integrates simultaneusly and n a single platfrm; gemetry, algebra, analysis, spreadsheet, drawing graphs, prbability and statistics; ensures equity f use during class tests, examinatins and baccalaureate. gives students the resurces t devte themselves t actually slving prblems and thereby highlights mathematical thinking, develping strategies and verificatin f results; 5/23

allws an interdisciplinary apprach, encuraging students t apply knwledge and skills in handling technlgical tls in ther subjects such as physics, chemistry, bilgy, ecnmics, scilgy and gegraphy. The chice f technlgical tl t accmpany this prgram is separately defined in a specificatin 1 and revised in light f develpments in this area 2. This essential aspect f the syllabus nt nly mdifies pupil s learning techniques but it will als mean a prfund change in the teaching methds used by the teacher. This technlgical tl will make it pssible fr the teacher t divide teaching in units, t adpt a dynamic and interactive apprach and t intrduce the basics fr mathematical reasning in numerus varying situatins Intrductin f this tl prmtes grup wrk, the exchange f ideas and infrmatin and discussin n strategies t be applied. It gives the teacher a rle f mediatr in this exchange, in a class rm which thrugh the implementatin f this methdlgy will becme a labratry f mathematics. This syllabus aims by n means t see this technlgical tl as a simple help fr perfrming calculatins and technical tasks in mathematics. On the cntrary, a well-cnsidered use f this tl shall enable the pupil t gain a better understanding f mathematical structures intrinsically cnnected with the technical aspects f mathematics. It cntributes t the understanding and nt t the acquisitin f techniques. 3.2 Exercises, techniques and prblem slving Prblem slving plays an imprtant rle in the develpment f mathematical abilities as a key factr fr stimulating reasning. Examples and prblems can be taken frm everyday life. In additin, it is pssible t use artificial situatins as well as carry ut research and cnduct experiments. 1 Mathematics Syllabus Year 4 t Year 7: Characteristics f the technlgical tl t be implemented Ref.: 2010-D-571-en-2 2 Arrangements fr acquisitin f the calculatr freseen by the new mathematics syllabuses (apprved by the Bard f Gvernrs f the Eurpean Schls n 14, 15 and 16 April 2010 in Brussels) Ref.: 2010-D-242-en-3 6/23

In rder t understand the basic philsphy f this syllabus f mathematics and t put prblem-slving really int practice it is imprtant t distinguish between an exercise r a technique and slving a real-life prblem; acknwledging that the ne cannt be dne withut the ther. The fundamental bjective f this syllabus is t recgnise that bth play a rle and nt t limit mathematics t the use f mechanisms. An exercise r using a technique differs frm slving a real-life prblem in the fllwing ways. Exercise r mathematical technique The wrding sets ut what is t be dne and ften indicates the techniques t be used. The path fr finding the slutin is unambiguus. The slutin is btained by using skills r mechanisms gained previusly. It is pssible t estimate the time required fr btaining the slutin. The level f difficulty can be clearly defined and finding a slutin is evident fr thse abve that level. On the ther hand, finding the slutin is impssible fr thse wh have nt reached the level required. Real-life mathematical prblem The wrding can be pen and at the start it is nt yet clear what is being asked. At first it is nt always evident hw t reach the slutin. Slving the prblem requires ging int detail, seeing a relatinship, reflecting, drafting a strategy n hw t cntinue frm the start. T estimate the time required fr slving the prblem is difficult, r even impssible. The level f difficulty is nt the nly decisive factr. The prblem can be simple, interesting and des nt necessarily require skills acquired previusly. The prblem can be slved by persns with different level f cmpetences. Slving a real-life prblem invlves different steps and using basic r universal strategies. The steps can be described as fllws: 1. Understanding the prblem 2. Drafting a plan 3. Carrying ut the plan 4. Reflecting n the slutin btained. 7/23

Basic strategies include the fllwing amng thers: 1. Examining all pssible cases 2. Chsing apprpriate mathematical ntatin. 3. Drafting a strategy 4. Making an utline, a diagram, a graphical presentatin 5. Making reasning r a prf. Accrding t these ideas this syllabus f mathematics intends t establish a justified balance between mastering the fundamental and necessary techniques in mathematics and the develpment f mathematical reasning thrugh slving real-life prblems. These tw aspects are inseparable in the syllabus. In their daily wrk in the class rm the teacher is free t balance between these tw pillars f mathematics. Hwever, it is in their respnsibility t abide with the cntents f the three clumns and prepare the pupils accrding t the terms fr tests, exams and the Baccalaureate defined in the fllwing chapter. 4. ASSESSMENT OF LEARNING OUTCOMES 4.1. Functins and principles Assessment is bth a frmative and a summative prcess. Frmative assessment f learning utcmes is an nging prcess. Its purpse is t prvide infrmatin abut pupils learning. It shuld als be a basis fr pupils further achievement and plays an imprtant rle fr pupils, parents r guardians and Schl in the prvisin f educatinal guidance fr pupils. Assessment f learning utcmes need nt invlve the award f a mark reflecting perfrmance in every case and it shuld nt be punitive, but it shuld evaluate perfrmance. Fr teachers, the assessment f learning utcmes prvides an pprtunity t review the bjectives, methds and results f their teaching. Summative assessment prvides a clear statement f the knwledge and skills pssessed by a pupil at a particular pint in time. The fllwing general principles f assessment f learning utcmes shuld be bserved: perfrmance against all the bjectives as defined in the syllabus shuld be assessed. This will be dne thrugh the knwledge and skills set ut in the syllabus assessment must relate t wrk which has been cvered in the curse all types f wrk dne by the pupil n the curse shuld be a part f the assessment prcess - e.g. ral and written cntributins, class tests, practical wrk 8/23

pupils shuld be aware f the wrk t be dne and the standards t be achieved in rder t attain each level in the assessment scale pupils shuld knw hw their perfrmance cmpares with ther pupils, in the same r ther sectins; this requires c-rdinatin between the teachers f the same and different sectins t ensure cmparability. 4.2. Assessment specific t Mathematics 4.2.1. Summary f assessment rules In years 4 t 6 f secndary. Teachers assess the prgress made by pupils during the year by giving tw sets f marks, an A mark and a B mark, at the end f each semester. These marks can be given in whle r half marks and are determined as fllws: A mark: it reflects all aspects f student perfrmance, bth ral and written, which are nt a part f the B mark. Wrk dne at hme can be included in this mark; B mark : crrespnds in year 4, fr each f the semester reprts, t the average scre f the tw B assessments taken each semester; these assessments will cnsist f tw tests taken in lessn time r ne such test and a semester examinatin; crrespnds in year 3 5, fr the first semester reprt, t the mark btained in the 1 st semester examinatin (harmnised r nt) and fr the secnd semester reprt, t the mark btained in the harmnised 2 nd semester examinatin; crrespnds in year 6, fr the first semester reprt, t the mark btained in the 1 st semester examinatin and fr the secnd semester reprt, t the mark btained in the 2 nd semester examinatin; 3 Harmnised Exam at the end f the 5 th year and the written examinatins leading t marks B in the 5 th year with Annexe III. Ref.: 3512-D-97 9/23

In year 7 f secndary. Prgress made by pupils is assessed thrugh: A mark: given at the end f each semester. The mark reflects all aspects f student perfrmance, bth ral and written, which are nt a part f the B mark. Wrk dne at hme can be included in this mark; B mark: crrespnding t the marks btained in the part examinatins f the Baccalaureate accrding t the Arrangements fr implementing the Regulatins fr the Eurpean Baccalaureate; the mark btained in the written Baccalaureate exam All these marks are expressed t ne decimal place. The details f the current rules n assessment can be btained in the fllwing dcuments n the website f the Eurpean Schls, at www.eursc.eu Digest f decisins f the Bard f Gvernrs General Rules f the Eurpean Schls Prvisin cncerning the Harmnised Exam at the end f the 5 th year Prvisin cncerning the Eurpean Baccalaureate 4.2.1. Specific assessment resulting frm the intrductin f technlgical tls The intrductin f technlgical tls fr this syllabus must naturally affect the methds f assessment. Hwever, this specific assessment must be dne within the existing regulatry framewrk. It is simply an additinal element that a teacher must take int accunt when assessing and determining the final mark f students. This verall final mark will cntinue t reflect all elements that are relevant in assessing the academic prgress f each student. Pupil s A mark, frm years 4 t 7 An assessment f a pupil s mastery f skills and use f technlgical tls is an additinal element which the teacher must take int accunt when determining the A mark f a pupil. It is fr teachers themselves t decide n hw the mastery f technlgical tls shuld be reflected in this mark, bearing in mind the pupil s age and the level f curse being fllwed. 10/23

Pupil s B mark, frm years 4 t 7 T meet the basic philsphy f this syllabus, the B marks must evaluate n the ne hand: the skills f students in mastering, understanding and implementing the techniques and basic cncepts f mathematics withut using any technlgical tl by means f a "pen and paper" assessment. n the ther: the ability t apply technlgical tls within the cntext f slving exercises, prblems, reasning r mathematical prfs. Reslving these issues shuld nt be riented twards the exclusive use f a technlgical tl and the reslutin f certain parts f these exercises shuld be perfectly pssible and feasible withut this aid. The weighting between these tw assessments must take int accunt the age and level f pupil and it will be the respnsibility f the Eurpean Schls t harmnise all tests, examinatins and the baccalaureate accrding t the table belw. THE B-TESTS IN THE CLASSES S4 t S7 Class 1 st semester 2 nd semester 4 th class mathematics 4p/week 4 th class mathematics 6p/week 1 st B-test withut a tl 2 nd B-test with a tl 1 st B-test withut a tl 2 nd B-test with a tl 1 st B-test withut a tl 2 nd B-test with a tl 1 st B-test withut a tl 2 nd B-test with a tl 5 th class mathematics 4p/week December exam : 1 perid withut a tl 1 perid with a tl Harmnised exam in June: 1 perid withut a tl 1 perid with a tl 5 th class mathematics 6p/week December exam : 1 perid withut a tl 2 perids with a tl Harmnised exam in June: 1 perid withut a tl 2 perids with a tl 6 th class mathematics December exam : 1 perid withut a tl Exam in June: 1 perid withut a tl 11/23

Class 1 st semester 2 nd semester 3p/week 2 perids with a tl 2 perids with a tl 6 th class mathematics 5p/week December exam : 1 perid withut a tl 3 perids with a tl Exam in June: 1 perid withut a tl 3 perids with a tl 6 th class mathematics further level 3p/week First semester B-test ver 2 perids : Minimum 1 perid withut a tl Secnd semester B-test ver 2 perids : Minimum 1 perid with a tl 7 th class mathematics further level 3p/week First semester B-test ver 2 perids : Minimum 1 perid withut a tl Secnd semester B-test ver 2 perids : Minimum 1 perid with a tl THE PRE BAC AND THE BACCALAUREATE 7 th class Pre Bac Baccalaureate 7 th class mathematics 3p/week Pre Bac : 1 hur withut a tl 2 hurs with a tl Baccalaureate : 1 hur withut a tl 2 hurs with a tl 7 th class mathematics 5p/week Pre Bac : 1 hur withut a tl 3 hurs with a tl Baccalaureate : 1 hur withut a tl 3 hurs with a tl 7 th class mathematics further level 3p/week 3p/sem. N Pre Bac Oral exam: With r withut tl, the indicatin is given by the teacher separately n each subject. 12/23

4.2.3 Examining the advanced mathematics curse It is the respnsibility f the teacher t clarify whether the use f a calculatr is allwed during B tests given in s6 and s7 by referring t the table abve. Each ral examinatin questin shuld clearly state whether the use f the calculatr is allwed r nt. Partial use f the calculatr during an ral examinatin is nt allwed. If the ral examinatin questin des nt allw the use f the calculatr then the candidate must hand in their calculatr t the teacher after the chice f questin and, if the use is allwed, the teacher must check that it is in exam mde befre the candidate ges t the preparatin rm. Unlike the preceding cmpulsry part f the prgram the descriptin f each ptinal tpic gives nly a general verview f the cntent. Small adjustments in the cntent, linked t specific prgrams r requirements f natinal universities in different cuntries f the Eurpean Unin remain pssible. It is up t the teacher t make the necessary changes. Hwever, fr the sake f readability and cmparability f this part f the prgram, teachers in charge f this curse must keep an accurate recrd f the adjustments made t the chsen ptins. This recrd will accmpany the ral exam questins frwarded t the inspectr respnsible fr mathematics in the Eurpean Schls. This will ensure that all such infrmatin (statement f the subject matter and the ral exam) is available t external examiners appinted fr the ral tests.. 4.2.4 Criteria fr evaluating the advanced mathematics ral exam The ral examinatin gives the students an pprtunity t express themselves n a mathematical tpic. "Besides the validity f the answer, we attach paramunt imprtance t the basis f the argument and the relevance f justificatin withut neglecting the quality f ral expressin." Mathematics requirements: (2 +6 = 8 pints ttal) The plan f the presentatin: (2 pints) The student must shw that the tpic in which the questin is set is familiar and justify the apprach they will implement. Specifically, they must: 13/23

identify the tpic; clarify the cncepts and methds being implemented; shw the ability t set the given prblem in a mathematical cntext. The develpment f the slutin: (6 pints) During the slutin f the questin the student must: recall necessary definitins; use apprpriate vcabulary; shw a cnsistent, lgical apprach; shw mastery f any cmputatinal techniques that are used (with r withut a calculatr). Additinal questins They are nt predetermined and depend n the quality f the presentatin f the student. They are nt predetermined and depend n the quality f the presentatin f the student. They are designed t: assess the knwledge level f students n the tpic f the questin chsen(mainly if the student develpment can be imprved; braden the questin (extraplatin). 14/23

Practical requirements: (2 pints) During the slutin f the questin they will als be evaluated n the fllwing: clear cmmunicatin skills and use f an apprpriate vcabulary; gd use and management f the blackbard; ability t adapt t an ral examinatin. 15/23

5. THE WRITTEN PAPERS IN MATHEMATICS IN THE BACCALAUREATE EXAMINATIONS 5.1. Preliminary remark This chapter sets ut the guidelines t be fllwed fr the setting and structure f the Baccalaureate written papers fr the 3 and 5 weekly perids mathematics curses examinatins. It expands n the relevant prvisins laid dwn in the Arrangements fr implementing the Regulatins fr the Eurpean Baccalaureate and may nt under any circumstances replace r verride thse prvisins. Detailed cnsultatin f that dcument, which is nt included in this preamble as it is updated by the OSGES and sent t the schls fr each Baccalaureate sessin, is therefre abslutely essential. 5.2. General guidelines fr the mathematics examinatins 5.2.1. Subject matter f the examinatins The written examinatins in mathematics test the full range f the subject matter cvered in year 7, as defined by the 3-perid and 5-perid syllabuses respectively, althugh they may als test cncepts r techniques acquired in year 6. Under n circumstances shuld the papers include questins ffering a chice and they must cver all the themes defined by the syllabuses. Details n that subject are given in paragraph 5.3, entitled Detailed structure f the mathematics papers in the Baccalaureate examinatins. 5.2.2. Time allwed fr the examinatins The ttal time allwed fr the written papers in mathematics and the amunt f time alltted t the part withut the technlgical tl, called part A, and the part with the technlgical tl, called part B, is laid dwn in the table entitled The Pre-Bac (part examinatins) and the Baccalaureate in paragraph 4.2.2. On the day f the mathematics written papers, in bth the Pre-Bac and the Baccalaureate, the examinatins will start at the fllwing times: start f the examinatin with the technlgical tl, part B: 09.00; start f the examinatin withut the technlgical tl, part A: 14.00. Fr SEN students, the prvisins in frce remain unchanged and are fully applicable. The extra time breaks dwn prprtinally t the amunt f time alltted t each part f the examinatin. 5.2.3. Marking scale fr the examinatins The written examinatin papers in mathematics are marked ut f a ttal f 100: 16/23

in the 3 weekly perids curse, the part withut the technlgical tl, called part A, accunts fr 40 marks, and the part with the technlgical tl, called part B, fr 60 marks. in the 5 weekly perids curse, the part withut the technlgical tl, called part A, accunts fr 30 marks, and the part with the technlgical tl, called part B, fr 70 marks. The final mark fr the examinatins des nt make a distinctin between the marks achieved in each f the tw parts: this final mark ut f 100 is the sum f the marks achieved separately in the part withut and in the part with the technlgical tl. Mre detailed recmmendatins fr setting the marking scale are given in paragraph 5.4, entitled Setting f Baccalaureate examinatin questin papers and marking scale. 5.2.4. Equipment fr examinatins In accrdance with the Arrangements fr implementing the Regulatins fr the Baccalaureate, candidates may use nly the fficial sheets f paper prvided fr that purpse. In that cntext, it shuld als be pinted ut that scripts written in pencil are nt accepted. Apart frm the technlgical tl determined by the grup f experts t accmpany the mathematics syllabuses, n ther equipment r frmularies are allwed during the written papers in mathematics. The mdels f technlgical tl and the versins f the sftware t be used with them are determined by the grup f experts. The grup f experts decisins will be cmmunicated t the schls befre the end f the schl year preceding the Baccalaureate year and will be indicated n the frnt page f the examinatin papers entitled Ntice t Candidates. Use f the technlgical tl is allwed nly in the part f the examinatin with the technlgical tl, als called part B. 17/23

5.3. Detailed structure f the mathematics papers in the Baccalaureate examinatins 5.3.1. Structure f the 3-perid mathematics curse examinatin paper The 3 weekly perids mathematics curse examinatin paper must cmply with the framewrk and the prvisins set ut in the fllwing table. 3-PERIOD MATHEMATICS COURSE EXAMINATION PAPER EXAMINATION WITHOUT TECHNOLOGICAL TOOL PART A EXAMINATION WITH TECHNOLOGICAL TOOL PART B TIME ALLOWED: 60 MINUTES TIME ALLOWED: 120 MINUTES MARKING SCALE: 40 MARKS MARKING SCALE: 60 MARKS This part cmprises 8 questins, each wrth 5 marks. These questins are designed strictly t test the basic knwledge and skills laid dwn in the first 2 clumns f the syllabus fr this curse. The questins are cnfined t testing a well-defined skill r cmpetence and may nt, therefre, cntain sub-questins. The 8 questins cver all the tpics set by the syllabus and break dwn as fllws: 5 analysis questins; 2 questins n prbabilities; 1 questin n statistics. This part cmprises 3 parts. The 3 parts refer t the 3 clumns f the syllabus fr this curse. The 3 parts cver all the tpics set by the syllabus and break dwn as fllws: analysis: 25 marks; prbabilities: 15 marks; statistics: 20 marks. The part n analysis takes the frm f ne exercise wrth 10 marks and ne exercise wrth 15 marks. The part n prbabilities takes the frm f ne exercise wrth 15 marks. 18/23

The part n statistics takes ne f the fllwing tw frms: 2 exercises each wrth 10 marks; 1 exercise nly, wrth 20 marks. An exercise wrth 10 marks must cnsist f exactly 3 subquestins. An exercise wrth 15 marks must cnsist f a minimum f 4 and a maximum f 5 sub-questins. An exercise wrth 20 marks must cnsist f a minimum f 5 and a maximum f 6 sub-questins. The number f marks which a sub-questin is wrth may nt be greater than 5. 19/23

5.3.2. Structure f the 5-perid mathematics curse examinatin paper The 5 weekly perids mathematics curse examinatin paper must cmply with the framewrk and the prvisins set ut in the fllwing table. 5-PERIOD MATHEMATICS COURSE EXAMINATION PAPER EXAMINATION WITHOUT TECHNOLOGICAL TOOL PART A EXAMINATION WITH TECHNOLOGICAL TOOL PART B TIME ALLOWED: 60 MINUTES TIME ALLOWED: 180 MINUTES MARKING SCALE: 30 MARKS MARKING SCALE: 70 MARKS This part cmprises 7 questins, wrth a minimum f 2 and a maximum f 6 marks, s that the sum ttal f 30 marks alltted t this part is respected. These questins are designed strictly t test the basic knwledge and skills laid dwn in the first 2 clumns f the syllabus fr this curse. The questins are cnfined t testing a well-defined skill r cmpetence and may nt, therefre, cntain sub-questins. The 7 questins cver all the tpics set by the syllabus and break dwn as fllws: 1 analysis questin; 1 gemetry questin; 1 prbabilities questin; This part cmprises 4 parts: 3 parts wrth 20 marks and ne part wrth 10 marks. The 4 parts refer t the 3 clumns f the syllabus fr this curse. The 4 parts cver all the tpics set by the syllabus and break dwn as fllws: analysis: 20 marks; gemetry: 20 marks; prbabilities: 20 marks; sequences and/r cmplex numbers: 10 marks. The different parts take the fllwing frm: analysis, gemetry and prbabilities: a single exercise each wrth 20 marks; 20/23

1 questin n sequences; 1 questin n cmplex numbers; the sixth and seventh questins cncern tw separate tpics chsen frm amngst analysis, spatial gemetry and prbabilities. the part n sequences can cnsist f a single exercise, wrth 10 marks, n series nly r n cmplex numbers nly, r f tw exercises, wrth 5 marks each, ne n sequences, the ther n cmplex numbers. An exercise wrth 20 marks must cnsist f a minimum f 4 and a maximum f 8 sub-questins. The number f marks which a sub-questin is wrth may nt be greater than 5. 5.4. Setting f Baccalaureate examinatin questin papers and marking scale Guidelines fr the setting f Baccalaureate written examinatin paper questins: the wrding f the questins shuld allw candidates clearly t identify the frm in which they are suppsed t present their answer (simple result, a methd, the stages in a calculatin, a line f reasning, etc.); sub-questins cmpsed f a series f further sub-questins are nt allwed; in setting questins fr the parts with the technlgical tl, the fllwing recmmendatins shuld als be fllwed: the initial questins shuld enable candidates t becme familiar with the tpic t be dealt with; the mst pen-ended r the mst difficult parts f the questin shuld be at the end f the exercise; the wrding shuld make clear t candidates whether the answer t a sub-questin can be fund nly by using the technlgical tl; the marking scale must clearly indicate the number f marks which each f the sub-questins is wrth; the number f marks which a sub-questin is wrth is dependent n the skills and techniques which candidates have t deply in rder t find the slutin. Hwever, this number f marks shuld in n way be a yardstick f the degree f difficulty alne f the sub-questin. Finally, the number f marks which a sub-questin is wrth may nt be greater than 5; 21/23

the mdel answers accmpanying the examinatin papers give a pssible slutin and nt the slutin which candidates are suppsed t prduce. It is up t markers, and it is their respnsibility, t mark with discernment and t judge the mathematical validity f any apprach r slutin which might differ frm the mdel answers within the framewrk set abve. 5.5. Practical rganisatin f Baccalaureate mathematics examinatins In all the Eurpean Schls the mathematics written examinatins will be rganised in accrdance with the guidelines belw. In rder t take accunt f the particularities and cnstraints f the different Eurpean Schls, details f the arrangements which need t be made t implement these guidelines will be determined in each schl. 5.5.1. Mathematics examinatin withut the technlgical tl: Part A The part f the examinatin withut the technlgical tl must be cnducted withut any technlgical devices. It is a pen and paper examinatin, withut any mathematics frmulary. Candidates have nly the fficial examinatin sheets (final script and rugh wrk) freseen fr the different examinatin papers. During this part f the examinatin, candidates may nt have at their dispsal the technlgical tls r devices freseen by the syllabuses. 5.5.2. Mathematics examinatin with the technlgical tl: Part B The schls must guarantee that fr the part with the technlgical tl, candidates calculatrs have the unbiased examinatin mde ( press-t-test functinality) enabled. The grup f experts is respnsible fr making available t the schls an infrmatin mem and update n this press-t-test functinality f the technlgical tl. This mem will be included in the Arrangements fr implementing the Regulatins fr the Baccalaureate. Candidates wh hand in their scripts mre than ten minutes befre the scheduled end f the examinatin must give them t an invigilatr, wh must ensure that each such candidate leaves the examinatin rm with his r her technlgical tl. Cllectin f the scripts during the last ten minutes f the examinatin must prceed in accrdance with the prvisins in frce. Fr the examinatins, the schls must plan in advance t ensure that there is a sufficient number f technlgical tls with the presst-test functinality enabled and f suitable replacement batteries. 22/23

6. WRITTEN PAPERS IN MATHEMATICS IN THE PRE-BAC (PART EXAMINATIONS) Fr the mathematics written papers in the Pre-Bac, paragraphs 5.2.2; 5.2.3; 5.2.4; 5.4 and 5.5 are applicable. As is the case fr the Baccalaureate written papers, under n circumstances shuld these papers include questins ffering a chice. The Pre-Bac written papers in year 7 must be harmnised as far as pssible. 7. WRITTEN PAPERS IN THE YEARS 5 AND 6 EXAMINATIONS In all the Eurpean Schls the mathematics written examinatins in years 5 and 6 will be rganised in accrdance with the guidelines belw. In rder t take accunt f the particularities and cnstraints f the different Eurpean Schls, details f the arrangements which need t be made t implement these guidelines will be determined in each schl. The length f the papers in these examinatins and the time allwed fr the parts withut and with the technlgical tl respectively are set ut in the table entitled B tests in years s4-s7 in paragraph 4.2.2. Fr all these examinatins, paragraphs 5.4 Setting f Baccalaureate examinatin questin papers and marking scale and 5.5 Practical rganisatin f Baccalaureate mathematics examinatins are applicable. There shuld be a break f at least ten minutes between the part f the examinatin withut the technlgical tl and the part with the technlgical tl. If this break is nt lnger than 15 minutes, the students may nt leave the examinatin rm. Under n circumstances may the necessary break time between these tw parts be cunted twards the ttal amunt f time allwed fr the mathematics examinatins. Cntrary t the prvisins f the secnd indent f paragraph 5.5.1 and by way f an exceptin, depending n the schl s cnstraints, the technlgical tls may be put n the flr, in their cases, at the student s place in the examinatin rm during the examinatin withut the technlgical tl. Fr SEN students, the prvisins in frce remain unchanged and are fully applicable. The extra time breaks dwn prprtinally t the amunt f time alltted t each part f the examinatin. Fr the harmnised mathematics examinatins at the end f year 5, the prvisins f the dcument Harmnised assessment at the end f year 5 and the written examinatins leading t the B marks in year 5 shuld als be respected. 23/23