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Contents

1. Nature of the subject ...........................................................................................................3  

2. Aims and assessment objectives .........................................................................................3  

3. Subject outline .....................................................................................................................5  

4. Prior learning .......................................................................................................................8  

5. Mathematics and the IB Learner Profile .......................................................................10  

6. Mathematics and Core Components ...............................................................................11  

7. Course structure and planning ........................................................................................13  

8. Assessment ............................................................................................................................15  

9. Academic Honesty .................................................................................................................16  

     

 

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1. Nature of the subject The nature of mathematics can be summarized in a number of ways: for example, it can be seen as a well-defined body of knowledge, as an abstract system of ideas, or as a useful tool. For many people it is probably a combination of these, but there is no doubt that mathematical knowledge provides an important key to understanding the world in which we live. Mathematics can enter our lives in a number of ways: we buy produce in the market, consult a timetable, read a newspaper, time a process or estimate a length. Mathematics, for most of us, also extends into our chosen profession: artists need to learn about perspective; musicians need to appreciate the mathematical relationships within and between different rhythms; economists need to recognize trends in financial dealings; and engineers need to take account of stress patterns in physical materials. Scientists view mathematics as a language that is central to our understanding of events that occur in the natural world. The IB Diploma program Mathematics SL caters for students who already possess knowledge of basic mathematical concepts, and who are equipped with the skills needed to apply simple mathematical techniques correctly. The majority of these students will expect to need a sound mathematical background as they prepare for future studies in subjects such as chemistry, economics, psychology and business administration. The course focuses on introducing important mathematical concepts through the development of mathematical techniques. The intention is to introduce students to these concepts in a comprehensible and coherent way, rather than insisting on the mathematical rigour required for mathematics HL. Students should, wherever possible, apply the mathematical knowledge they have acquired to solve realistic problems set in an appropriate context. The internally assessed component, the exploration, offers students the opportunity for developing independence in their mathematical learning. Students are encouraged to take a considered approach to various mathematical activities and to explore different mathematical ideas. This course does not have the depth found in the mathematics HL courses. Students wishing to study subjects with a high degree of mathematical content should therefore opt for a mathematics HL course rather than a mathematics SL course.

(Adapted from the IBO “Mathematics Guide”)

2. Aims and assessment objectives

The aims of all mathematics courses in group 5 are to enable students to:

1. enjoy mathematics, and develop an appreciation of the elegance and power of mathematics

2. develop an understanding of the principles and nature of mathematics

3. communicate clearly and confidently in a variety of contexts

4. develop logical, critical and creative thinking, and patience and persistence in problem-solving

     

 

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5. employ and refine their powers of abstraction and generalization

6. apply and transfer skills to alternative situations, to other areas of knowledge and to future developments

7. appreciate how developments in technology and mathematics have influenced each other

8. appreciate the moral, social and ethical implications arising from the work of mathematicians and the applications of mathematics

9. appreciate the international dimension in mathematics through an awareness of the universality of mathematics and its multicultural and historical perspectives

10. appreciate the contribution of mathematics to other disciplines, and as a particular “area of knowledge” in the TOK course.

The course objectives

Problem-solving is central to learning mathematics and involves the acquisition of mathematical skills and concepts in a wide range of situations, including non-routine, open-ended and real-world problems. Having followed a DP mathematics SL course, students will be expected to demonstrate the following.

1. Knowledge and understanding: recall, select and use their knowledge of mathematical facts, concepts and techniques in a variety of familiar and unfamiliar contexts.

2. Problem-solving: recall, select and use their knowledge of mathematical skills, results and models in both real and abstract contexts to solve problems.

3. Communication and interpretation: transform common realistic contexts into mathematics; comment on the context; sketch or draw mathematical diagrams, graphs or constructions both on paper and using technology; record methods, solutions and conclusions using standardized notation.

4. Technology: use technology, accurately, appropriately and efficiently both to explore new ideas and to solve problems.

5. Reasoning: construct mathematical arguments through use of precise statements, logical deduction and inference, and by the manipulation of mathematical expressions.

6. Inquiry approaches: investigate unfamiliar situations, both abstract and real-world, involving organizing and analyzing information, making conjectures, drawing conclusions and testing their validity.

(Adapted from the IBO “Mathematics Guide”)

 

     

 

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3. Subject outline

A. Content/concepts to be taught

The course of Mathematics SL is consisted of the following topics:

Topic 1 Algebra

The aim of this topic is to introduce students to some basic algebraic concepts and applications. It includes arithmetic and geometric sequences and series, elementary treatment of exponents - logarithms and the binomial theorem.

Topic 2 Functions and equations

The aims of this topic are to explore the notion of a function as a unifying theme in mathematics, and to apply functional methods to a variety of mathematical situations. It is expected that extensive use will be made of technology in both the development and the application of this topic. The topic introduces structural concepts of a function such as domain, association and range, followed by the basic operations of composition and inversion. The graph of a function is a central theme of the topic, including the investigation of key features and transformations. Specific functions studied on this topic are: linear, quadratic, rational (only ratios of linear expressions), exponential and logarithmic. The topic also contains algebraic techniques for solving quadratic, exponential and logarithmic equations and graphical techniques for a variety of equations where analytic approaches cannot be applied.

Topic 3 Circular functions and trigonometry

The aims of this topic are to explore the circular functions and to solve problems using trigonometry. The topic begins with the definition of the trigonometric ratios, accompanied with the basic trigonometric identities and the use of the double angle formulas for sine and cosine. An analytic study of the basic circular functions and of the composite function ( ) sin[ ( )]f x a b x c d= + +  takes place and solving techniques for trigonometric equations are being developed, in order both to support the investigation of real life situations. The topic also contains approaches to measure circles and methods to solve triangles with the use of the sine and cosine rule.

Topic 4 Vectors

The aim of this topic is to provide an elementary introduction to vectors, including both theoretical approaches and applications. The exploration in vectors takes place in two and three dimensions. It begins with the definition of the notion introducing the operations geometrically and algebraically and it focuses on the scalar product and the vector equation of a straight line.

     

 

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Topic 5 Statistics and probability

The aim of this topic is to introduce basic concepts. It is expected that the majority of the calculations required will be done using technology, and the emphasis is being given on understanding and interpreting the results obtained, in context. The topic begins with the basics of descriptive statistics, such as measures of central tendency and measures of spread, accompanied with the appropriate tables graphs and charts. It also contains linear correlation of bivariate data and the equation of the regression line of y on x. As regards probabilities, the topic begins with definition and rules and it is supported with the use of Venn diagrams, tree diagrams and tables of outcomes. The notions of conditional probability and independence are also included. In the end students are exposed to the concept of discrete random variables end especially to the Binomial and normal distribution.

Topic 6 Calculus

The aim of this topic is to introduce students to the basic concepts and techniques of differential and integral calculus and their applications. The topic begins with informal ideas of limit and convergence. Derivative is introduced as rate of change and interpreted as gradient function, including the calculations of tangents and normals. Students develop the skills to evaluate the derivatives of a range of different types of functions. Derivatives are being used as a tool for the investigation of the specific features of functions such as monotonicity, turning points, concavity, inflexions and for the optimization in real life problems and applications. As regards integration, students become familiar with the evaluation of simple indefinite and definite integrals and they learn how to calculate areas under curve, areas between curves and volumes of revolution about the x-axis. The last part of the topic allows students to deepen their understanding in calculus applying the basics of the above notions in kinematic problems involving displacement, velocity and acceleration functions.

B. Skills to be developed

The teaching of mathematics aims at developing the following skills:

1. Use of properties-identities and formulas, performing manipulations in simple and complex mathematical expressions.

2. Use of technology such as Graphic Display Calculator and different kinds of mathematical software such as Graphical Analysis, Autograph, Scientific Workplace e.t.c.

3. Use of different forms of mathematical representation such as sketching, drawing, tables, diagrams, graphs, charts, models e.t.c.

4. Use of appropriate mathematical language such as terminology, notation and symbols.

5. Use of definitions and key terms.

     

 

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6. Use of different proving methods and reasoning such as direct proof, inductive and deductive proof/reasoning, reductio ad absurdum, counter examples e.t.c.

7. Organizing, structuring and communicating a train of mathematical thoughts, concepts and arguments in a coherent, easy to follow and logically structured way.

8. Developing mathematical intuition, making conjectures and use of analytical thinking and tools.

9. Developing abstraction and generalization as well as passing from the general to the specific through the construction of examples.

10. Understanding and developing different mathematical perspectives as problem-solving starting points such as algebraic, geometrical, analytical and numerical ones and understanding strengths and weaknesses of each one of them.

11. Mathematical modelling of real-world problems as well as interpretation of mathematical results within real-world context.

C. Teaching methods within a real-life context

Despite the attitude that mathematics is all around us and everything can be described through its use this structural interconnection of mathematics and real-world is neither self-evident nor easily established. Let us call the process of translating a real-world problem into mathematics mathematicalization. The students should be introduced into mathematicalization slowly, progressively, methodically and systematically passing from very simple examples/cases to more complex ones. The variety of topics in the syllabus creates a conducive environment to this end.

The first step in this process is for the student to learn which parts of a given real-world problem can be translated into mathematics. Simultaneously the student should learn how to identify which concepts and tools from his mathematical inventory are appropriate for this translation to take place. To this end in the process of teaching of every single topic of the syllabus the teacher should provide students with carefully chosen examples that demonstrate the strengths and limitations of the specific topic-related concepts and tools in the mathematicalization process. Initially, the examples will be taught using majorly frontal teaching but overtime and as students become familiarized with such problems they will be used as starting points for in-class discussions as well as for more constructivistic teaching approaches.

The second step in the process is for the student to perform the translation correctly by using appropriately chosen terminology, notation, symbols and representation forms/tools such as graphs, charts, tables, diagrams e.t.c. To this end when teachers induce a new representation tool should directly connect it to real-world cases. Initially, this will happen through frontal teaching but over time and as students gain experience teachers will proceed into more interactive and finally constructivistic methods.

The third step is the pure mathematical processing of the data. Here the student is just called to apply correctly his mathematical knowledge.

     

 

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The fourth step is for the student to learn to perform the inverse-translation process. He has to put back within the real-world context his mathematically reached results. He has to learn to interpret them by assigning meaning to them according to the context of the problem. He has to learn whether the results are meaningful and make sense within the specific framework. For the teacher the challenging part here is to choose a variety of examples which lead from totally meaningful results to totally meaningless ones covering as fully as possible the in-between range of meanings. Again here the teacher will proceed gradually from frontal teaching to constructivistic methods according to the level of the class.

Finally, the student needs to develop awareness of the limitations of the chosen mathematical tools. This will possibly lead him to adopt a different mathematical perspective. This in turn will generate from slightly to completely different results. This will push the student to compare the different approaches and discuss strengths and limitations, pros and cons, the scope of each approach. The teacher should deliberately and carefully proceed to this final stage and only after he assures that the student has built a solid foundation of the previous steps. This final stage although admittedly the culminating and most interesting one in the whole mathematicalization process is time and energy consuming. Taking into account the broad syllabus and the specific time limits, one can see that there will not be many opportunities to take this final step over the two years.

4. Prior learning

Mathematics is a linear subject, and it is expected that most students embarking on a Diploma Programme (DP) mathematics course will have studied mathematics for at least 10 years. There will be a great variety of topics studied, and differing approaches to teaching and learning. Thus students will have a wide variety of skills and knowledge when they start the mathematics SL course. Most will have some background in arithmetic, algebra, geometry, trigonometry, probability and statistics. Some will be familiar with an inquiry approach, and may have had an opportunity to complete an extended piece of work in mathematics.

Topics that are considered to be prior learning for the mathematics SL course are:

Topic Content

Number Routine use of addition, subtraction, multiplication and division using integers, decimals and fractions, including order of operations.

Simple positive exponents.

Simplification of expressions involving roots (surds or radicals).

Prime numbers and factors, including greatest common factors and least common multiples.

Simple applications of ratio, percentage and proportion, linked to similarity.

Definition and elementary treatment of absolute value (modulus), | a | .

Rounding, decimal approximations and significant figures, including appreciation of errors.

Expression of numbers in scientific notation that is, a ×10! , 1≤ a <10 , Ζ∈k .

     

 

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Sets and numbers Concept and notation of sets, elements, universal (reference) set, empty (null) set, complement, subset, equality of sets, disjoint sets.

Operations on sets: union and intersection.

Commutative, associative and distributive properties.

Venn diagrams.

Number systems: natural numbers N; integers Z ; rationals Q and irrationals; real numbers R.

Intervals on the real number line using set notation and using inequalities. Expressing the solution set of a linear inequality on the number line and in set notation.

Mappings of the elements of one set to another. Illustration by means of sets of ordered pairs, tables, diagrams and graphs.

Algebra

Algebra

Manipulation of simple algebraic expressions involving factorization and expansion, including quadratic expressions.

Rearrangement, evaluation and combination of simple formulae. Examples from other subject areas, particularly the sciences, should be included.

The linear function and its graph, gradient and y-intercept.

Addition and subtraction of algebraic fractions.

The properties of order relations: < , ≤ , > , ≥ .

Solution of equations and inequalities in one variable, including cases with rational coefficients.

Solution of simultaneous equations in two variables.

Trigonometry Angle measurement in degrees. Compass directions and three figure bearings.

Right-angle trigonometry. Simple applications for solving triangles.

Pythagoras’ theorem and its converse.

Geometry Simple geometric transformations: translation, reflection, rotation, enlargement. Congruence and similarity, including the concept of scale factor of an enlargement.

The circle, its centre and radius, area and circumference. The terms “arc”, “sector”, “chord”, “tangent” and “segment”.

Perimeter and area of plane figures. Properties of triangles and quadrilaterals, including parallelograms, rhombuses, rectangles, squares, kites and trapeziums (trapezoids); compound shapes.

Volumes of prisms, pyramids, spheres, cylinders and cones.

Coordinate geometry

Elementary geometry of the plane, including the concepts of dimension for point, line, plane and space. The equation of a line in the form y =mx +c.

Parallel and perpendicular lines, including the conditions

1 2m m=  and 1 2 1.m m⋅ = −

Geometry of simple plane figures.

The Cartesian plane: ordered pairs (x,y) , origin, axes.

     

 

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Mid-point of a line segment and distance between two points in the Cartesian plane and in three dimensions.

Statistic

and

Probability

Descriptive statistics: collection of raw data; display of data in pictorial and diagrammatic forms, including pie charts, pictograms, stem and leaf diagrams, bar graphs and line graphs.

Obtaining simple statistics from discrete and continuous data, including mean, median, mode, quartiles, range, interquartile range.

Calculating probabilities of simple events. (Adapted from the IBO “Mathematics Guide”)

5. Mathematics and the IB Learner Profile The aim of the IBDP program is to develop internationally minded people who, recognizing their common humanity and shared guardianship of the planet, help to create a better and more peaceful world. Main idea of the program is the development of the IB learner profile, which can be built in a certain academic environment where the participation in each subject promotes its progress.

The process of teaching and learning in mathematics aim to actively promote the development of the following IB learner attributes: • Mathematics  is  a  global  and  multi-­‐disciplinary  language.  The  effective  use  of  this  language  

requires  multiple  modes  of  communication,  which  need  to  be  mutually  reinforcing  and  consistent. Throughout the course students will be asked to communicate this language and collaborate during in-class assignments with classmates of different background knowledge and in many cases from different academic environments. In this way they learn to be communicative and caring.

• Mathematical knowledge provides an important key to understanding the world in which we live.

Throughout the course students are asked to adapt mathematical ideas in a variety of different real life situations. They learn to recognize problems, to consider approaches of solving and to make well thought out decisions in a critical manner. This procedure develops them mathematically, changes the way they think about things and helps them to become knowledgeable and thinkers.

     

 

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• True or false? This question without doubt is closely interwoven with mathematics. Throughout

the course students have the opportunity to reflect on their own work. They learn how to review a procedure, to evaluate a method or to consider what is next. At the same time  they  understand  that  there  are  different  perspectives  in  order  to  approach  a  notion,  which  can  be  equally  effective  or  not.  In  this  way  they  become  reflective, while the power of observation is being confirmed. They also become open minded as they appreciate the importance of a different point of view.

• During their response to the internal assessment,  students  have  the  opportunity  to investigate  a  

specific  area  of  mathematics, working with unfamiliar types of problems.This exploration  enables them to experience the satisfaction of applying mathematical processes independently and sustains their love for learning. In this framework students become inquirers and learn to be risk takers.

• Math is unforgiving, if a student tries to pretend to work at or understand the subject. A good

understanding of math and its elegance can streamline problem solving and make students more effective and efficient. Students are expected to take responsibility for their own work and to manage their time in and out of the class. Multiple forms of homework and different types of assessment, always related with concrete criteria within predetermined time deadlines help students to become principled and balanced.

6. Mathematics and Core Components  

Mathematics  and  TOK  

The study of Mathematics support students in their TOK course. During classes students have the opportunity to:

• Initiate discussions on mathematics as a global language independent of local sociocultural differences, promoting the attitude that mathematics is a common human heritage. They are also encouraged to see mathematics as a global tool independent of local sociocultural structures that helps us to describe both natural and social phenomena. In that way a substantial international mindedness attitude will be promoted in class.

• Initiate discussions on the scientific structure of the discipline. It is important for students to

understand that Mathematics is language with its own “alphabet” (symbols and notations), its own “grammar” and “syntax”. Still this language needs a semantic field on which to act. This is provided by definitions of concepts and axioms. The action of language on the semantic field generates new knowledge on the form of theorems, propositions and lemmata. In that way students will gradually be aware of the nature of the subject and consequently the nature of mathematical knowledge.

     

 

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• Use techniques that help them to develop learning awareness relevant to mathematics and reflect on their mathematical knowledge. To this end teachers attempt to distinguish among different aspects of mathematical learning such as skills and techniques, concepts and ideas, different mathematical perspectives and finally attitudes about mathematics. In that way students will be aware of the different layers of their own learning, from the more specific and applicable to the more general and abstract, in order to identify, after reflection takes place, areas of strengths and weaknesses.

• Develop interdisciplinary links among mathematics, natural sciences and social sciences.

Simultaneously students will be helped to see the power of mathematics as an omnipotent tool in various fields and to enhance their conceptual understanding through specific applications possibly relevant to their own life and interests.

Mathematics and Extended Essay

It is not often for a SL student to complete an extended essay in mathematics. But for those who have a particular interest for the subject, during Math SL course they will have the opportunity to develop the skills and techniques relevant to research process and writing.

Mathematics and CAS.

The study of Mathematics support students in their TOK course. During classes students have the opportunity to : • Interact in a challenging and creative in-class environment that calls for decision making and

innovation on their part. An environment that challenges students’ perspectives, values, mental habits and behavioral patterns. An environment that forces them to reconsider their ways, adapt themselves to new situations and transcend their comfort zone.

• Work towards real-context problems whose solutions generate significant outcomes and calls for reflection.

• To implement practices that promote organizational, planning, recording and monitoring

progress skills and abilities.

• Develop reflection skills, techniques of self-improvement and a mentality that transforms the formal impersonal in-school learning process into a personal learning for which they are responsible.

All the above cultivated attitudes, skills and perspectives in conjunction with students’ ability to transfer them among different environments will support students to complete their CAS tasks in the best way.

     

 

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7. Course structure and planning The course of Mathematics SL consists of the study of the six following topics:

Topic 1: Algebra 1.1 Arithmetic and Geometric sequences and series 1.2 Exponents and Logarithms 1.3 The Binomial theorem

Topic 2: Functions and equations

2.1 Concept of function 2.2 The graph of a function 2.3 Transformations of graphs 2.4 The quadratic function

2.5 The rational function to the form ( ) ax bf xcx d+

=+

2.6 Exponential and Logarithmic functions 2.7 Solving equations 2.8 Applications to real life situations

Topic 3: Circular functions and trigonometry

3.1 The circle 3.2 Trigonometric ratios 3.3 The Pythagorean identity and double angle formulas for sine and cosine 3.4 The circular functions 3.5 Trigonometric equations 3.6 Solution of triangles

Topic 4: Vectors

4.1 The notion of vector 4.2 The scalar product 4.3 Vector equation of a line 4.4 Lines in space

Topic 5: Statistics and probability

5.1 Introductory concepts of descriptive statistics 5.2 Measures of central tendency and measures of spread 5.3 Cumulative frequency (tables-graphs-estimations) 5.4 Linear correlation of bivariate data and regression line 5.5 Introductory concepts of probability 5.6 Conditional probability and independence 5.7 Probability distribution and expected value 5.8 Binomial distribution 5.9 Normal distribution

Topic 6: Calculus

6.1 Derivative as rate of change and as gradient function – tangents and normals 6.2 Derivatives of basic functions and rules of differentiation 6.3 Turning points – inflexions – Graphical behavior of functions – Optimization 6.4 Indefinite integration as anti-differentiation 6.5 Anti-differentiation with boundary condition – Definite integrals – Areas –Volumes 6.6 Kinematic problems

     

 

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Course planing

During the first year of studies students will cover paragraphs 1.2 and 1.3 from topic 1, topics 2, 3 and from topic 5 paragraphs 5.1 to 5.4 , with the remaining ones to be taught during the second year.

Proposed course outline

1st Semester 2nd Semester

IB1 The binomial theorem

Straight line

Introductory concepts of functions

Quadratic functions and equations

Exponential-Logarithmic functions and equations

Circular functions and trigonometry

Statistics

IA Exploration

IB2 Sequences and series

Differentiation

Integration

Probability

Vectors

Revision (two weeks)

Presentation and topic selection for the IA Exploration takes place during the 2nd semester of the first year and it is being completed in the beginning of the 2nd semester of the second year.

Daily workload and classwork

A variety of teaching methods are used in order to accommodate for students’ diverse learning needs.

• Lectures • Individual/group student practice ( in class and homework) • Peer or self - assessment exercises • Small scale assignments based on investigation or modelling • Group presentations • Tests-Quizzes

Students in Mathematics SL will be expected to:

• Study the material delivered during the previous class, using resources such as class notes, course booklets and textbooks.

• Complete assigned homework within predetermined deadlines. This homework is consisted of an appropriate number of exercises before every class, booklets with review exercises based on exam style questions after Christmas/Easter/Summer breaks and small scale assignments as practice towards IA Exploration needs.

• Participate effectively in class activities and discussions • Sit two revision tests on average and several quizzes on a term basis

     

 

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8. Assessment The school’s assessment policy provides details on overall assessment philosophy and practice. This section outlines assessment details related to the subject and compatible with the overall school policy.

In-school assessment

Assessment components that determine a student’s term grade is related with:

• Personal engagement of the student with the lesson, including active class participation and cooperation with classmates, personal motivation and inquiry, willingness for reflection and improvement.

• Diligence regarding due completion of assigned homework

• Performance on tests and quizzes. Tests will be pre-warned and cover a wide predefined range

of material but the use of unwarned quizzes may also be employed. Tests are largely based on exam style questions and are marked according to specific assessment criteria.

Students are marked using the IBDP 1-7 scale. The term grade awarded to students will be a reflection of the student's performance relative to all of the above elements. The term grade will reflect the student’s overall level of achievement in relation to the specified learning outcomes according to the teacher’s professional judgement, based on the overview of assessment information on each student.

All mathematics examinations are simulations of the final IB exam. The length of the exam increases as students’ progress through the IBDP (from approx. 1.5 hours in the IB1 mid-term exam to 3 hours in the IB2 mid-term exam). The mid-term exam in the second year exactly models the final IB exam in terms of length, number and nature of questions to be answered. Student papers in all 3 internal examination sessions are marked by the class teacher and the corresponding grades have an increased weighting towards the final year grade in accordance to the school’s internal regulations. A sample of examination scripts will be cross-marked between Math teachers to ensure consistency of marking, in accordance to the school’s assessment policy. The first year average grade largely determines the predicted grade which is reported by the school in students’ applications to universities (see general regulations)

Final IBDP grade in Mathematics SL

The final IB Diploma grade in Mathematics SL is derived from the student’s performance in externally and internally assessed tasks, as outlined in section 7 and in detail in Appendix.

Grade Descriptors

Achievement levels are described in the corresponding IBO document as follows:

Grade 7 Demonstrates a thorough knowledge and understanding of the syllabus; successfully applies mathematical principles at a sophisticated level in a wide variety of contexts; successfully uses problem-solving techniques in challenging situations; recognizes patterns and structures, makes generalizations and justifies conclusions; understands and explains the significance and reasonableness of results and draws full and relevant conclusions; communicates mathematics in a clear, effective and concise manner, using correct techniques, notation and terminology; demonstrates the ability to integrate knowledge, understanding and skills from different areas of the course; uses technology proficiently.

     

 

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Grade 6 Demonstrates a broad knowledge and understanding of the syllabus; successfully applies mathematical principles in a variety of contexts; uses problem-solving techniques in challenging situations; recognizes patterns and structures, and makes some generalizations; understands and explains the significance and reasonableness of results, and draws relevant conclusions; communicates mathematics in a clear and effective manner, using correct techniques, notation and terminology; demonstrates some ability to integrate knowledge, understanding and skills from different areas of the course; uses technology proficiently.

Grade 5 Demonstrates a good knowledge and understanding of the syllabus; successfully applies mathematical principles in performing routine tasks; successfully carries out mathematical processes in a variety of contexts, and recognizes patterns and structures; understands the significance of results and draws some conclusions; successfully uses problem-solving techniques in routine situations; communicates mathematics effectively using suitable notation and terminology; demonstrates an awareness of the links between different areas of the course; uses technology appropriately.

Grade 4 Demonstrates a satisfactory knowledge of the syllabus; applies mathematical principles in performing some routine tasks; successfully carries out mathematical processes in straightforward contexts; shows some ability to recognize patterns and structures; uses problem-solving techniques in routine situations; has limited understanding of the significance of results and attempts to draw some conclusions; communicates mathematics adequately, using some appropriate techniques, notation and terminology; uses technology satisfactorily.

Grade 3 Demonstrates partial knowledge of the syllabus and limited understanding of mathematical principles in performing some routine tasks; attempts to carry out mathematical processes in straightforward contexts; communicates some mathematics, using appropriate techniques, notation or terminology; uses technology to a limited extent.

Grade 2 Demonstrates limited knowledge of the syllabus; attempts to carry out mathematical processes at a basic level; communicates some mathematics but often uses inappropriate techniques, notation or terminology; uses technology inadequately.

Grade 1 Demonstrates minimal knowledge of the syllabus; demonstrates little or no ability to use mathematical processes, even when attempting routine tasks; is unable to make effective use of technology

(Grade Descriptors, IBO)

9. Academic Honesty In terms of academic honesty, students will be expected to act in accordance to the school-wide academic honesty policy and will be supported in their effort by frequent reinforcement of corresponding principles and practices. Special attention is being given in the cases of Exploration and Extended Essay. Both essays must be entirely student’s own. In terms of daily school life teachers are aware of academic misconduct instances in the case of homework and test. In such cases school’s academic policy is being fully employed. Still the best way is to prevent such practices by nurturing to students a sense of responsibility of their own learning and respect for the work of others.

     

 

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Appendix: Assessment Outline

The student’s final mark is determined externally by their performance in final examination and internally with the Exploration. An outline of the assessment components is given bellow.

External assessment Internal assessment

Paper 1 Paper 2 Exploration

Syllabus content

All six topics All six topics Any area of mathematics

from the syllabus or beyond

Details

No calculator allowed

information booklet provided

Section A

Compulsory

short-response questions based on the

whole syllabus (45 marks)

Section B

Compulsory

extended-response questions based on the

whole syllabus (45 marks)

Graphic display calculator required

information booklet provided

Section A

Compulsory

short-response questions based on the

whole syllabus (45 marks)

Section B

Compulsory

extended-response questions based on the

whole syllabus (45 marks)

It is an integral part of the course and is compulsory for all students. The final report has to be approximately 6 to 12 pages

long.

Total marks 90 marks 90 marks 20 marks

Component time

1 hr 30 min

1 hr 30 min

Presentation and topic selection takes place during the 2nd semester of the first year and it is being completed in the beginning of the 2nd semester of the second year.

Weighting 40% 40% 20%

     

 

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Assessment details

External assessment

Final examination in Math SL consists of two papers, which will contribute 80% of the final mark for the course.

Paper 1 (Duration1 hr 30 min)

This paper is divided into two sections and it is worth 90 marks, representing 40% of the final mark.

• Section A: consists of compulsory short-response questions based on the whole syllabus. It is worth 45 marks, representing 20% of the final mark. The intention of this section is to test students’ knowledge across the breadth of the syllabus. However; it should not be assumed that the separate topics are given equal emphasis.

• Section B: consists of a small number of compulsory extended-response questions based on the whole syllabus. It is worth 45 marks, representing 20% of the final mark. Individual questions may require knowledge of more than one topic. The intention of this section is to test students’ knowledge of the syllabus in depth. The range of syllabus topics tested in this paper may be narrower than that tested in section A.

Calculators Students are not permitted access to any calculator. Questions will mainly involve analytic approaches to solutions, rather than requiring the use of a graphic display calculator (GDC). Mathematics SL information booklet Each student has access to a copy of the information booklet during the examination.

Paper 2 (Duration1 hr 30 min)

This paper is divided into two sections and it is worth 90 marks, representing 40% of the final mark.

• Section A: consists of compulsory short-response questions based on the whole syllabus. It is worth 45 marks, representing 20% of the final mark. The intention of this section is to test students’ knowledge across the breadth of the syllabus. However; it should not be assumed that the separate topics are given equal emphasis.

• Section B: consists of a small number of compulsory extended-response questions based on the whole syllabus. It is worth 45 marks, representing 20% of the final mark. Individual questions may require knowledge of more than one topic. The intention of this section is to test students’ knowledge of the syllabus in depth. The range of syllabus topics tested in this paper may be narrower than that tested in section A.

Calculators Students must have access to a GDC at all times. However, not all questions will necessarily require the use of the GDC. Regulations covering the types of GDC allowed are provided in the Vade Mecum. Mathematics SL information booklet Each student has access to a copy of the information booklet during the examination. (Adapted from the IBO “Mathematics Guide”)

     

 

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Internal assessment

Internal assessment Exploration is an integral part of the course and is compulsory for all students. It enables students to demonstrate the application of their skills and knowledge, and to pursue their personal interests, without the time limitations and other constraints that are associated with written examinations.

Internal assessment in mathematics SL is an individual exploration. This is a piece of written work that involves investigating an area of mathematics. It is marked according to the following five assessment criteria.

The exploration is internally assessed by the teacher and externally moderated by the IB.

Marks allocation Criterion A Communication 4 Criterion B Mathematical presentation 3 Criterion C Personal engagement 4 Criterion D Reflection 3 Criterion E Use of mathematics 6

Total 20