The IB DP Mathematics: analysis and approaches course recognizes the need for analytical expertise in a world where innovation is increasingly dependent on a deep understanding of mathematics. The focus is on developing important mathematical concepts in a comprehensible, coherent and rigorous way, achieved by a carefully balanced approach. Students are encouraged to apply their mathematical knowledge to solve abstract problems as well as those set in a variety of meaningful contexts. Mathematics: analysis and approaches has a strong emphasis on the ability to construct, communicate and justify correct mathematical arguments. Students should expect to develop insight into mathematical form and structure, and should be intellectually equipped to appreciate the links between concepts in different topic areas. Students are also encouraged to develop the skills needed to continue their mathematical growth in other learning environments. The internally assessed exploration allows students to develop independence in mathematical learning. Throughout the course students are encouraged to take a considered approach to various mathematical activities and to explore different mathematical ideas.

Mathematics SL Analysis and Approaches is a course designed for students who wish to study a good level of mathematics, but not at a higher level. It will appeal to students who are interested in exploring real and abstract applications of mathematical concepts. They will enjoy problem solving and generalisation. This course is suitable for students who may go on to further study in subjects that have a mathematical background, for example economics, geography and chemistry.  

The course contains investigative and inquiry-based learning, supporting students in their internally assessed exploration task. There is some content that is common with the Mathematics SL Applications and Interpretations course but the Mathematics SL Analysis and Approaches has a greater emphasis on calculus, and theoretical approaches.

Aims of the course is to enable students to:

• develop a curiosity and enjoyment of mathematics, and appreciate its elegance and power
• develop an understanding of the concepts, principles and nature of mathematics
• communicate mathematics clearly, concisely and confidently in a variety of contexts
• develop logical and creative thinking, and patience and persistence in problem solving to instil confidence in using
• mathematics
• employ and refine their powers of abstraction and generalization
• take action to apply and transfer skills to alternative situations, to other areas of knowledge and to future developments
• in their local and global communities
• appreciate how developments in technology and mathematics influence each other
• appreciate the moral, social and ethical questions arising from the work of mathematicians and the applications of
• mathematics
• appreciate the universality of mathematics and its multicultural, international and historical perspectives
• appreciate the contribution of mathematics to other disciplines, and as a particular “area of knowledge” in the TOK
• course
• develop the ability to reflect critically upon their own work and the work of others
• independently and collaboratively extend their understanding of mathematics.

Key features of the Curriculum

• Available only at standard level (SL)
• The minimum prescribed number of hours is 150
• The course will take place over a 2 year period
• Students are assessed both internally and externally
• Paper 1 and paper 2 are externally set and externally marked. Together, they contribute 80% of the final mark for the course. Both papers are 1 hour and 30 minutes each.
• Paper 1 consists of compulsory short-response questions. Questions on paper 1 will vary in terms of length and level of difficulty. A Graphic Display Calculator (GDC) is required for this paper, but not every question will necessarily require its use. The intention of paper 1 is to test students’ knowledge and understanding across the breadth of the syllabus.
• Paper 2 consists of compulsory extended-response questions. Questions on paper 2 will vary in terms of length and level of difficulty. A Graphic Display Calculator (GDC) is required for this paper, but not every question will necessarily require its use. Knowledge of all topics is required for this paper. The intention of this paper is to assess students’ knowledge and understanding of the syllabus in depth. The range of syllabus topics tested in this paper may be narrower than that tested in paper 1. Questions of varying levels of difficulty and length are set.
• Internal assessment is a mathematical exploration that is internally assessed by the teacher and externally moderated by the IB using assessment criteria that relate to the objectives for mathematics. The specific purposes of the exploration are to:
• develop students’ personal insight into the nature of mathematics and to develop their ability to ask their own questions about mathematics
• provide opportunities for students to complete a piece of mathematical work over an extended period of time
• enable students to experience the satisfaction of applying mathematical processes independently Internal assessment 84 Mathematics: applications and interpretation guide
• provide students with the opportunity to experience for themselves the beauty, power and usefulness of mathematics
• encourage students, where appropriate, to discover, use and appreciate the power of technology as a mathematical tool
• enable students to develop the qualities of patience and persistence, and to reflect on the significance of their work
• provide opportunities for students to show, with confidence, how they have developed mathematically.

… the internal assessment represents 20% of the students’ grade.   

Assessments:

Paper 1 – No technology allowed.

Section A: compulsory short-response questions based on the syllabus.

Section B: compulsory extended-response questions based on the syllabus.

Duration: 1 hour 30 minutes                           [Weighting: 40%]

Paper 2 – Technology allowed.

Section A: compulsory short-response questions based on the syllabus.

Section B: compulsory extended-response questions based on the syllabus

Duration: 1 hour 30 minutes                           [Weighting: 40%]

Internal Assessment – Mathematics exploration

Development of investigational, problem-solving and modelling skills and the exploration of an area of mathematics                                         [Weighting: 20%]

Assessment 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. The assessment objectives are common to Mathematics: analysis and approaches and to Mathematics: applications and interpretation.

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

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

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; use appropriate notation and terminology.

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

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

Inquiry approaches: Investigate unfamiliar situations, both abstract and from the real world, involving organizing and analysing information, making conjectures, drawing conclusions, and testing their validity. The exploration is an integral part of the course and its assessment, and is compulsory for both SL and HL 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.

Course Outline:

Topics:

            Topic 1:           Number & Algebra                  (1.1-1.7)          19 hours

            Topic 2:           Functions                                (2.1-2.10)         21 hours

            Topic 3:           Geometry & Trigonometry      (3.1-3.7)           25 hours

            Topic 4:           Statistics & Probability            (4.1-4.11)         27 hours

            Topic 5:           Calculus                                  (5.1-5.11)         28 hours

                    IA:           Internal Assessment                                       30 hours

                                                            Total Teaching Hours:            150 hours

Plan:

Year 1:            60% of the syllabus

            ————————————————————————————–

            Topic 1:          Number & Algebra

• 1.1 Numbers – Rounding – Scientific Form
• 1.2 Methods of Proof
• 1.3 Sequences/Series (in general)
• 1.4 Arithmetic Sequences/Series
• 1.5 Geometric Sequences/Series
• 1.6 Applications of G.S. – Percent Growth
• 1.7 The Binomial Theorem

            ————————————————————————————–

            Topic 2:          Functions

• 2.1 Lines (or Linear Functions)
• 2.2 Quadratics (or Quadratic Functions)
• 2.3 Functions, Domain, Range, Graph
• 2.4 Composition of Functions:
• 2.5 The Inverse Function:
• 2.6 Transformation of Functions
• 2.7 Asymptotes
• 2.8 Exponents (the Exponential Function )
• 2.9 Logarithms (the Logarithmic Function: )
• 2.10 Exponential Equations

            ————————————————————————————–

            Topic 3:          Geometry & Trigonometry

• 3.1 3D Geometry
• 3.2 Triangles – Sine & Cosine Rules
• 3.3 Applications of 3D Geometry – Navigation
• 3.4 The Unit Circle – Arcs & Sectors
• 3.5 The Unit Circle – , , &
• 3.6 Trigonometric Identities and Equations
• 3.7 Exponential Equations

            ————————————————————————————–

            Topic 4:          Statistics & Probability

• 4.1 Basic Concepts of Statistics
• 4.2 Measures of Central Tendency
• 4.3 Frequency Tables – Grouped Data
• 4.4 Regression

            ————————————————————————————–

Year 2:            40% of the syllabus

            ————————————————————————————–

            Topic 4:          Statistics & Probability (continued)

• 4.5 Elementary Set Theory
• 4.6 Probability
• 4.7 Conditional Probability – Independent Events
• 4.8 Tree Diagrams
• 4.9 Distributions – Discrete Random Variables
• 4.10 Binomial Distribution – 
• 4.11 Normal Distribution – 

————————————————————————————–

Year 2:            40% of the syllabus  (continued …)

————————————————————————————–

            Topic 5:          Calculus

• 5.1 Using Limits to Define the Derivative of a Function
• 5.2 Derivatives of Known Functions – Rules
• 5.3 Tangent & Normal Lines (defined at a point )
• 5.4 The Chain Rule
• 5.5 Monotonicity & Extrema
• 5.6 Concavity & Points of Inflection
• 5.7 Optimization
• 5.8 The Indefinite Integral
• 5.9 Integration by Substitution
• 5.10 The Definite Integral (Areas and Volumes)
• 5.11 Kinematics (Displacement, Velocity & Acceleration)

——————————————————————————————————————–

Alternative Plan:

            Swap               Year 1             § 4.1, § 4.2, § 4.3 and § 4.4

            With                 Year 2             § 5.1, § 5.2, § 5.3 and § 5.4

——————————————————————————————————————–

            Curriculum Links                                 GCD Skills (Notes)

            IA: Additional Resources                    Formula Booklet

            Video Library & Complete Course Notes (PDF)

——————————————————————————————————————–

Projects:        

Topic 1:          

Topic 2:          

Topic 3:           What in the Daylights!                                     [trigonometric transformations]

Topic 4:           The Sum of It All  (Data Collection)                [probability, binomial/normal]

Topic 5:           Roller Coaster Design                                    [continuity, derivatives, tangents]

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