Mathematics SL
Course Guide for Graduates in 2017
Philosophy:
The IB Diploma Programme mathematics standard level course is for students with knowledge of basic mathematical concepts who are able to apply mathematical techniques correctly. The course provides students with a sound mathematical background to prepare for future studies in subjects such as chemistry, economics, psychology and business administration. Students will be introduced to important mathematical concepts through the development of mathematical techniques in a way that emphasizes subject comprehension rather than mathematical rigor. Students should, where possible, apply the acquired mathematical knowledge to solve realistic problems. The course will enable you to:
- Appreciate the multicultural, international, and historical perspectives of mathematics
- Enjoy the course and develop an appreciation of the elegance, power and usefulness of mathematics
- Develop logical, critical and creative thinking
- Develop an understanding of the principles and nature of mathematics
- Employ and refine powers of abstraction and generalization
- Develop patience and persistence in problem solving
- Appreciate the consequences arising from technological developments
- Transfer skills to alternative situations and to future developments
- Communicate clearly and confidently in a variety of contexts
Course outline:
There are six topics to the Mathematics SL course. The topics are listed here together, but will be taught in a different order over the two years, to allow for a gradual improvement in skills, and a grouping of topics by theme.
Topic 1 Algebra The aim of this topic is to introduce students to some basic algebraic concepts and applications. Sub-topics in this section:
- Arithmetic sequences and series
- The binomial theorem
- Elementary treatment of exponents and logarithms
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. Sub-topics in this section:
- Concept of function
- Identity function. Inverse function
- The graph of a function and its equation
- Transformations of graphs
- The quadratic function
- The reciprocal function
- Exponential functions and their graphs
Topic 3 Circular functions and trigonometry The aims of this topic are to explore circular functions and to solve problems using trigonometry. Sub-topics in this section:
- The circle: radian measure of angles; length of an arc; area of a sector
- Relationship between trigonometric ratios
- The circular functions
- Solving trigonometric equations in a finite interval, both graphically and analytically
Topic 4 Vectors The aim of this topic is to provide an introduction to vectors, including both algebraic and geometric approaches. Sub-topics in this section:
- Vectors as displacements in the plane and in three dimensions
- The scalar product of two vectors
- The angle between two lines
Topic 5 Statistics and probability The aim of this topic is to introduce statistics and probability concepts. It is expected that most of the calculations required will be done using technology, but explanations of calculations by hand may enhance understanding. The emphasis is on in context understanding and interpreting of results obtained. Sub-topics in this section:
- Concepts of population, sample, random sample, discrete and continuous data.
- Continuous and discrete data. Presentation of data: frequency distributions (tables); frequency histograms with equal class intervals
- Statistical measures and their interpretations
- Concepts of trial, outcome, equally likely outcomes
- Binominal and Normal distribution
Topic 6 Calculus The aim of this topic is to introduce students to the concepts and techniques of differential and integral calculus and their applications. Sub-topics in this section:
- Informal ideas of limit and convergence
- The chain rule for composite functions. The product and quotient rules
- The second derivative. Extension to higher derivatives
- Anti-differentiation with a boundary condition to determine the constant term
Assessment:
Exam paper 1– Mental calculations only |
Externally assessed – 40% |
Exam paper 2 – Calculators allowed |
Externally assessed – 40% |
Exploration – Course work project |
Internally assessed – 20% |
- Exams are written in May of the second year
- Paper one is completed without the use of calculators
- Paper two is completed with the use of calculators
- The Exploration is a piece of work based on different areas of the syllabus, demonstrating mathematical investigation and modeling techniques
- The Explorations is introduced in May of the first year and is handed in by October of the second year
- Check Managebac for all major assessment due dates
Math Studies
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Mathematics HL (Online)
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