- IB Courses
- 0 (Registered)
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29
Dec
$399.00
$39.00
Applications and Interpretation: Course description
- Mathematics: applications and interpretation will develop mathematical thinking, often in the context of a practical problem and using technology to justify conjectures.
- This course recognizes the increasing role that mathematics and technology play in a diverse range of fields in a data-rich world.
- It emphasizes the meaning of mathematics in context by focusing on topics that are often used as applications or in mathematical modeling. To give this understanding a firm base, this course also includes topics that are traditionally part of a pre-university mathematics course such as calculus and statistics.
- The course makes extensive use of technology to allow students to explore and construct mathematical models.
- Applications and interpretation is a course aiming to address the needs of students who enjoy seeing mathematics used in real-world contexts and to solve real-world problems.
- Applications and interpretation at HL is a course aiming to address the needs of students with a strong mathematical background, who get pleasure and satisfaction when exploring challenging problems and who are comfortable to undertake this exploration using technology. The course gives great emphasis on modeling, statistics, and graph theory.
- Applications and interpretation at SL is a course aiming to address the needs of students who are weak in math and do not wish to undertake math after high school. The course gives a great emphasis on technology to solve practical problems.
Course Content
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Number and Algebra
15-
Lecture1.1Scientific notation
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Lecture1.2Arithmetic sequences and series
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Lecture1.3Geometric sequences and series
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Lecture1.4Financial applications
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Lecture1.5Exponents and logarithms
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Lecture1.6Approximation
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Lecture1.7Amortization and annuity
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Lecture1.8Equations and Systems
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Lecture1.9Laws of logarithms
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Lecture1.10Rational exponents
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Lecture1.11Sum of infinite geometric sequences
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Lecture1.12Complex numbers
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Lecture1.13Modulus–argument (polar) form
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Lecture1.14Matrices
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Lecture1.15Eigenvalues and Eigenvectors
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Functions
10-
Lecture2.1Straight lines
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Lecture2.2Functions
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Lecture2.3The Graph of a functions
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Lecture2.4Key features of graphs
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Lecture2.5Modelling
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Lecture2.6Modelling skills
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Lecture2.7Composite functions and inverse functions
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Lecture2.8Transformation of graphs
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Lecture2.9Further modelling
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Lecture2.10Scaling using logarithms and Linearizing data
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Geometry and Trigonometry
15-
Lecture3.1Three-dimensional space
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Lecture3.2Triangle trigonometry
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Lecture3.3Applications of trigonometry
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Lecture3.4The circle
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Lecture3.5Perpendicular bisectors
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Lecture3.6Voronoi diagrams
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Lecture3.7Trigonometric ratios beyond acute angles
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Lecture3.8Planar transformations
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Lecture3.9Vectors
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Lecture3.10Vector equation of a line
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Lecture3.11Vector kinematics
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Lecture3.12Products of vectors
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Lecture3.13Introduction to graph theory
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Lecture3.14Further matrices
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Lecture3.15Graph algorithms
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Probability and Statistics
20-
Lecture4.1Essential understandings
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Lecture4.2Collection of data and sampling
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Lecture4.3Presentation of data
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Lecture4.4Measures of central tendency and dispersion
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Lecture4.5Linear correlation of bivariate data
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Lecture4.6Probability and expected outcomes
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Lecture4.7Probability calculations
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Lecture4.8Discrete random variables
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Lecture4.9The binomial distribution
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Lecture4.10The normal distribution and curve
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Lecture4.11Further linear regression
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Lecture4.12Hypothesis testing
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Lecture4.13Collecting and analysing data
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Lecture4.14Non-linear regression
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Lecture4.15Variance
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Lecture4.16The central limit theorem
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Lecture4.17Confidence intervals
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Lecture4.18The Poisson distribution
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Lecture4.19Population tests
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Lecture4.20Markov chains
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Calculus
18-
Lecture5.1Introduction to differentiation
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Lecture5.2Increasing and decreasing functions
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Lecture5.3Derivatives of power functions
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Lecture5.4Tangents and normals
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Lecture5.5Introduction to integration
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Lecture5.6Stationary points
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Lecture5.7Optimisation
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Lecture5.8Area of a region
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Lecture5.9Further differentiation
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Lecture5.10Further graph properties
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Lecture5.11Further integration
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Lecture5.12Area and volume
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Lecture5.13Kinematics
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Lecture5.14Differential equations
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Lecture5.15Graphical approximations to differential equations
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Lecture5.16Numerical solutions to differential equations
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Lecture5.17Qualitative and analytical techniques for coupled systems
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Lecture5.18Second order differential equations
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About the Instructor
David is a professor of mathematics education at the Aphy School. His research focuses on social and cultural factors as well as educational policies and practices that facilitate mathematics engagement, learning, and performance, especially for underserved students. Alphy School collaborates with teachers, schools, districts, and organizations to promote mathematics excellence and equity for young people.
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$399.00
$39.00
The aims of all mathematics courses are 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 instill 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.
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