IB Mathematics: Applications and interpretation HL

IB Mathematics Applications and interpretation HL 1
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

Total learning: 78 lessons Time: 53 weeks
  • Number and Algebra
    15
    • Lecture1.1
      Scientific notation
    • Lecture1.2
      Arithmetic sequences and series
    • Lecture1.3
      Geometric sequences and series
    • Lecture1.4
      Financial applications
    • Lecture1.5
      Exponents and logarithms
    • Lecture1.6
      Approximation
    • Lecture1.7
      Amortization and annuity
    • Lecture1.8
      Equations and Systems
    • Lecture1.9
      Laws of logarithms
    • Lecture1.10
      Rational exponents
    • Lecture1.11
      Sum of infinite geometric sequences
    • Lecture1.12
      Complex numbers
    • Lecture1.13
      Modulus–argument (polar) form
    • Lecture1.14
      Matrices
    • Lecture1.15
      Eigenvalues and Eigenvectors
  • Functions
    10
    • Lecture2.1
      Straight lines
    • Lecture2.2
      Functions
    • Lecture2.3
      The Graph of a functions
    • Lecture2.4
      Key features of graphs
    • Lecture2.5
      Modelling
    • Lecture2.6
      Modelling skills
    • Lecture2.7
      Composite functions and inverse functions
    • Lecture2.8
      Transformation of graphs
    • Lecture2.9
      Further modelling
    • Lecture2.10
      Scaling using logarithms and Linearizing data
  • Geometry and Trigonometry
    15
    • Lecture3.1
      Three-dimensional space
    • Lecture3.2
      Triangle trigonometry
    • Lecture3.3
      Applications of trigonometry
    • Lecture3.4
      The circle
    • Lecture3.5
      Perpendicular bisectors
    • Lecture3.6
      Voronoi diagrams
    • Lecture3.7
      Trigonometric ratios beyond acute angles
    • Lecture3.8
      Planar transformations
    • Lecture3.9
      Vectors
    • Lecture3.10
      Vector equation of a line
    • Lecture3.11
      Vector kinematics
    • Lecture3.12
      Products of vectors
    • Lecture3.13
      Introduction to graph theory
    • Lecture3.14
      Further matrices
    • Lecture3.15
      Graph algorithms
  • Probability and Statistics
    20
    • Lecture4.1
      Essential understandings
    • Lecture4.2
      Collection of data and sampling
    • Lecture4.3
      Presentation of data
    • Lecture4.4
      Measures of central tendency and dispersion
    • Lecture4.5
      Linear correlation of bivariate data
    • Lecture4.6
      Probability and expected outcomes
    • Lecture4.7
      Probability calculations
    • Lecture4.8
      Discrete random variables
    • Lecture4.9
      The binomial distribution
    • Lecture4.10
      The normal distribution and curve
    • Lecture4.11
      Further linear regression
    • Lecture4.12
      Hypothesis testing
    • Lecture4.13
      Collecting and analysing data
    • Lecture4.14
      Non-linear regression
    • Lecture4.15
      Variance
    • Lecture4.16
      The central limit theorem
    • Lecture4.17
      Confidence intervals
    • Lecture4.18
      The Poisson distribution
    • Lecture4.19
      Population tests
    • Lecture4.20
      Markov chains
  • Calculus
    18
    • Lecture5.1
      Introduction to differentiation
    • Lecture5.2
      Increasing and decreasing functions
    • Lecture5.3
      Derivatives of power functions
    • Lecture5.4
      Tangents and normals
    • Lecture5.5
      Introduction to integration
    • Lecture5.6
      Stationary points
    • Lecture5.7
      Optimisation
    • Lecture5.8
      Area of a region
    • Lecture5.9
      Further differentiation
    • Lecture5.10
      Further graph properties
    • Lecture5.11
      Further integration
    • Lecture5.12
      Area and volume
    • Lecture5.13
      Kinematics
    • Lecture5.14
      Differential equations
    • Lecture5.15
      Graphical approximations to differential equations
    • Lecture5.16
      Numerical solutions to differential equations
    • Lecture5.17
      Qualitative and analytical techniques for coupled systems
    • Lecture5.18
      Second order differential equations

About the Instructor

David David

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:

  1. develop a curiosity and enjoyment of mathematics, and appreciate its elegance and power
  2. develop an understanding of the concepts, principles, and nature of mathematics
  3. communicate mathematics clearly, concisely and confidently in a variety of contexts
  4. develop logical and creative thinking, and patience and persistence in problem-solving to instill confidence in using mathematics
  5. employ and refine their powers of abstraction and generalization
  6. 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
  7. appreciate how developments in technology and mathematics influence each other
  8. appreciate the moral, social and ethical questions arising from the work of mathematicians and the applications of mathematics
  9. appreciate the universality of mathematics and its multicultural, international and historical perspectives
  10. appreciate the contribution of mathematics to other disciplines and as a particular “area of knowledge” in the TOK course
  11. develop the ability to reflect critically upon their own work and the work of others
  12. independently and collaboratively extend their understanding of mathematics.
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