Mathematics:

Application and Interpretation

Ms. Sheikh

Course Description

The IB DP Mathematics: applications and interpretation course recognize the increasing role that mathematics and technology play in a diverse range of fields in a data-rich world. As such, it emphasizes the meaning of mathematics in context by focusing on topics that are often used as applications or in mathematical modelling. To give this understanding a firm base, this course includes topics that are traditionally part of a pre-university mathematics course such as calculus and statistics. Students are encouraged to solve real-world problems, construct and communicate this mathematically and interpret the conclusions or generalizations. Students should expect to develop strong technology skills, and will be intellectually equipped to appreciate the links between the theoretical and the practical concepts in mathematics. All external assessments involve the use of technology. 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

Unit Titles

• This course prepares the student for the required Standard Level IB examination in Mathematical Studies. This IB course is weighted by applying an additional 1.0 quality point value assigned to the final grade upon completion of the course. Topics covered in this course include:

Topic 1: Numbers and Algebra

Topic 2: Functions

Topic 3: Geometry and trigonometry

Topic 4: Statistical applications

Topic 5: Calculus

Topic 1: Numbers and Algebra

Operation with numbers in Scientific notation form, Arithmetic Sequences and series, Geometric sequences and series, Use of Sigma notation for the sum of Geometric sequences, Financial applications of geometric sequences and series, Compound interest and annual depreciation, Law of exponents with integer exponents, Approximation: decimal places, significant figures, Upper and lower bounds of rounded numbers. Percentage errors, Amortization and annuities using technology Use technology: system of linear equations in up to 3 variables, Polynomial equations.

Topic 2: Functions:

Different forms of the equation of straight line, Concept of Functions, analyzing graph of functions, inverse function, Linear models, Quadratic models, Exponential growth and decay models, Direct/inverse variation: Cubic models, Sinusoidal models

Topic 3: Geometry and Trigonometry

The distance between two points in three-dimensional space, and their mid point; volume and surface area of three-dimensional solids including right-pyramid, right cone, sphere, hemisphere and combinations of these solids; the size of angle two intersecting lines or between a line and a plane. Use of sine, cosine and tangent ratios to find the sides and angles of right-angled triangles; the sine rule, not including the ambiguous case; the cosine rule; area of triangle as 1/2 ab SinC. Application of right and non-right-angled trigonometry, including Pythagoras theorem. Context may include use of bearings; angles of elevations and depression; construction of labelled diagram from written statements. The Circle: length of an arc; area of a sector. Equations of perpendicular bisector. Voronoi diagrams; sites, vertices, edge, cells; addition of a site to an existing Voronoi diagram; nearest neighbor interpolations; applications including the “toxic waste dump” problem.

Topic 4: Probability and statistics

The aim of the content in the statistics and probability topic is to introduce students to important concepts, techniques and representations used in statistics and probability and their meaningful application in the real world. Students should be given the opportunity to approach this topic in a practical way, to understand why certain techniques are used and to interpret the results. The use of technology such as simulations, spreadsheets, statistics software and statistics apps can greatly enhance this topic. It is expected that most of the calculations required will be carried out using technology, but explanations of calculations by hand may enhance understanding. students will deal with missing data, interquartile range (IQR), outliers, cumulative frequency, median, mode, mean, BOX and whisker diagram, Measures of central tendency.

Topic 5: Calculus

Introduction of concept of limit, Derivative interpreted as gradient function and as a rate of change. Increasing and Decreasing functions. Estimation of the value a limit from a table or graph. Tangents and normal at a given points and their equations, Introduction of integration as antidifferentiation of functions. Definite integrals using technology. Link between antiderivatives, definite integrals and area. Optimization. Approximating areas using trapezoidal rule.

In additions you will be able to demonstrate your ability to:

1. Read, interpret, and solve problems using appropriate mathematical terms.

2. Organize and represent information in tabular, graphical, and diagrammatic forms.

3. Know and use appropriate notations and terminology.

4. Formulate a mathematical argument and communicate it clearly.

5. Select and use appropriate mathematical strategies and techniques.

6. Demonstrate an understanding of both the significance and the reasonableness of results.

7. Recognize patterns and structures in a variety of situations and make generalizations.

8. Recognize and demonstrate an understanding of the practical applications of mathematics.

9. Use appropriate technological devices as mathematical tools.

10. Demonstrate an understanding and the appropriate use of mathematical modeling

IB Learner Profile

The aim of all IB programs is to develop internationally minded people who strive to be:

1. Inquirers 6. Open-minded

2. Knowledgeable 7. Caring

3. Thinkers 8. Risk-Takers

4. Communicators 9. Balanced

5. Principled 10. Reflective

Because of this, I will not be up in front of class telling you how to do things as much as I will be guiding you to learn how to understand the concepts on your own or with your classmates. This math course will require much more reading than your previous math courses. Please do not skim over the material. The changes in vocabulary and notation from your previous courses to this course are great and will be vital to your success in this class.