Applications and Interpretations is a Mathematics course that focuses on the application of mathematical concepts to real-world scenarios. This course is well-suited for students who are interested in pursuing careers in fields such as Business, Economics, the Natural Sciences (other than Physics) and the Social Sciences, as it emphasizes the practical use of Mathematics in these areas, including the use of mathematical models to interpret and analyse data. Students studying this course are encouraged to think critically and creatively. Proficiency in English is encouraged as much of the exam requires reading a situation and then applying the correct mathematics accordingly. 

It is important for students to carefully consider their interests and career goals when choosing which IB Mathematics course to study. Both courses are valuable in their own right and will lead students to successful careers, but understanding the differences between them can help students make an informed decision about which course is best aligned with their particular ambitions and aspirations. 

The IB DP Mathematics: applications and interpretation course recognizes 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.

• • 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.

Prerequisite Knowledge 

• • Standard Level

    • • Algebra Skills 

        1. Simplifying Expressions

        2. Solving Equations

        3. Solving Hard Equations (including square roots)

        4. Factoring and Expanding Brackets

        5. Forming Equations from Real World Scenarios 

      • Graphing Skills

        1. Linear Graphing

        2. Quadratic Graphing

        3. This topic is a big deal. Graphs are a foundation for many key topics in IB Maths. Spend some time perfecting this before you begin the course. 

      • Trigonometry

        1. Pythagorean Theorem

        2. Right Triangle Trigonometry

  •  Higher Level - In Addition to the Standard Level Knowledge Above

    • • Students who wish to take Mathematics: applications and interpretation at higher level will have good algebraic skills and experience of solving real-world problems. They will be students who get pleasure and satisfaction when exploring challenging problems and who are comfortable to undertake this exploration using technology.

• Statistics and Probability

  1. Students are required to learn a variety of statistic tests and probability functions. Not only does this require deep mathematical understanding, but the ability to read a problem and using context clues identify the appropriate statistical test to use

  2. This is an area that most students will be brand new to. Therefore it is essential they like learning new mathematics and doing mathematical investigations

The final grade (1-7) is a combined grade based on the Internal Assessment (written investigative report/exploration) and the External Assessment (examinations) 

Standard Level

Internal Assessment 20% 

External Assessment 80% - All exams require a calculator 

• Paper 1 - 40% - Short Response Questions. 80 Marks in 90 Minutes

• Paper 2 - 40% - Extended Response Questions. 80 Marks in 90 Minutes

Higher Level

Internal Assessment 20% 

External Assessment 80% - All exams require a calculator

• Paper 1 - 30% - Short Response Questions. 110 Marks in 120 Minutes

• Paper 2 - 30% - Extended Response Questions. 110 Marks in 120 Minutes

• Paper 3 - 20% - 2 Difficult Investigative Problems. 55 Marks in 75 Minutes 

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: applications and interpretation and to Mathematics: analysis and approaches.

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.

The goal of each course is to finish the syllabus by Christmas of G12. This leaves the second semester of grade 12 free to revise and prepare for the upcoming exams. Therefore, a rough outline of the two year course is typically as follows.

Grade 11

8 Units and 8 Unit Exams - 70% of the Class Grade

End of Year Cumulative Exam (Mock Exam) - 30% of the Class Grade

Introduction to the Internal Assessment (Exploration) 

This is introduced in February of Grade 11 and every month there are mini-deadlines the students are expected to meet. The final draft is then submitted in December of G12. 

Grade 12

4 Units and 4 Unit Exams - 70% of the Class Grade

G12 Mock Exams - 30% of the Class Grade

Resources and Necessary Equipment 

Students are Responsible for…

• A graphical display calculator. The TI-84 Plus CE-T is the recommended calculator as it is what will be used by the teacher when demonstrating how to use the calculator. 

• A tablet or laptop

Students will be given access to…

• Class notebooks

• Class Textbooks

Concepts Students will Develop and Related ATL Skills

1. Make sense of problems and persevere in solving them. Thinking

2. Reason abstractly and quantitatively.Thinking

3. Construct viable arguments and critique the reasoning of others.Transfer

4. Model with mathematics. Logic

5. Use appropriate tools strategically. Research

6. Attend to precision. Communication

7. Look for and make use of structure. Form

8. Look for and express regularity in repeated reasoning.Communication

Inquiry Based Learning

Despite the exam based rigors and time constraints in the Mathematics courses of the Diploma Program, Inquiry Based Learning is still a prime driver of the way lessons are delivered here at DISV.

 In the DP subject guide we find a short paragraph about the need for inquiry, problem solving and critical thinking. Teachers are encouraged to take approaches and use tools "intrinsically linked to the IB learner profile, which encourages learning by experimentation, questioning and discovery." 

However, applying generic features of inquiry, such as the IB's learner profile, across disciplines risks losing sight of the specific nature of inquiry in mathematics.

The guide addresses this issue by presenting a cycle of mathematical inquiry in the form of a flow chart (see image). The cycle's five steps - four processes (in rectangles) and one conditional operation that leads to a decision (in a rhombus) - are presented without explanation. We review each step below.

• Explore the content

The first step combines a process (explore) with the field of inquiry (content). In its simplicity, the step masks a complex relationship. The source of the content (curriculum, teacher or student) and the students' first contact with the content (through a teacher's question or a prompt) are both important - one might even say crucial - in motivating the class to explore. 

There is also the issue of what 'explore' means for different content. While the step suggests that the nature of 'explore' does not change, this is not the case. The form of exploration has to be worked out in conjunction with the content for each new inquiry. Exploration could mean, amongst others, generating more examples of the same type, testing different types of cases or delving into the structure of one case.

• Make a conjecture

A conjecture normally arises in the classroom when students notice a result or property occurs more than once and speculate that the pattern will hold in the future. How is the conjecture related to the content of the first step? Does this step mean that the only legitimate content for inquiry is that which will yield a pattern and is, therefore, susceptible to a conjecture?

• Test the conjecture

The process by which a student determines the conditions under which a conjecture is true or not has the potential to lead to deep mathematical learning. Unfortunately, the binary choice in the IB cycle - either accept or reject the conjecture - restricts that potential.

The either-or approach to conjectures is not how mathematicians think. They might accept the conjecture in forming a generalisation, but only within certain constraints. For example, a straight line is the shortest distance between two points in Euclidean geometry, but that is not necessarily the case in non-Euclidean geometry. When students reason that "conjecture A is true within constraint B, but is not true outside that constraint", their inquiry acquires greater depth.

• Justify

'Justify' is a curious term as a discrete step in mathematical inquiry. A student might justify a decision, but the proof of a generalisation requires rigorous deductive reasoning. Whether such reasoning rests on structural analysis or employs algebraic tools, it amounts to far more than the term 'justify' suggests.

• Extend

The final step implies that inquiry is never-ending. There are always new contexts in which students can test a generalisation; there are always connections that can be made to other fields of inquiry. While this is true, is it helpful to have 'extend' as a separate and necessary part of mathematical inquiry? After all, students also need to learn how to decide when an inquiry has reached a satisfactory conclusion.

• Mr. Andy Hutchinson |  ahutchinson@danubeschool.com 

• Mr.Chee Wong |  cwong@danubeschool.com 

Appointments: Arrange by email.