What do we know about rational functions? - This routine helps us to activate our prior knowledge about rational functions, which are functions that can be expressed as a ratio of two polynomials. What are the key features of rational functions? - This routine helps us to identify the important characteristics of rational functions, such as asymptotes, intercepts, and the behavior of the function as the input variable approaches positive or negative infinity. How do reciprocal functions relate to rational functions? - This routine helps us to make connections between rational functions and their reciprocal functions, which are functions that can be expressed as 1 over the original function. What is the general form of a reciprocal function? - This routine prompts us to recall the general form of a reciprocal function, which is y = 1/x. How do the graphs of rational and reciprocal functions differ? - This routine encourages us to compare and contrast the graphs of rational and reciprocal functions, noting similarities and differences in their behavior. What real-world situations can be modeled using rational and reciprocal functions? - This routine prompts us to think about real-world scenarios that can be described using these types of functions, such as the spread of disease or the movement of celestial bodies. What are some common misconceptions about rational and reciprocal functions? - This routine helps us to identify common misunderstandings or errors that people may have when working with these functions. What strategies can we use to solve problems involving rational and reciprocal functions? - This routine prompts us to think about problem-solving techniques, such as graphing or algebraic manipulation, that can be used to analyze and solve problems involving these functions. How can we apply our understanding of rational and reciprocal functions in other contexts? - This routine encourages us to reflect on the broader applications of our knowledge, such as in fields like engineering, economics, or physics.

How do we choose the axioms underlying mathematics? Is this an act of faith? “Mathematics is the language with which God wrote the Universe” – Galileo TOK concepts: perspectives and evidence.

Curriculum: IB DP Unit: Calculus Subject: Mathematics Concepts: Integration by substitution Resource: Worksheet

Binomial worksheet: Describes the algebraic expansion of powers of a binomial. What happens when we multiply a binomial by itself ... many times?

This worksheet helps the learner to Identify Maximum/ minimum and justify the result. Determine Point of inflexion and justify the result.

Aim of the worksheet is to enhance the skills of arithemtic & Geometric sequence and series.

This worksheet helps the students to how to plot the points on the grid ,draw a line of best fit and identify what type of correlation.

Two vectors are equal if they have the same magnitude and direction.

The statement “This statement is false” presents a classic paradox, often referred to as the liar paradox. This paradox raises intriguing questions about truth, logic, and the foundations of mathematics.To analyze the statement “This statement is false” and its implications on the view of mathematics as an area of knowledge, I can further explore this concept, such as language, reason, and the nature of mathematics itself

Task Overview: In this task, we will explore the concepts of inductive reasoning as applied in scientific inquiry and mathematical induction. While both methods involve drawing conclusions based on observed patterns or examples, they differ significantly in their underlying principles and applications. By comparing and contrasting these approaches, we aim to deepen our understanding of how reasoning methods vary across disciplines.

Justifying the use of statistics to mislead others raises ethical and epistemological concerns, particularly in the context of knowledge and mathematics. Here’s an exploration of how this can occur and the implications for evidence and certainty.

IB AA HL & SL Revision worksheet Integral calculus This worksheet focuses on Calculus describes rates of change between two variables and the accumulation of limiting areas. Understanding these rates of change and accumulations allow us to model, interpret and analyze realworld problems and situations. Calculus helps us to understand the behaviour of functions and allows us to interpret the features of their graphs Command Terms: Show that : Obtain the required result (possibly using information given) without the formality of proof. “Show that” questions do not generally require the use of a calculator. Find:Obtain an answer showing relevant stages in the working

This worksheet structure should help students practice applying the binomial theorem, understanding binomial coefficients, and exploring related concepts

Revision worksheet Differentiation

Trigonometry worksheets are designed to reinforce understanding of these concepts through practice problems of varying difficulty levels.

Exam-style questions on complex numbers in the IB Mathematics curriculum often cover a range of topics, testing both theoretical understanding and problem-solving skills. Here are some typical types of questions you might encounter.

In contemplating the role of mathematics in understanding the universe, one must navigate a complex landscape of philosophical inquiry, scientific discovery, and cognitive theory. The proposition that mathematics might not merely describe the universe but represent the fundamental language or logical system employed by the brain to interact with reality challenges conventional notions about the nature of mathematics and its relationship to the cosmos.

The following points are discussed with evidences First-order knowledge questions: What are the various ways language impacts the understanding of mathematical concepts? How do mathematical symbols contribute to the precision and clarity of mathematical communication? In what ways does linguistic variation influence the acquisition of mathematical knowledge across different cultures? How does the use of different languages affect the interpretation and application of mathematical principles? What role does symbolic representation play in simplifying complex mathematical ideas? Second-order knowledge questions: To what extent does linguistic diversity in mathematics contribute to a deeper appreciation of cultural perspectives in mathematical reasoning? How can standardized mathematical symbols bridge language barriers and facilitate global mathematical collaboration? How does the interpretation of mathematical symbols differ based on cultural and linguistic contexts? How might the development of a universal mathematical language enhance the communication and understanding of mathematical concepts worldwide?

Knowledge questions: How can calculus be used to inform both theory-led and data-led modeling approaches in understanding complex phenomena? Theory-led vs. Data-led Modeling: Harnessing Knowledge for Predictive Relationships