In this DP Mathematics AI 2.1 subtopic, students learn to change between the different forms of the equation of a straight line. They use the properties of parallel and perpendicular lines to write equations of lines using the Desmos activity "Parallel and Perpendicular Lines." Students also get open-ended practice with line equations and plan a slalom skiing route.

Overview

Lesson 1: Equations of a Straight Line and Intercepts / Solution

Lesson 2: Finding Gradients / Solution

Lesson 3: Slalom! / Solution

These DP Mathematics AI 2.2-2.3 materials contain sets of questions and an exploration to help students understand inverse functions. Students answer the questions and provide the reasoning for their answers to emphasise the importance of understanding over simply knowing. There is also a handout to help students with some basic approaches to reproducing graphs. Students often think that graphs are difficult because of the accuracy required, so encourage sketches instead of drawings.

Overview

Teacher Notes

Lesson 1: Recognizing Functions Questions

Lesson 2: Domain and Range Questions ( A / B )

Lesson 3: Mathematical Models Questions ( A / B )

Lesson 4: Inverse Functions Exploration

Lesson 5: Inverse Functions Questions ( A / B )

Lesson 6: Tips for Displaying Graphs

This DP Mathematics AI 2.4 section covers introductory concepts surrounding curves, lines and graphs. There is a brief overview of the concepts and the two activities make connections between drawing curves with straight lines and drawing in perspective. GeoGebra and the GDC are the main technological tools in both activities. This topic should be taught alongside section 2.5, which looks at related concepts for individual classes of curves in more detail.

Overview

Teacher Notes

Lesson 1: Key Features of a Function

Lesson 2: Graphing Arts

This DP Mathematics SL 2.6 set is designed around three activities highlighting the application of mathematical models. Activity 1 shows students how to write a mathematical essay through a guided IA on earthquakes that uses modelling, regressions and applications. Activity 2 is designed to use the modelling process to create, fit and use theoretical models. Activity 3 applies quadratic models to Olympic diving and teaches principles of systematic mathematical modeling.

Overview

Lesson 1: Let's Make an IA on "Earthquakes" with Guidance / Solution

Lesson 2: Let's Go on a Vacation / Solution

Lesson 3: How to Become an Olympic Champion by Using Quadratic Models / Solution

In this DP Mathematics AI 2.8 set, students begin with a reciprocal function using a table of points and then list the characteristics of this transformation. They find asymptotes and a visual understanding of curve shape. They sketch graphs of reciprocal functions of different types of functions. They also learn the characteristics and graphical representations of rational expressions and how to graph them without technology.

Overview

Lesson 1: Reciprocal Functions / Teacher Notes

Lesson 2: Rational Functions / Teacher Notes

In this DP Mathematics AI AHL 2.8 unit, students investigate the effects of a, b, c, and d when parent function y = f(x) is transformed into y = af(b(x+c)) + d. Initially, they work with quadratics and then consider further functions. Throughout the set, students are encouraged to use technology (e.g., GDC or Desmos) to “see” the effects of these parameters. This will help strengthen the connections between the algebra and the graphs of the functions.

Overview

Lesson 1: Transformations of Quadratics / Solution

Lesson 2: Combined Transformations on Quadratics / Solution

Lesson 3: Function Transformations / Solution

In this DP Mathematics AI AHL 2.9 unit, students investigate real-world applications of five modelling skills in this teaching materials set: exponential models, natural logarithmic models, sinusoidal models, logistic models, and piecewise models. All modelling activities are approached theoretically at first and then practical applications into real-life situations through neatly applied scaffolding techniques. Students are also guided to model the problem without a GDC in some cases.

Overview

Lesson 1: Radiocarbon Dating, Half-life and Agroforestry / Solution

Lesson 2: Modelling Life Expectancy / Solution

Lesson 3: MS PAC Rule and Modelling Periodicity in Various Cases / Solution

Lesson 4: COVID-19 Spread and Mould Growth Experiment / Solution

Lesson 5: Cappadocia Balloon Tour / Solution

In this DP Mathematics AI HL 2.10 set, students investigate a mathematical approach to linearization, linear and log scales comparisons, and applications of log scales to real-life data and mathematical models. Because this is a long set, teachers may choose only to cover some of the activities in the class and use others for homework or assessment, but at least three of the six activities should be used.

Overview

Lesson 1: Pure Mathematical Approach to Linearization / Solution

Lesson 2: Math Applications of Linearization on Science Experiment / Solution

Lesson 3: Kleiber's Famous Mouse-to-Elephant Line / Solution

Lesson 4: How to Read Log Scales / Solution

Lesson 5: When Will Emily Have 1M Followers? / Solution

Lesson 6: Attenuation of X-Ray in Muscle and in Bone / Solution

This set of DP Mathematics AI HL 2.13 materials will allow the students to model real-world data using a variety of non-linear functions (quadratic, cubic, quartic, exponential, sinusoidal, etc). Models can be created using both algebraic and technological means. Students also have the opportunity to determine which model is better for the given data, justifying their choices using the coefficient of determination or the sum of square residuals.

Overview

Lesson 1: Non-Linear Regressions / Solution

Lesson 2: Dice Decay / Solution

This DP Mathematics AA AIHL 2.16 set comprises two documents for students to use. The notes provide a scaffolding structure that helps students discover the main properties of the five transformations required at Higher Level. Students explore modulus equations and inequations. It follows the flipped-classroom model, where students watch videos to learn the skills required before attending class. Then, class time can be used to compare solutions and discuss methodologies.

Overview

Lesson 1: HL Graph Transformation Notes / Solution

Lesson 2: Modules, Equations and Inequalities / Solution