3. Geometry and Trigonometry (AA SL)

Teacher

Curriculum

5 Sections
26 Lessons
10 Weeks

Expand all sectionsCollapse all sections

3 D Geometry
4
Graphs and composite Transformation of trigonometric functions
4
Trigonometric Identities and solving equations
7
Circle radian, arc and sector
2
- 4.0
  Circular sector Lesson
- 4.2
  Circular sector – Question Bank (Qn 1 – 10)
Solutions of Triangle
10

Overview

This section of the IBDP Mathematics AA SL curriculum provides students with a thorough understanding of geometric and trigonometric concepts, extending their knowledge of two-dimensional and three-dimensional shapes, coordinate geometry, and trigonometric functions. The emphasis is on real-world applications, critical thinking, and problem-solving. Students will explore a variety of topics including 3D coordinate geometry, mensuration, solving triangles, and circular functions, which will prepare them for more complex mathematical modeling and analysis.

Key Concepts:

1. 3D Coordinate Geometry:

Introduction to three-dimensional coordinates.
Finding the distance between two points in 3D space.
Calculation of midpoints and section formulae.

2. Mensuration and 3D Shapes:

Volume and surface area of common 3D shapes including cubes, spheres, cylinders, cones, and pyramids.
Application of mensuration formulas to real-life objects and problems.

3. Solving Triangles:

Solving right-angled triangles using Pythagoras’ theorem, sine, cosine, and tangent.
Solving non-right-angled triangles using the sine rule and cosine rule.
Applications involving angles of elevation, depression, and bearings.

4. Circular Geometry and Sectors:

Calculation of arc lengths and areas of sectors of circles.
Understanding angles in radians and their application in measuring circular sectors.

5. Unit Circle and Trigonometric Identities:

Exploration of the unit circle and its use in defining trigonometric functions.
Introduction to basic trigonometric identities and solving trigonometric equations.

6. Circular Functions and Transformations:

Graphing and analyzing sine, cosine, and tangent functions.
Understanding amplitude, period, phase shift, and vertical shifts in the context of circular functions.
Transformations of trigonometric graphs, including reflections, stretches, and translations.

Learning Outcomes:

Upon completion of this topic, students will be able to:

Apply geometric and mensuration principles to solve problems involving 3D shapes.
Calculate distances, midpoints, and volumes of real-world objects.
Solve problems involving right-angled and non-right-angled triangles using trigonometric rules.
Understand and apply the unit circle in defining and analyzing trigonometric functions.
Solve trigonometric equations and apply transformations to trigonometric graphs.