United University

Geometry Grade 9. Vectors on a plane. Collection 1

Course Difficulty Icon Intermediate
Course Type Icon Course
Course Duration Icon 12 hours

This interactive course introduces 9th-grade students to vectors on a plane. Through visual lessons, exercises, and interactive activities, students will explore the foundations of vector geometry. They will examine vector properties, operations, and applications, such as vector addition, scalar multiplication, and dot products. By the end of the course, learners will confidently use vector concepts to solve geometric problems and deepen their understanding of spatial relationships.

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This interactive course introduces 9th-grade students to vectors on a plane. Through visual lessons, exercises, and interactive activities, students will explore the foundations of vector geometry. They will examine vector properties, operations, and applications, such as vector addition, scalar multiplication, and dot products. By the end of the course, learners will confidently use vector concepts to solve geometric problems and deepen their understanding of spatial relationships.

Key Features of the Course

  • Interactive tasks, tests, and exercises tailored for students
  • Step-by-step exploration of vector concepts and operations
  • Focus on conceptual understanding and problem-solving
  • Engaging activities based on real-world mathematical applications

Course Modules

Module 1: Vectors on a Plane

  • Lesson 6: Vectors. Magnitude and Direction. Collinear Vectors. Equal Vectors
  • Solve problems and complete exercises
  • Solve problems and complete exercises
  • Lesson 7: Vector Coordinates
  • Solve problems and complete exercises
  • Solve problems and complete exercises
  • Lesson 8: Vector Addition and Subtraction
  • Solve problems and complete exercises
  • Lesson 9: Scalar Multiplication of a Vector
  • Solve problems and complete exercises
  • Lesson 10: Dot Product of Vectors
  • Solve problems and complete exercises
  • Solve problems and complete exercises
  • Independent Homework #2 (§§ 6–10)
  • Take the tests
  • Knowledge Check Assignments for §§ 6–10
  • Complete the tasks
  • Review Exercises for Section 2
  • For § 6
  • For § 7
  • For § 8
  • For § 9
  • For § 10
  • Key Concepts in Section 2
  • The Greatest Mathematician of His Time
  • Key Concepts in Section 2

Expected Learning Outcomes

  • Give examples of equal, opposite, and collinear vectors
  • Explain:
    • what vectors are; vector magnitude and direction; unit vectors; zero vectors; collinear and opposite vectors; vector coordinates; vector sum and difference; scalar multiplication
    • how to define and position a vector from a given point
    • the rules for finding the vector sum and scalar multiplication
  • Formulate:
    • definitions of equal vectors and the dot product
    • properties of vector operations
  • Illustrate and identify vectors in diagrams:
    • vectors equal or opposite to a given one, collinear vectors (including using coordinates), result of sum, difference, or scalar multiple
  • Calculate:
    • vector coordinates, vector sum and difference, scalar multiple of a vector
    • vector magnitude and angle between two vectors
  • Justify vector equality and collinearity
  • Apply definitions and properties to solve problems

This comprehensive course enhances students’ understanding of vectors and their applications in geometry. Through structured lessons and practice, learners build essential skills in mathematical reasoning, vector manipulation, and spatial analysis. The course integrates conceptual clarity with engaging, practical problem-solving.

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