United University

Geometry Grade 10. Coordinates, vectors, geometric transformations in space. Collection 1

Course Difficulty Icon Intermediate
Course Type Icon Course
Course Duration Icon 10 hours

This interactive course introduces 10th-grade students to the concepts of coordinates, vectors, and geometric transformations in space. It offers a structured exploration of essential topics such as the rectangular coordinate system in space, vector operations, equations of a plane and a sphere, and geometric transformations like symmetry and parallel translation. Through interactive problem-solving and practice exercises, students will strengthen their understanding of three-dimensional geometric relationships and analytical skills.

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This interactive course introduces 10th-grade students to the concepts of coordinates, vectors, and geometric transformations in space. It offers a structured exploration of essential topics such as the rectangular coordinate system in space, vector operations, equations of a plane and a sphere, and geometric transformations like symmetry and parallel translation. Through interactive problem-solving and practice exercises, students will strengthen their understanding of three-dimensional geometric relationships and analytical skills.

Key Features of the Course

  • Interactive learning through problem-solving tasks and exercises
  • Development of analytical and spatial reasoning skills
  • Aligned with national curriculum standards in mathematics
  • Engaging review tasks and independent assignments for consolidation

Course Modules

Module 1: Coordinates, Vectors, Geometric Transformations in Space

  • Lesson 13: Rectangular Coordinates in Space
  • Solve problems and complete exercises 13.1 - 13.70
  • Test your competence
  • Lesson 14: Vectors in Space. Operations on Vectors
  • Solve problems and complete exercises 14.1 - 14.90
  • Test your competence
  • Lesson 15: Vector Coordinates. Operations on Vectors Given by Coordinates
  • Solve problems and complete exercises 15.1 - 15.90
  • Test your competence
  • Independent Homework #6
  • Complete the tests
  • Review tasks for §§ 13-15
  • Complete the tasks
  • Lesson 16: Scalar Product of Vectors
  • Solve problems and complete exercises 16.1 - 16.65
  • Test your competence
  • Lesson 17: Simplest Geometric Loci of Points in Space. Equations of a Plane and a Sphere
  • Solve problems and complete exercises 17.1 - 17.96
  • Test your competence
  • Lesson 18: Coordinate and Vector Methods for Solving Problems
  • Solve problems and complete exercises 18.1 - 18.65
  • Test your competence
  • Lesson 19: Transformations in Space
  • Solve problems and complete exercises 19.1 - 19.50
  • Test your competence
  • Independent Homework #7
  • Complete the tests
  • Review tasks for §§ 16-17
  • Complete the tasks
  • Review Exercises for Section 4

Expected Learning Outcomes

  • Uses the analogy between vectors and coordinates on a plane and in space.
  • Understands the importance of the vector-coordinate method in mathematics.
  • Performs operations on vectors.
  • Applies vectors to model and calculate geometric and physical quantities.
  • Finds the distance between two points, the coordinates of the midpoint of a segment, and the coordinates of points symmetric with respect to the origin and coordinate planes.
  • Uses coordinates in space to measure distances and angles.

This course builds strong geometric fundamentals and analytical skills by integrating theoretical knowledge with practical problem-solving. Students will explore geometry through a logical, three-dimensional approach, enhancing both academic performance and mathematical thinking.

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