Competences

• • a)Manage and master the core concepts such as cartesian plane, distance formula, midpoint formula and equations of lines and curves;
  • b)Manage applications of coordinate principles to solve mathematical problems including finding distances, areas and angles between geometric figures;
  • c)Manage vector operations such as addition, subtraction, dot and cross product and their geometric representations and the main differences between a vector and a line;
  • d)Demonstrate the ability to visualize objects in space and accurately describe their orientation, position, and scale.e) analyse and interpret the relationships between algebraic and geometric representations;
  • e)Deal with various problems involving circles, parabola and ellipse and applying circle geometry in practical scenarios such as engineering and physical problems;
  • f)Manage and master vector geometric concepts such as graphing, algebraic representations in 2- and 3-dimensions and explain the connection between linear and vector geometry;
  • g)Manage graphing software and tools to help students visualise and understand the concepts involved;
  • h)Create and utilise assessment tools to evaluate student`s understanding of analytic and vector geometry namely quizzes, online games and practical exercises.

Knowledge

• • • a)Define the cartesian plane, the formulae for distance, mid-point, slope, line, intersection points, equations for circles and conic sections and more;
    • b)Define and describe the equation of a circle in expanded form, in standard form and from the derivation of the  locus of a point;
    • c)Identify and explain transformations of circles, tangents to circles and concentric circles, orthogonality, and circles touching externally or internally;
    • d)Define and recognise the equation and shape of the ellipse, the parabola and the hyperbola;
    • e)Identify, represent  and discuss vectors and vector operations both graphically and algebraically;
    • f)Identify and compare algebraic representations of analytic with vector geometry;
    • g)Identify vector equations of lines and planes and solving problems and representing them graphically;
    • h)Identify and correct common student errors;
    • i)Define concepts and operations of vectors, how to project one vector on to another and the ability to solve problems involving force, motion and equilibrium;
    • j)Describe historic insights about the development of coordinate geometry including Euclidean Geometry and the origins of Analytic geometry with Rene Descartes;
    • k)Describe the mathematical theories that underpin coordinate geometry and how they evolved over time.

Skills

• • • a)Work and discuss different coordinate systems namely cartesian, and polar, and analyse problems systematically with logical steps;
    • b)Draw circles accurately using the given centre and radius;
    • c)Show pedagogical skills namely for curricular development, instructional strategies, and assessment techniques which determine the fundamentals of good teaching;
    • d)Solve geometric problems analytically using algebraic methods;
    • e)Construct and present proofs involving coordinate geometry, enhancing logical reasoning;
    • f)Shift from concrete geometric shapes to abstract mathematical concepts;
    • g)Master the use of coordinate geometry formulas to solve complex problems, including real-world applications;
    • h)Visualise and manipulate objects in multiple dimensions, accurately interpreting directions and orientations in space relevant to scientific contexts;
    • i)Perform and analyse geometric transformations, interpreting their numerical effects with precision;
    • j)Apply good communication skills to explain clearly complex coordinate geometry concepts both verbally and in writing;
    • k)Show proficiency in using precise mathematical terminology and notation when teaching coordinate geometry;
    • l)Show constructive feedback that helps students improve their geometric reasoning and problem-solving skills.
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