Grade 11 Finite Mathematics 1

Content standard

The learners demonstrate knowledge and understanding of 1. Symmetries in nature and art 2. Different linear transformations (geometric approach) 3. Tiling and Tessellations 4. Frieze Patterns 5. the Golden Ratio in nature and art 6. Fibonacci Sequence in nature and art 7. Fractals

Performance standard

By the end of the quarter, the learners are able to contribute to a class exhibit of artworks inspired by geometric symmetries, tessellations, Frieze patterns, the golden ratio, the Fibonacci sequence, or fractals. Each artwork should be accompanied by a description detailing the mathematics involved.

Learning competencies (13)

• FINM1-G11-Q1-01

  identify and describe symmetries in nature and art

  • a. reflection
  • b. rotational
  • c. line of symmetry
  • d. center of rotation
  • e. angle of rotation

• FINM1-G11-Q1-02

  illustrate various geometric transformations (translation, reflection, rotation, dilation, and glide reflection);

• FINM1-G11-Q1-03

  identify polygons that can tesselate the plane;

• FINM1-G11-Q1-04

  generate tessellations using geometric transformations;

• FINM1-G11-Q1-05

  construct Escher-type tessellations;

• FINM1-G11-Q1-06

  identify the geometric transformations that generate a given Frieze pattern;

• FINM1-G11-Q1-07

  define and explain the golden ratio, golden rectangle, golden spiral, and golden angles;

• FINM1-G11-Q1-08

  identify the golden ratio, golden rectangle, golden spiral, and golden angles in nature and art;

• FINM1-G11-Q1-09

  define the Fibonacci sequence and investigate its historical origin;

• FINM1-G11-Q1-10

  identify examples of Fibonacci sequence in nature and art;

• FINM1-G11-Q1-11

  explain the connection between the Golden Ratio and the Fibonacci sequence;

• FINM1-G11-Q1-12

  define and identify fractals in nature and art; and

• FINM1-G11-Q1-13

  generate fractals with or without the use of technology.

Content standard

The learners demonstrate knowledge and understanding of 1. Fundamental concepts of matrices and basic operations 2. Elementary row operations 3. Determinants and their properties 4. Fundamental concepts of linear programming 5. Graphical method 6. Simplex Method

Performance standard

By the end of the quarter, the learners are able to model real-world situations using matrices and matrix operations. They are also able to formulate linear programming models and solve them using either the graphical or simplex method.

Learning competencies (18)

• FINM1-G11-Q2-01

  illustrate matrix and its components (e.g., row, column, dimensions, and order of a matrix);

• FINM1-G11-Q2-02

  perform matrix operations (addition, subtraction, scalar multiplication, multiplication, transposition);

• FINM1-G11-Q2-03

  apply properties of matrix operations (commutative, associative, distributive, zero matrix, identity matrix, etc.);

• FINM1-G11-Q2-04

  represent systems of linear equations using matrices;

• FINM1-G11-Q2-05

  apply row operations to solve a system of linear equations;

• FINM1-G11-Q2-06

  define the inverse of a matrix;

• FINM1-G11-Q2-07

  calculate the inverse of a matrix using row operations;

• FINM1-G11-Q2-08

  use row operations to determine if a system of linear equations is independent (unique solution), dependent consistent (infinitely many solutions), or inconsistent (no solution);

• FINM1-G11-Q2-09

  compute the determinant of a 2×2 and a 3×3 matrix;

• FINM1-G11-Q2-10

  use the determinant to test matrix invertibility;

• FINM1-G11-Q2-11

  use Cramer’s rule to solve an independent system of linear equations ( 2×2 and 3×3);

• FINM1-G11-Q2-12

  illustrate linear programming and its significance in decision- making;

• FINM1-G11-Q2-13

  formulate real-world problems into linear programming models;

• FINM1-G11-Q2-14

  graph the feasible region in a Linear Programming Problem;.

• FINM1-G11-Q2-15

  determine the optimal solutions to a Linear Programming Problem using the Corner Point Theorem;

• FINM1-G11-Q2-16

  solve linear programming problems of two variables by graphical method, with or without technology;

• FINM1-G11-Q2-17

  construct an initial simplex tableau from an LP problem; and

• FINM1-G11-Q2-18

  perform simplex iterations to obtain an optimal solution to an LP problem.