Grade 11 Finite Mathematics 2

Content standard

The learners demonstrate knowledge and understanding of 1. Fundamental Principles of Counting 2. Combination and permutation 3. Variations in Counting 4. Probability of an event 5. Addition of probabilities 6. Conditional probability and independent events

Performance standard

By the end of the quarter, the learners are able to apply combinations and permutations in counting the number of ways to select and arrange objects. In addition, they are able to solve problems involving probabilities.

Learning competencies (16)

• FINM2-G11-Q1-01

  use the addition and multiplication principles to count elements of a set;

• FINM2-G11-Q1-02

  differentiate between a combination and a permutation of objects;

• FINM2-G11-Q1-03

  calculate the number of combinations and permutations of n objects taken k at a time;

• FINM2-G11-Q1-04

  apply the properties of combinations to count the elements of a set;

• FINM2-G11-Q1-05

  solve problems involving combinations and permutations;

• FINM2-G11-Q1-06

  compute the number of ways of arranging

  • a. a set with non-distinct elements
  • b. a set of objects in a circle

• FINM2-G11-Q1-07

  compute the number of ways of distributing objects (distinct and non-distinct) into groups;

• FINM2-G11-Q1-08

  solve counting problems using combinatorial techniques;

• FINM2-G11-Q1-09

  illustrate sample spaces and events by listing elements;

• FINM2-G11-Q1-10

  calculate the probability of an event by (a) listing and (b) using counting techniques;

• FINM2-G11-Q1-11

  determine if two or more events are mutually exclusive;

• FINM2-G11-Q1-12

  calculate the probability of the complement of an event and the union of two events;

• FINM2-G11-Q1-13

  differentiate between simple and conditional probability;

• FINM2-G11-Q1-14

  calculate conditional probabilities;

• FINM2-G11-Q1-15

  determine if two events are independent; and

• FINM2-G11-Q1-16

  solve probability problems using the laws of probability and Bayes’ Rule.

Content standard

The learners demonstrate knowledge and understanding of 1. Divisibility 2. Greatest common divisor and least common multiple 3. Modular Arithmetic 4. Fundamental concepts of graph theory 5. Graph connectivity and transversability 6. Spanning Trees and Shortest Paths

Performance standard

By the end of the quarter, the learners are able to perform number-theoretic operations (GCD, LCM, modular arithmetic) and solve problems involving applications of modular arithmetic and linear Diophantine equations. In addition, they are able to solve problems involving graph theory algorithms (Eulerian and Hamiltonian paths and circuits, spanning trees, shortest paths), and discuss the applications of graphs in transportation, communication, network design, productivity, etc., through a presentation or written work.

Learning competencies (16)

• FINM2-G11-Q2-01

  prove properties of divisibility of integers;

• FINM2-G11-Q2-02

  illustrate prime and composite integers and the fundamental theorem of Arithmetic by formulating the prime factorization of positive integers;

• FINM2-G11-Q2-03

  compute the GCD and LCM of two positive integers by prime factorization and the Euclidean algorithm;

• FINM2-G11-Q2-04

  solve linear Diophantine Equation using the Euclidean Algorithm;

• FINM2-G11-Q2-05

  illustrate congruence modulo m and its properties

• FINM2-G11-Q2-06

  perform arithmetic operations and solve linear equations modulo m;

• FINM2-G11-Q2-07

  solve problems involving modular arithmetic (UPC codes, ISBN, Luhn’s algorithm for credit card number verification);

• FINM2-G11-Q2-08

  illustrate elements of a graph (vertices/nodes, edges/arcs) and the different types of graphs (simple, directed, complete, bipartite, connected, path, cycle, tree, regular, etc.);

• FINM2-G11-Q2-09

  explore some real-life situations where graphs are utilized;

• FINM2-G11-Q2-10

  differentiate between Eulerian and Hamiltonian paths/circuits;

• FINM2-G11-Q2-11

  apply Euler’s theorem to determine the existence of Eulerian paths and circuits;

• FINM2-G11-Q2-12

  apply Dirac’s condition for the existence of Hamiltonian circuits;

• FINM2-G11-Q2-13

  identify Eulerian and Hamiltonian circuits and paths in a connected graph;

• FINM2-G11-Q2-14

  explain spanning trees and their significance;

• FINM2-G11-Q2-15

  apply Breadth-First Search (BFS) and Depth-First Search (DFS) algorithms to find spanning trees in a connected graph; and

• FINM2-G11-Q2-16

  apply different methods to find shortest paths (Dijktra’s algorithm, Floyd-Warshall algorithm).