Grade 9 Mathematics

Content standard

1. simple geometric concepts and notations. 2. perpendicular and parallel lines, and angles formed by parallel lines cut by a transversal. 3. relations and functions. 4. graphs of linear functions, and the identification of domain and range, slope, intercepts, and zeros.

Performance standard

illustrate and describe points, lines, rays, line segments, angles, and planes. construct perpendicular and parallel lines. determine the measure of the angles formed by parallel lines cut by a transversal. identify relations and functions. graph a linear function and identify the domain and range, intercepts, slope, and zeros.

Learning competencies (11)

• MATH-G9-Q1-01

  illustrate and describe point, line, ray, line segment, angle, and plane using models and geometric notations.

  Measurement and Geometry

• MATH-G9-Q1-02

  construct perpendicular and parallel lines.

  Measurement and Geometry

• MATH-G9-Q1-03

  identify the relationships between angles formed by parallel lines cut by a transversal.

  Measurement and Geometry

• MATH-G9-Q1-04

  determine angle measures involving angle pairs, parallel and perpendicular lines, and parallel lines cut by a transversal.

  Measurement and Geometry

• MATH-G9-Q1-05

  identify relations that are functions based on the definitions of relations and functions.

  Number and Algebra

• MATH-G9-Q1-06

  determine the domain and the range of a function expressed in different representations.

  Number and Algebra

• MATH-G9-Q1-07

  express the relationship between two variables as a function.

  Number and Algebra

• MATH-G9-Q1-08

  determine the slopes (as rate of change) and the zeros of linear functions represented in:

  • a. graphs,
  • b. equations, and
  • c. tables of values.

  Number and Algebra

• MATH-G9-Q1-09

  graph a linear function and determine its:

  • a. domain,
  • b. range,
  • c. intercepts, and
  • d. slope.

  Number and Algebra

• MATH-G9-Q1-10

  represent linear relationships found in real-life situations using different representations.

  Number and Algebra

• MATH-G9-Q1-11

  solve problems involving linear functions.

  Number and Algebra

Content standard

1. parallelism and perpendicularity of lines. 2. different quadrilaterals and their properties. 3. congruence of triangles. 4. congruence proofs.

Performance standard

determine the conditions for lines to be parallel or perpendicular. use geometric properties to find unknown sides and angles of quadrilaterals. apply the triangle congruence postulates and theorems. construct and justify the construction of segments, angles, and triangles. construct proofs of the congruence of triangles.

Learning competencies (13)

• MATH-G9-Q2-01

  determine conditions that guarantee parallelism and perpendicularity of lines.

  Measurement and Geometry

• MATH-G9-Q2-02

  classify quadrilaterals based on formal definitions.

  Measurement and Geometry

• MATH-G9-Q2-03

  use properties of parallelograms to find measures of angles, sides, perpendicular height, and diagonals.

  Measurement and Geometry

• MATH-G9-Q2-04

  solve problems involving parallelograms, rectangles, squares, or rhombuses by applying their different properties.

  Measurement and Geometry

• MATH-G9-Q2-05

  prove properties of parallelograms by applying the relevant theorems.

  Measurement and Geometry

• MATH-G9-Q2-06

  derive the properties of trapezoids and kites by exploring the relationship between their parts and secondary parts.

  Measurement and Geometry

• MATH-G9-Q2-07

  solve problems on trapezoids and kites by applying their properties.

  Measurement and Geometry

• MATH-G9-Q2-08

  distinguish inductive and deductive reasoning for establishing proofs.

  Measurement and Geometry

• MATH-G9-Q2-09

  state postulates and theorems about defined and undefined terms in geometry, and formulates proofs involving them.

  Measurement and Geometry

• MATH-G9-Q2-10

  use the triangle congruence postulates and theorems to illustrate congruence of triangles, including CPCTC (definition of congruent triangles).

  Measurement and Geometry

• MATH-G9-Q2-11

  solve problems involving right triangle congruence theorems, isosceles triangle theorem, perpendicular bisector theorem, and midline theorem

  Measurement and Geometry

• MATH-G9-Q2-12

  construct and justify the construction of segments, angles and triangles, including, but not limited to, the triangle’s secondary parts and centers, using the triangle congruence postulates and theorems.

  Measurement and Geometry

• MATH-G9-Q2-13

  construct congruence proofs involving triangles or corresponding parts of triangles using a two-column proof.

  Measurement and Geometry

Content standard

1. quadratic equations and graphs of quadratic functions. 2. the solution of quadratic equations. 3. similarity of polygons. 4. special triangles. 5. direct and inverse variation.

Performance standard

represent quadratic relationships. interpret features of a parabola. express quadratic functions in different forms. sketch the graph of a quadratic function. solve quadratic equations. illustrate and apply similarity of polygons, including triangles. apply direct and inverse variation.

Learning competencies (16)

• MATH-G9-Q3-01

  represent real-life situations that can be modelled using quadratic relationships.

  Number and Algebra

• MATH-G9-Q3-02

  graph equations in two variables to represent quadratic relationships, such as 𝑦 = 𝑎𝑥², 𝑦 = 𝑎𝑥² + 𝑏, 𝑦 = 𝑎(𝑥 − 𝑏)².

  Number and Algebra

• MATH-G9-Q3-03

  interpret features of a parabola such as vertex, axis of symmetry, x–intercepts, opening direction, minimum or maximum value, zeros, and increasing and decreasing intervals.

  Number and Algebra

• MATH-G9-Q3-04

  transform the quadratic functions 𝑦 = 𝑎𝑥², 𝑦 = 𝑎𝑥² + 𝑏, 𝑦 = 𝑎(𝑥 − 𝑏)² and 𝑦 = 𝑎𝑥² + 𝑏𝑥 + 𝑐 into the form 𝑦 = 𝑎(𝑥 − ℎ)² + 𝑘, and vice versa.

  Number and Algebra

• MATH-G9-Q3-05

  sketch the graph of quadratic functions expressed in equation form.

  Number and Algebra

• MATH-G9-Q3-06

  analyze the effect of changing the values of the parameters on the behavior of its graph and on the properties of the quadratic function 𝑦 = 𝑎(𝑥 − ℎ)² + 𝑘.

  Number and Algebra

• MATH-G9-Q3-07

  find the zeros of quadratic functions in factored and standard form, graphically and algebraically.

  Number and Algebra

• MATH-G9-Q3-08

  solve quadratic equations by:

  • a. extracting square roots,
  • b. factoring, and
  • c. using the quadratic formula.

  Number and Algebra

• MATH-G9-Q3-09

  solve problems involving quadratic functions and equations

  Number and Algebra

• MATH-G9-Q3-10

  illustrate similarity of polygons.

  Measurement and Geometry

• MATH-G9-Q3-11

  illustrate and apply triangle similarity theorems in different situations.

  Measurement and Geometry

• MATH-G9-Q3-12

  solve problems involving triangle similarity.

  Measurement and Geometry

• MATH-G9-Q3-13

  solve problems involving measures of sides and angles of special triangles (30-60-90, 45-45-90).

  Measurement and Geometry

• MATH-G9-Q3-14

  illustrate real-life situations that involve direct variation and real-life situations that involve inverse variation.

  Number and Algebra

• MATH-G9-Q3-15

  translate a relationship between two quantities into a variation statement and/or a mathematical equation, given a table of values or a graph.

  Number and Algebra

• MATH-G9-Q3-16

  solve problems involving variation.

  Number and Algebra

Content standard

1. triangle theorems and triangle inequality theorems. 2. the trigonometric ratios and their application. 3. interpretation and analysis of data to assess whether the data may be misleading. 4. probabilities of simple and compound events.

Performance standard

apply triangle theorems and triangle inequality theorems. apply trigonometric ratios to solve right triangles. interpret and analyze data to assess whether the data may be misleading. determine the probabilities of simple and compound events.

Learning competencies (11)

• MATH-G9-Q4-01

  solve problems involving the perpendicular bisector theorem, isosceles triangle theorem, theorems on equilateral triangles, and the midline theorem.

  Measurement and Geometry

• MATH-G9-Q4-02

  explain theorems on triangle inequalities and apply these theorems in comparing measures in a triangle.

  Measurement and Geometry

• MATH-G9-Q4-03

  determine the values of the sine, cosine, and tangent trigonometric ratios corresponding to the angles of the special triangles.

  Measurement and Geometry

• MATH-G9-Q4-04

  find the values of the sine, cosine, and tangent ratios of any acute angle.

  Measurement and Geometry

• MATH-G9-Q4-05

  use the trigonometric ratios in solving right triangles.

  Measurement and Geometry

• MATH-G9-Q4-06

  illustrate angles of elevation and angles of depression.

  Measurement and Geometry

• MATH-G9-Q4-07

  solve real-life problems involving right triangles through the application of the trigonometric ratios.

  Measurement and Geometry

• MATH-G9-Q4-08

  interpret and analyze data from the digital media that are in tabular or graphical form to assess whether the data may be misleading.

  Data and Probability

• MATH-G9-Q4-09

  illustrate simple and compound events.

  Data and Probability

• MATH-G9-Q4-10

  determine the probabilities of simple and compound events.

  Data and Probability

• MATH-G9-Q4-11

  solve problems involving probabilities of simple and compound events.

  Data and Probability