# 1. Algebra

A. Factors of Polynomials
Common Monomial Factor
Difference of Two Squares
Sum and Difference of Two Cubes
Perfect Square Trinomials,
General trinomials
Problems Involving Factors of Polynomials

B. Rational Algebraic Expressions
Simplifying Rational Algebraic Expressions
Operations on Rational Algebraic Expressions. solves problems involving rational algebraic expressions.
• ##### Linear Equations and Inequalities in Two Variables

illustrates the rectangular coordinate system and its uses.* M8AL-Ie-1 8. illustrates linear equations in two variables. M8AL-Ie-3 9. illustrates the slope of a line. M8AL-Ie-4 10. finds the slope of a line given two points, equation, and graph.
writes the linear equation ax  by  c in the form y  mx  b and vice versa. M8AL-If-1 12. graphs a linear equation given (a) any two points; (b) the x – and y – intercepts; (c) the slope and a point on the line.
* M8AL-If-2 13. describes the graph of a linear equation in terms of its intercepts and slope.*** M8AL-If-3 14. finds the equation of a line given (a) two points; (b) the slope and a point; (c) the slope and its intercepts. M8AL-Ig-1 15. solves problems involving linear equations in two variables.

The Cartesian Coordinate Plane
• Systems of Linear Equations and Inequalities in Two Variables illustrates a system of linear equations in two variables. M8AL-Ih-1 17. graphs a system of linear equations in two variables.* M8AL-Ih-2 18. categorizes when a given system of linear equations in two variables has graphs that are parallel, intersecting, and coinciding. M8AL-Ih-3 19. solves a system of linear equations in two variables by (a) graphing; (b) substitution; (c) elimination.
. solves problems involving systems of linear equations in two variables.
illustrates linear inequalities in two variables. M8AL-IIa-1 22. differentiates linear inequalities in two variables from linear equations in two variables. M8AL-IIa-2 23. graphs linear inequalities in two variables. M8AL-IIa-3 24. solves problems involving linear inequalities in two variables. M8AL-IIa-4 25. solves a system of linear inequalities in two variables.*** M8AL-IIb-1 26. solves problems involving systems of linear inequalities in two variables. M8AL-IIb-2 27. illustrates a relation and a function. M8AL-IIc-1 28. verifies if a given relation is a function. M8AL-IIc-2 29. determines dependent and independent variables. M8AL-IIc-3 30. finds the domain and range of a function. M8AL-IId-1 31. illustrates a linear function. M8AL-IId-2 32. graphs a linear function’s (a) domain; (b) range; (c) table of
values; (d) intercepts; and (e) slope. 33. solves problems involving linear functions.

### Geometry Reasoning in Geometry

4. determines the relationship between the hypothesis and the conclusion of an if-then statement. M8GE-IIf-1 35. transforms a statement into an equivalent if-then statement. M8GE-IIf-2 36. determines the inverse, converse, and contrapositive of an if-then statement. M8GE-IIg-1 37. illustrates the equivalences of: (a) the statement and its contrapositive; and (b) the converse and inverse of a statement. M8GE-IIg-2 38. uses inductive or deductive reasoning in an argument. M8GE-IIh-1 39. writes a proof (both direct and indirect).
• #### Axiomatic Structure of Geometry

. illustrates the need for an axiomatic structure of a mathematical system in general, and in Geometry in particular: (a) defined terms; (b) undefined terms; (c) postulates; and (d) theorems.
• #### Triangle Congruence

illustrates triangle congruence.* M8GE-IIId-1 43. illustrates the SAS, ASA and SSS congruence postulates.* M8GE-IIId-e-1 44. solves corresponding parts of congruent triangles M8GE-IIIf-1 45. proves two triangles are congruent. M8GE-IIIg-1 46. proves statements on triangle congruence. M8GE-IIIh-1 47. applies triangle congruence to construct perpendicular lines and angle bisectors.

• #### Inequalities in a Triangle

illustrates theorems on triangle inequalities (Exterior Angle Inequality Theorem, Triangle Inequality Theorem, Hinge Theorem).*** M8GE-IVa-1 49. applies theorems on triangle inequalities. M8GE-IVb-1 50. proves inequalities in a triangle. M8GE-IVc-1 51. proves properties of parallel lines cut by a transversal.

• #### Parallel and Perpendicular Lines

determines the conditions under which lines and segments are parallel or perpendicular.

### Statistics and Probability

• #### Probability of simple events as applied using appropriate technology

illustrates an experiment, outcome, sample space and event.* M8GE-IVf-1 54. counts the number of occurrences of an outcome in an experiment: (a) table; (b) tree diagram; (c) systematic listing; and (d) fundamental counting principle.* M8GE-IVf-g-1 55. finds the probability of a simple event. M8GE-IVh-1 56. illustrates an experimental probability and a theoretical probability. M8GE-IVi-1 57. solves problems involving probabilities of simple events.
- in critical thinking
- problem solving, reasoning
- communicating
- making connections
- representations
- decisions in real life.