MATHEMATICS 2

COMPETENCY GOALS and OBJECTIVES

This course contains 6 core content areas and 42 objectives.  Instruction is organized to maximize student participation in the learning experience, as suggested in the Washington State K-12 Mathematics Learning Standards. The overall framework for the course is as follows. When instruction for core competency goals are developed, the number for the objective within the goal will become a hyperlink.

M2.1. Core Content: Modeling situations and solving problems

• M2.1.A Select and justify functions and equations to model and solve problems.  
• M2.1.B Solve problems that can be represented by systems of equations and inequalities.  
• M2.1.C Solve problems that can be represented by quadratic functions, equations, and inequalities.  
• M2.1.D Solve problems that can be represented by exponential functions and equations.  
• M2.1.E Solve problems involving combinations and permutations.

M2.3. Core Content: Conjectures and proofs, part I

• M2.3.A Use deductive reasoning to prove that a valid geometric statement is true.  
• M2.3.B Identify errors or gaps in a mathematical argument and develop counterexamples to refute invalid statements about geometric relationships.  
• M2.3.C Write the converse, inverse, and contrapositive of a valid proposition and determine their validity.  
• M2.3.D Distinguish between definitions and undefined geometric terms and explain the role of definitions, undefined terms, postulates (axioms), and theorems. 
  

M2.2. Core Content: Quadratic functions, equations, and relationships

• M2.2.A Represent a quadratic function with a symbolic expression, as a graph, in a table, and with a description, and make connections among the representations.  
• M2.2.B Sketch the graph of a quadratic function, describe the effects that changes in the parameters have on the graph, and interpret the x-intercepts as solutions to a quadratic equation.  
• M2.2.C Translate between the standard form of a quadratic function, the vertex form, and the factored form; graph and interpret the meaning of each form.  
• M2.2.D Solve quadratic equations that can be factored as (ax + b)(cx + d) where a, b, c, and d are integers.  
• M2.2.E Determine the number and nature of the roots of a quadratic function.  
• M2.2.F Solve quadratic equations that have real roots by completing the square and by using the quadratic formula.  
• M2.2.G Solve quadratic equations and inequalities, including equations with complex roots.  
• M2.2.H Determine if a bivariate data set can be better modeled with an exponential or a quadratic function and use the model to make predictions. 

M2.3. Core Content: Conjectures and proofs, part II

• M2.3.E Know, explain, and apply basic postulates and theorems about triangles and the special lines, line segments, and rays associated with a triangle.
• M2.3.F Determine and prove triangle congruence and other properties of triangles.
• M2.3.G Know, prove, and apply the Pythagorean Theorem and its converse.
• M2.3.H Solve problems involving the basic trigonometric ratios of sine, cosine, and tangent.
• M2.3.I Use the properties of special right triangles (30°–60°–90° and 45°–45°–90°) to solve problems.
• M2.3.J Know, prove, and apply basic theorems about parallelograms.
• M2.3.K Know, prove, and apply theorems about properties of quadrilaterals and other polygons.
• M2.3.L Determine the coordinates of a point that is described geometrically.
• M2.3.M Verify and apply properties of triangles and quadrilaterals in the coordinate plane. 
  

M2.4 Core Content: Probability

• M2.4.A Apply the fundamental counting principle and the ideas of order and replacement to calculate probabilities in situations arising from two-stage experiments (compound events).  

• M2.4.B Given a finite sample space consisting of equally likely outcomes and containing events A and B, determine whether A and B are independent or dependent, and find the conditional probability of A given B.   
• M2.4.C Compute permutations and combinations, and use the results to calculate probabilities.  
• M2.4.D Apply the binomial theorem to solve problems involving probability. 

M2.5. Additional Key Content

• M2.5.A Use algebraic properties to factor and combine like terms in polynomials.  
• M2.5.B Use different degrees of precision in measurement, explain the reason for using a certain degree of precision, and apply estimation strategies to obtain reasonable measurements with appropriate precision for a given purpose.  
• M2.5.C Solve problems involving measurement conversions within and between systems, including those involving derived units, and analyze solutions in terms of reasonableness of solutions and appropriate units.  
• M2.5.D Find the terms and partial sums of arithmetic and geometric series and the infinite sum for geometric series. 

M2.6. Core Processes: Reasoning, problem solving, and communication

• M2.6.A Analyze a problem situation and represent it mathematically.  
• M2.6.B Select and apply strategies to solve problems.  
• M2.6.C Evaluate a solution for reasonableness, verify its accuracy, and interpret the solution in the context of the original problem.  
• M2.6.D Generalize a solution strategy for a single problem to a class of related problems, and apply a strategy for a class of related problems to solve specific problems.  
• M2.6.E Read and interpret diagrams, graphs, and text containing the symbols, language, and conventions of mathematics.  
• M2.6.F Summarize mathematical ideas with precision and efficiency for a given audience and purpose.  
• M2.6.G Synthesize information to draw conclusions and evaluate the arguments and conclusions of others.  
• M2.6.H Use inductive reasoning to make conjectures, and use deductive reasoning to prove or disprove conjectures.

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