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Dallastown Area School District Mathematics Curriculum Map – Algebra 3/Trigonometry Lesson/Topic Exponents and Radicals Skill/Objective Use the properties of exponents to simplify expressions, also containing rational exponents Rationalizing numerators and denominators Lesson/Topic Polynomials Skill/Objective Perform operations on polynomials: add, subtract, FOIL Factor – special products, Difference of Squares, Perfect Square Trinomials Factor – trinomials with leading coefficient of one and leading coefficient other than one, with irrational roots Factor by Grouping Binomial Expansion with a power of two Lesson/Topic Rational Expressions Skill/Objective Find the domain of a rational expression Simplify by factoring Perform operations on rational expressions – add, subtract, multiply and divide 1 3/22/2011 Dallastown Area School District Mathematics Curriculum Map – Algebra 3/Trigonometry Simplify complex rational expressions Lesson/Topic Skill/Objective Keystone Review General Test Taking Strategies for answering multiple choice and free response questions. opportunities to expand on strengths and remediate areas of need as determined by the classroom diagnostic test Lesson/Topic Solving Equations Skill/Objective Solve linear equations by isolating the variable, including one step, to multi-step equations. Solve linear equations involving proportions and checking for extraneous roots. Solve quadratic equations using the following techniques: factoring, completing the square, extracting square roots, and quadratic formula. Solve quadratic equations and check for extraneous roots and double roots. Solve polynomial equations of higher degree by factoring, including checking for extraneous roots, and multiplicity of roots. Lesson/Topic Solving Inequalities Skill/Objective Solve linear inequalities by isolating the variable, including one step, to multi-step inequalities. Solve linear inequalities involving proportions. 2 3/22/2011 Dallastown Area School District Mathematics Curriculum Map – Algebra 3/Trigonometry Solve compound inequalities using sign charts to check for solutions. Lesson/Topic Functions Skill/Objective Determine the domain and range of Linear, Quadratic, Cubic, Exponential, Logarithmic, and Rational functions Perform operations on Linear, Quadratic, Cubic, Exponential, Logarithmic, and Rational functions, including composition. Find equation of linear functions given a point and slope or two points. Find equation of linear functions parallel and perpendicular to a given linear function. Find the equation of a parabola given the zeros, or a vertex and a point. Graph Linear, Quadratic, Cubic, Exponential, Logarithmic, and Rational functions in terms of shifts, reflections, stretches, and or asymptotes Analyze graphs of Linear, Quadratic, Cubic, Exponential, Logarithmic, and Rational functions, locating local minimums and maximums and in terms of increasing, decreasing, constant, even, odd, or neither, using interval notation. Lesson/Topic Trigonometry Skill/Objectives Use right triangle trig functions to solve word problems involving angles of elevation and depression. Derive the unit circle based on special triangles, determine the measurements of the angles in both degrees and radians, and determine the x and y coordinates of the angles. Use the unit circle to evaluate the six trigonometric functions in terms of their corresponding coordinates. 3 3/22/2011 Dallastown Area School District Mathematics Curriculum Map – Algebra 3/Trigonometry Lesson/Topic Matrices Skill/Objective Perform operations on matrices: addition, subtraction, and multiplication Use the TI-83 to solve systems of equations utilizing the rref calculation of the matrix function 4 3/22/2011