Analytic Geometry EOCT Resources Number and Quantity Perform arithmetic operations with complex numbers. MCC9‐12.N.CN.1 Know there is a complex number i such that i2 = −1, and every complex number has the form a+ bi with a and b real. http://www.purplemath.com/modules/complex.htm http://www.mathsisfun.com/numbers/complex-numbers.html MCC9‐12.N.CN.2 Use the relation i2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. http://www.regentsprep.org/Regents/math/algtrig/ATO6/practicepageadd.htm http://www.regentsprep.org/Regents/math/algtrig/ATO6/lessonadd.htm MCC9‐12.N.CN.3 (+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers. http://www.regentsprep.org/Regents/math/algtrig/ATO6/multprac.htm http://www.sparknotes.com/math/algebra2/complexnumbers/section3.rhtml https://www.khanacademy.org/math/algebra2/complex-numbers-a2/complex_numbers/v/dividing-complex- numbers Use complex numbers in polynomial identities and equations. MCC9‐12.N.CN.7 Solve quadratic equations with real coefficients that have complex solutions. http://www.regentsprep.org/Regents/math/algtrig/ATE3/quadcomlesson.htm http://www.youtube.com/watch?v=d2w6i8FpYC8 https://www.khanacademy.org/math/algebra2/complex-numbers-a2/complex_numbers/v/complex-roots-from-the- quadratic-formula Algebra Seeing Structure in Expressions A.SSE Interpret the structure of expressions http://www.virtualnerd.com/common-core/hsa-algebra/HSA-SSE-expressions-seeing-structure/A/1/1a/variables- definition http://www.virtualnerd.com/common-core/hsa-algebra/HSA-SSE-expressions-seeing-structure/A/1/1a/coefficient- definition http://www.virtualnerd.com/common-core/hsa-algebra/HSA-SSE-expressions-seeing-structure/A/1/1a/constant- definition http://www.virtualnerd.com/common-core/hsa-algebra/HSA-SSE-expressions-seeing-structure/A/1/1a/constant- definition http://www.virtualnerd.com/common-core/hsa-algebra/HSA-SSE-expressions-seeing-structure/A/1/1a/factor- definition http://www.virtualnerd.com/common-core/hsa-algebra/HSA-SSE-expressions-seeing-structure/A/1/1a/numerical- algebraic-expressions http://www.virtualnerd.com/common-core/grade-6/6_EE-expression-equations/A/2/2c/order-of-operations- definition Write expressions in equivalent forms to solve problems http://www.virtualnerd.com/common-core/hsa-algebra/HSA-SSE-expressions-seeing-structure/B/3/3c/power-of- quotient-formula http://www.virtualnerd.com/common-core/hsa-algebra/HSA-SSE-expressions-seeing-structure/B/3/3c/function- definition http://www.virtualnerd.com/common-core/hsa-algebra/HSA-SSE-expressions-seeing-structure/B/3/3a/trinomial- factorization-example http://www.virtualnerd.com/common-core/hsa-algebra/HSA-SSE-expressions-seeing-structure/B/3/3a/solve-by- factoring http://www.virtualnerd.com/common-core/hsa-algebra/HSA-SSE-expressions-seeing-structure/B/3/3a/perfect- square-trinomial-shortcut Analytic Geometry EOCT Resources Perform arithmetic operations on polynomials http://www.virtualnerd.com/common-core/hsa-algebra/HSA-APR-polynomial-rational-expressions- arithmetic/A/1/addition-example http://www.virtualnerd.com/common-core/hsa-algebra/HSA-APR-polynomial-rational-expressions- arithmetic/A/1/binomial-multiplication-distributive-property http://www.virtualnerd.com/common-core/hsa-algebra/HSA-APR-polynomial-rational-expressions- arithmetic/A/1/sum-and-difference-product-formula-example http://www.virtualnerd.com/common-core/hsa-algebra/HSA-APR-polynomial-rational-expressions- arithmetic/A/1/subtraction-example Create equations that describe numbers or relationships http://www.virtualnerd.com/common-core/hsa-algebra/HSA-CED-/A/4/isolate-variable-from-formula http://www.virtualnerd.com/common-core/hsa-algebra/HSA-CED-/A/4/literal-equation-definition http://www.virtualnerd.com/common-core/hsa-algebra/HSA-CED-/A/1/compound-and-word-problem-solution http://www.virtualnerd.com/common-core/hsa-algebra/HSA-CED-/A/1/growth-word-problem http://www.virtualnerd.com/common-core/hsa-algebra/HSA-CED-/A/1/decay-word-problem Solve equations and inequalities in one variable http://www.youtube.com/watch?v=srJn2ZUYB4M http://www.youtube.com/watch?v=1SmJq3-SWZo http://www.youtube.com/watch?v=Y8dq2G4XZCc http://www.youtube.com/watch?v=Y6tLqfkCA4A http://www.youtube.com/watch?v=1SmJq3-SWZo http://www.youtube.com/watch?v=srJn2ZUYB4M Solve systems of equations http://www.virtualnerd.com/pre-algebra/inequalities-multi-step-equations/no-solution-equation-example.php http://www.virtualnerd.com/pre-algebra/inequalities-multi-step-equations/no-solution-definition.php http://www.virtualnerd.com/algebra-1/systems-equations-inequalities/solve-substitution-one-quadratic.php http://www.virtualnerd.com/algebra-2/linear-systems/equations-solution-by-graphing.php http://www.virtualnerd.com/algebra-2/linear-systems/equations-find-map-coordinates.php http://www.virtualnerd.com/algebra-2/linear-systems/equations-infinite-solutions-word-problem.php Functions Interpret functions that arise in applications in terms of the context MCC9‐12.F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Increasing and Decreasing: http://www.youtube.com/watch?v=AGkTQW1qGMo Intercepts: http://www.purplemath.com/modules/intrcept.htm Relative Mins and Maxs: http://www.youtube.com/watch?v=Hoyv3-BMAGc Domain and Range: http://www.purplemath.com/modules/fcns2.htm MCC9‐12.F.IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Analyze functions using different representations. Rate of Change: http://www.youtube.com/watch?v=jkksI-mkwd0 MCC9‐12.F.IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Graphing Quadratic Functions: http://www.youtube.com/watch?v=tjroyVI8El4 Linear and Quadratic Functions: http://www.purplemath.com/modules/index.htm Transformation of Functions: http://www.youtube.com/watch?v=Ccq1aQDCfVE Analytic Geometry EOCT Resources MCC9‐12.F.IF.7a Graph linear and quadratic functions and show intercepts, maxima, and minima. Graphing Quadratic Functions: http://www.youtube.com/watch?v=tjroyVI8El4 MCC9‐12.F.IF.8a Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. http://www.youtube.com/watch?v=xGOQYTo9AKY http://www.purplemath.com/modules/sqrquad.htm http://www.mathsisfun.com/algebra/factoring-quadratics.html Geometry Understand congruence in terms of rigid motions MCC9‐12.G.CO.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. http://www.youtube.com/watch?v=YHwSe-0c7Xo http://ceemrr.com/Geometry1/HingeTheorem/HingeTheorem_print.html MCC9‐12.G.CO.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. http://www.mathwarehouse.com/geometry/triangles/triangle-inequality-theorem-rule-explained.php MCC9‐12.G.CO.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. http://www.mathwarehouse.com/geometry/congruent_triangles/ http://www.basic-mathematics.com/congruent-triangles.html http://www.youtube.com/watch?v=-k1ECA6jWsY http://www.virtualnerd.com/geometry/congruent-triangles/proof-asa-aas-hl/definition-asa-triangle-congruence- postulate http://www.virtualnerd.com/geometry/congruent-triangles/proof-sss-sas/coordinate-plane-congruence http://www.analyzemath.com/Geometry/congruent_triangles.html http://www.regentsprep.org/Regents/math/geometry/GP4/Ltriangles.htm http://www.nexuslearning.net/books/ml-geometry/Chapter4/ML%20Geometry%204- 4%20ASA%20and%20AAS.pdf Prove geometric theorems MCC9‐12.G.CO.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints. http://feromax.com/cgi-bin/ProveIt.pl http://www.youtube.com/watch?v=sBUsOXUyqSQ MCC9‐12.G.CO.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180 degrees; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. http://www.regentsprep.org/Regents/math/geometry/GPB/theorems.htm MCC9‐12.G.CO.11 Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles