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- Algebra
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**(13)** - Calculus, pre-calculus
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**(13)** - Reasoning and proof
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**TMM001**College Algebra**(174)****TMM001.1**Functions*******(96)****TMM001.1.1**Represent functions verbally, numerically, graphically and algebraically, including linear, quadratic, polynomial, rational, root/radical/power, exponential, logarithmic and piecewise-defined functions.*******(60)****TMM001.1.2**Determine whether an algebraic relation or given graph represents a function.*******(4)****TMM001.1.3**Perform transformations of functions – translations, reflections and stretching and shrinking.*******(14)****TMM001.1.4**Perform operations with functions – addition, subtraction, multiplication, division and composition.*******(10)****TMM001.1.5**Analyze the algebraic structure and graph of a function, including those listed in (1.1), to determine intercepts, domain, range, intervals on which the function is increasing, decreasing or constant, the vertex of a quadratic function, asymptotes, whether the function is one-to-one, whether the graph has symmetry (even/odd), etc., and given the graph of a function to determine possible algebraic definitions.*******(56)****TMM001.1.6**Find inverses of functions listed in (1.1) and understand the relationship of the graph of a function to that of its inverse.*******(5)****TMM001.1.7**Use the Remainder and Factor Theorems for polynomial functions.*******(8)****TMM001.1.8**Use functions, including those listed in (1.1), to model a variety of real-world problem-solving applications.*******(39)**

**TMM001.2**Equations/Systems*******(79)****TMM001.2.1**Understand the difference between an algebraic equation of one, two or more variables and a function, and the relationship among the solutions of an equation in one variable, the zeros of the corresponding function, and the coordinates of the x-intercepts of the graph of that function.*******(19)****TMM001.2.2**Determine algebraically and graphically whether the graph of an equation exhibits symmetry.*******(2)****TMM001.2.3**Solve a variety of equations, including polynomial, rational, exponential, and logarithmic, including equations arising in application problems.*******(43)****TMM001.2.4**Solve a system of linear equations graphically and algebraically by substitution and elimination, and solve application problems that involve systems of linear equations.*******(16)****TMM001.2.5**Solve polynomial and rational inequalities graphically and algebraically.*******(6)**

**TMM001.3**Identify and express the conics in standard rectangular form, graph the conics, and solve applied problems involving conics.**(8)****TMM001.4**Perform operations with matrices – addition, subtraction, scalar multiplication and matrix multiplication, including applications with matrices. Use matrices to solve systems of linear equations, including the Gaussian and Gauss-Jordan elimination methods, using a matrix inverse to solve a matrix equation, and Cramer’s Rule.**(6)****TMM001.5**Model real-world data with functions for prediction and analysis, including determining the appropriateness of a model and using hand-held calculator or computer regression capability.**(3)****TMM001.6**Use the Rational Zeros Theorem and the Fundamental Theorem of Algebra to find the zeros of and factor a polynomial into linear factors over the complex numbers.**(6)****TMM001.7**Solve a nonlinear system of equations graphically and algebraically, including nonlinear systems of equations arising in application problems.**(4)****TMM001.8**Solve a linear and nonlinear system of inequalities, including linear and nonlinear systems of inequalities arising from application problems.**(3)****TMM001.9**Express general terms of various sequences (e.g., arithmetic and geometric), write series in summation notation, find the sum of arithmetic and geometric series, and use the Binomial Theorem.**(1)**

**TMM002**Pre-Calculus**(251)****TMM002.1**Functions*******(110)****TMM002.1.1**Represent functions verbally, numerically, graphically and algebraically, including linear, quadratic, polynomial, rational, root/radical/power, piecewise-defined, exponential, logarithmic, trigonometric and inverse trigonometric functions.*******(69)****TMM002.1.2**Determine whether an algebraic relation or given graph represents a function.*******(4)****TMM002.1.3**Perform transformations of functions – translations, reflections and stretching and shrinking.*******(22)****TMM002.1.4**Perform operations with functions – addition, subtraction, multiplication, division and composition.*******(10)****TMM002.1.5**Analyze the algebraic structure and graph of a function, including those listed in (1.1), to determine intercepts, domain, range, intervals on which the function is increasing, decreasing or constant, the vertex of a quadratic function, asymptotes, whether the function is one-to-one, whether the graph has symmetry (even/odd), etc., and given the graph of a function to determine possible algebraic definitions.*******(64)****TMM002.1.6**Find inverses of functions listed in (1.1) and understand the relationship of the graph of a function to that of its inverse.*******(7)****TMM002.1.7**Use the Remainder and Factor Theorems for polynomial functions.*******(8)****TMM002.1.8**Use functions, including those listed in (1.1), to model a variety of real-world problem-solving applications.*******(44)**

**TMM002.2**Equations/Systems*******(104)****TMM002.2.1**Understand the difference between an algebraic equation of one, two or more variables and a function, and the relationship among the solutions of an equation in one variable, the zeros of the corresponding function, and the coordinates of the x-intercepts of the graph of that function.*******(18)****TMM002.2.2**Determine algebraically and graphically whether the graph of an equation exhibits symmetry.********(2)****TMM002.2.3**Solve a variety of equations, including polynomial, rational, exponential, and logarithmic, trigonometric and inverse trigonometric, including equations arising in application problems.*******(45)****TMM002.2.4**Solve a system of linear equations graphically and algebraically by substitution and elimination, and solve application problems that involve systems of linear equations.*******(18)****TMM002.2.5**Identify and express the conics (quadratic equations in two variables) in standard rectangular form, graph the conics, and solve applied problems involving conics.*******(24)****TMM002.2.6**Solve polynomial and rational inequalities graphically and algebraically.*******(6)**

**TMM002.3**Sequences/Series*******(15)****TMM002.3.1**Represent sequences verbally, numerically, graphically and algebraically, including both the general term and recursively.*******(13)****TMM002.3.2**Write series in summation notation, and represent sequences of partial sums verbally, numerically and graphically.*******(3)****TMM002.3.3**Identify and express the general term of arithmetic and geometric sequences, and find the sum of arithmetic and geometric series.*******(5)**

**TMM002.4**More Trigonometry*******(41)****TMM002.4.1**Express angles in both degree and radian measure.*******(3)****TMM002.4.2**Define the six trigonometric functions in terms of right triangles and the unit circle.*******(8)****TMM002.4.3**Solve right and oblique triangles in degrees and radians for both special and non-special angles, and solve application problems that involve right and oblique triangles.*******(31)****TMM002.4.4**Verify trigonometric identities by algebraically manipulating trigonometric expressions using fundamental trigonometric identities, including the Pythagorean, sum and difference of angles, double-angle and half-angle identities.*******(13)****TMM002.4.5**Solve a variety of trigonometric and inverse trigonometric equations, including those requiring the use of the fundamental trigonometric identities listed in (4.4), in degrees and radians for both special and non-special angles. Solve application problems that involve such equations.*******(4)**

**TMM002.5**Vectors*******(3)****TMM002.5.1**Represent vectors graphically in both rectangular and polar coordinates and understand the conceptual and notational difference between a vector and a point in the plane.*******(2)****TMM002.5.2**Perform basic vector operations both graphically and algebraically – addition, subtraction and scalar multiplication.*******(3)****TMM002.5.3**Solve application problems using vectors.*******(1)**

**TMM002.6**Perform operations with matrices – addition, subtraction, scalar multiplication and matrix multiplication, including applications with matrices. Use matrices to solve systems of linear equations, including the Gaussian and Gauss-Jordan elimination methods, using a matrix inverse to solve a matrix equation, and Cramer’s Rule.**(7)****TMM002.7**Model real-world data with functions for prediction and analysis, including determining the appropriateness of a model and using hand-held calculator or computer regression capability.**(2)****TMM002.8**Use the Rational Zeros Theorem and the Fundamental Theorem of Algebra to find the zeros of and factor a polynomial into linear factors over the complex numbers.**(5)****TMM002.9**Solve a nonlinear system of equations graphically and algebraically, including nonlinear systems of equations arising in application problems.**(3)****TMM002.10**Solve a linear and nonlinear system of inequalities, including linear and nonlinear systems of inequalities arising from application problems.**(2)****TMM002.11**Use the Binomial Theorem.**(1)****TMM002.12**Understand how to eliminate the xy-term in the general quadratic equation in two variables by the rotation of axes, and identify and graph conics with rotated axes.**(0)****TMM002.13**Graph complex numbers in the complex plane in both rectangular and polar form, perform operations on such numbers – addition, subtraction, multiplication and division, and use DeMoivre’s Theorem to find the nth roots of a complex number.**(4)****TMM002.14**Convert points and equations between rectangular and polar form, graph polar functions, solve polar equations, identify and express the conics in standard polar form for graphing, and solve applied problems involving conics in polar form.**(4)****TMM002.15**Identify and graph a curve defined by parametric equations by making a table of values and, when possible, eliminating the parameter.**(3)****TMM002.16**Understand the average rate of change of the graph of a function or equation on an interval, and informally understand the instantaneous rate of change of the graph of a function or equation at a point and its connection to the slope of the graph at the point, including application problems.**(1)**

**TMM003**Trigonometry**(60)****TMM003.1**Functions*******(18)****TMM003.1.1**Represent trigonometric and inverse trigonometric functions verbally, numerically, graphically and algebraically; define the six trigonometric functions in terms of right triangles and the unit circle.*******(14)****TMM003.1.2**Perform transformations of trigonometric and inverse trigonometric functions – translations, reflections and stretching and shrinking (amplitude, period and phase shift).*******(9)****TMM003.1.3**Analyze the algebraic structure and graph of trigonometric and inverse trigonometric functions to determine intercepts, domain, range, intervals on which the function is increasing, decreasing or constant, asymptotes, whether the function is one-to-one, whether the graph has symmetry (even/odd), etc., and given the graph of a function to determine possible algebraic definitions.*******(7)****TMM003.1.4**Use trigonometric and inverse trigonometric functions to model a variety of real-world problem-solving applications.*******(5)**

**TMM003.2**Equations*******(3)****TMM003.3**Angles/Triangles*******(33)****TMM003.4**Identities*******(12)****TMM003.5**Vectors*******(3)****TMM003.5.1**Represent vectors graphically in both rectangular and polar coordinates and understand the conceptual and notational difference between a vector and a point in the plane.*******(2)****TMM003.5.2**Perform basic vector operations both graphically and algebraically – addition, subtraction and scalar multiplication.*******(3)****TMM003.5.3**Solve application problems using vectors.*******(1)**

**TMM003.6**Graph complex numbers in the complex plane in both rectangular and polar form, perform operations on such numbers — addition, subtraction, multiplication and division, and use DeMoivre’s Theorem to find the n^{th}roots of a complex number.**(4)****TMM003.7**Convert points and equations between rectangular and polar form, graph polar functions, solve polar equations, identify and express the conics in standard polar form for graphing, and solve applied problems involving conics in polar form.**(4)****TMM003.8**Identify and graph a curve defined by parametric equations by making a table of values and, when possible, eliminating the parameter.**(3)**

*** Denotes required items for transfer credit**