Comal Independent School District Pre-AP Pre-Calculus Scope and Sequence

Transcription

1 Comal Independent School District Pre- Pre-Calculus Scope and Sequence Third Quarter Assurances. The student will plot points in the Cartesian plane, use the distance formula to find the distance between two points, use the midpoint formula to find the midpoint of a line segment, and use a coordinate plane and geometric formulas The student will sketch graphs of equations, find x- and y- intercepts, use symmetry to sketch graphs, find equations of and sketch graphs of circles, and use graphs of equations in solving real-life The student will find and use slope to graph linear equations, to identify parallel and perpendicular lines, and The student will determine whether relations are functions, use function notation, find the domains of functions, and use functions to solve real-life The student will add, subtract, multiply, and divide functions, find the composition of functions, and use combinations and compositions of functions The student will analyze graphs of quadratic functions, write quadratic functions in standard form and use the results to sketch graphs of functions, and use quadratic functions The student will use transformations to sketch graphs of polynomial functions, determine the end behavior of graphs of polynomial functions, and find and use zeros of polynomial The student will use long division and synthetic division to divide polynomials, and use the Remainder and Factor Theorems. The student will perform operations with the imaginary unit i, and find complex solutions of quadratic equations. The student will find rational and complex zeros of polynomial The student will find the domains, and the horizontal, vertical, and slant asymptotes of graphs; and use rational functions to model and solve real-life The student will recognize a conic as the intersection of a plane and a double-napped cone, write equations of parabolas in standard form and graph them, and use the reflective property of parabolas to solve real-life The student will write equations of ellipses in them, use properties of ellipses problems, and find eccentricities of ellipses. The student will write equations of hyperbolas in them, use properties of hyperbolas to solve real-life problems, and classify conics from their general equations. Pre- Pre-Calculus Page 1 of 5 Revised January 2011

2 Third Quarter Vocabulary Unit 5: and Their Graphs Unit 6: Polynomial and Rational Unit 7: Topics in Analytic Geometry Cartesian Plane Quadratic Conic Scatter Plot Parabola Parabola Pythagorean Theorem Axis of Symmetry Ellipse Distance Formula Vertex Hyperbola Midpoint Formula Polynomial Focus x- and y- intercepts Leading Coefficient Major/Minor Axis Symmetry Zeros Eccentricity Slope/Rate of Change Long/Synthetic Division Parametric Point-Slope Form Remainder and Factor Theorems Slope-Intercept Form Complex Number Parallel Conjugate Perpendicular Asymptote Independent Dependent Domain Composition Pre- Pre-Calculus Page 2 of 5 Revised January 2011

3 Comal Independent School District Pre- Pre-Calculus Scope and Sequence Third Quarter Concept Foundational Topic TEKS Statement Specificity Unit 5 and Their Graphs The student defines functions, describes characteristics of functions, and translates among verbal, numerical, graphical, and symbolic representations of functions, including polynomial, rational, power (including radical), exponential, logarithmic, trigonometric, and piecewisedefined The student interprets the meaning of the symbolic representations of functions and operations on functions to solve meaningful (P.1A) Describe parent functions symbolically and graphically, including f(x) = x n, f(x) = 1n x, f(x) = log a x, f(x) = 1/x, f(x) = e x, f(x) = x, f(x) = a x, f(x) = sin x, f(x) = arcsin x, etc. (P.1B) Determine the domain and range of functions using graphs, tables, and symbols (P.1C) Describe symmetry of graphs of even and odd functions (P.1D) Recognize and use connections among significant values of a function (zeros, maximum values, minimum values, etc.), points on the graph of a function, and the symbolic representation of a function (P.2A) Apply basic transformations, including a f(x), f(x) + d, f(x - c), f(b x), and compositions with absolute value functions, including f(x), and f( x ), to the parent functions (P.2B) Perform operations including composition on functions, find inverses, and describe these procedures and results verbally, numerically, symbolically, and graphically The student will plot points in the Cartesian plane, use the distance formula to find the distance between two points, use the midpoint formula to find the midpoint of a line segment, and use a coordinate plane and geometric formulas to model and solve real-life The student will sketch graphs of equations, find x- and y- intercepts, use symmetry to sketch graphs, find equations of and sketch graphs of circles, and use graphs of equations in solving reallife The student will find and use slope to graph linear equations, to identify parallel and perpendicular lines, and to model and solve real-life The student will determine whether relations are functions, use function notation, find the domains of functions, and use functions to solve real-life The student will add, subtract, multiply, and divide functions, find the composition of functions, Pre- Pre-Calculus Page 3 of 5 Revised January 2011 Chapter 1, Sections 1, 2, 3, 4, 8 Model It activities near the end each exercise Animated Pre-Calculus, Dana Center Clarifying Activities: ctivities/precal.php Laying the Foundations : 1.4: Piecewise p. 43, LTF A Generic Function p. 35, LTF Describing Graphs p.135, LTF (Use after Ch. 1) 9 Days

4 Concept Foundational Topic TEKS Statement Specificity Unit 5 cont. The student uses functions and their properties, tools and technology, to model and solve meaningful (P.3A) Investigate properties of trigonometric and polynomial functions and use combinations and compositions of functions Chapter 1 Cont. Unit 6 Polynomial and Rational The student defines functions, describes characteristics of functions, and translates among verbal, numerical, graphical, and symbolic representations of functions, including polynomial, rational, power (including radical), exponential, logarithmic, trigonometric, and piecewisedefined The student uses functions and their properties, tools and technology, to model and solve meaningful (P.1A) see above (P.1B) see above (P.1D) see above (P.1E) Investigate the concepts of continuity, end behavior, asymptotes, and limits and connect these characteristics to functions represented graphically and numerically (P.3A) see above (P.3B) use functions such as logarithmic, exponential, trigonometric, polynomial, etc. to model real-life data (P.3D) use properties of functions to analyze and solve problems and make predictions The student will analyze graphs of quadratic functions, write quadratic functions in standard form and use the results to sketch graphs of functions, and use quadratic functions The student will use transformations to sketch graphs of polynomial functions, determine the end behavior of graphs of polynomial functions, and find and use zeros of polynomial The student will use long division and synthetic division to divide polynomials, and use the Remainder and Factor Theorems. Limits Chapter 2, Sections 1, 2, 3, 4, 5, 6, 7 Model It Activity Animated Pre-Calculus 2.6: Rational p.76, LTF 12 Days The student will perform operations with the imaginary unit i, and find complex solutions of quadratic equations. The student will find rational and complex zeros of polynomial The student will find the domains, and the horizontal, vertical, and slant asymptotes of graphs, and use rational functions Pre- Pre-Calculus Page 4 of 5 Revised January 2011

5 Concept Foundational Topic TEKS Statement Specificity Unit 7 Topics in Analytic Geometry (Conics) The student uses conic sections, their properties, and parametric representations, as well as tools and technology, to model physical situations. (P.5A) Use conic sections to model motion, such as the graph of velocity vs. position of a pendulum and motions of planets (P.5B) Use properties of conic sections to describe physical phenomena such as the reflective properties of light and sound The student will recognize a conic as the intersection of a plane and a doublenapped cone, write equations of parabolas in them, and use the reflective property of parabolas to solve real-life The student will write equations of ellipses in them, use properties of ellipses to model and solve real-life problems, and find eccentricities of ellipses. The student will write equations of hyperbolas in them, use properties of hyperbolas to solve real-life problems, and classify conics from their general equations. Chapter 10, Sections 2, 3, 4; Include Parametric Mode Model It Activity Animated Pre-Calculus Conics in Parametric Form p.317, LTF 10 Days Pre- Pre-Calculus Page 5 of 5 Revised January 2011