Northampton County Schools Pre-Calculus Mathematics Pacing Guide

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1 Northampton County Schools Pre-Calculus Mathematics Pacing Guide Grading Periods Included 1 st Six Weeks 2 nd Six Weeks 3 rd Six Weeks Northampton County Schools Department of Curriculum & Instruction K-12 Mathematics Geneva N. Squire, Coordinator Fall 2008 Pacing guides are subject to change as a result of benchmark assessment results.

2 Northampton County Schools Pre-Calculus Pacing Guide The pacing guide illustrates the relative weight of the goals and objectives within the course. The pacing guide should be used by teachers to plan the course of work for the year, prepare daily lesson plans, and construct instructionally valid summative and formative assessments. Interpretation of Columns on the Math Pacing Guide No. Heading Column information 1 Obj.# Obj. =Objective number (Goal and Objective within the goal). Some of the goals have sublevel content as well. 2 Objective Statements 3 Supplemental Materials/Textbook Correlation Statements of unit titles and specific objectives. Each specific objective begins with an action verb and makes a complete sentence when combined with the stem The learner will be able to... Valuable formative assessments can be located at the links below. Indicators: DPI Resources: Shador: Listserv If you wish to receive announcements and updates relevant to high school mathematics for the state of North Carolina, you may join the listserv by providing your name, address, school name, school address and phone number to

3 Unit Titles/Competency and Objective Statements Supplementary Materials/Textbook Correlation Obj # (The Learner will be able to:) st Six Weeks (Topics should have covered) 1.01 Transform relations in two dimensions; describe algebraically and geometrically the results. Use the quadratic relations (parabola, circle, ellipse, hyperbola) to model and solve problems; justify results. (a) Solve using tables, graphs, and algebraic properties. (b) Interpret the constants and coefficients in the context of the 2.01 Use functions (polynomial, power, rational, exponential, logarithmic, logistic, piecewise, and greatest integer) to model and solve problems; justify results Solve using graphs and algebraic properties. Interpret the constants, coefficients, and bases in the context of the For sets of data, create and use calculator-generated models of linear, polynomial, exponential, trigonometric, power, logistic, and logarithmic functions. (a) Interpret the constants, coefficients, and bases in the context of the data. (b) Check models for goodness-of-fit; use the most appropriate model to draw conclusions or make predictions Use the composition and inverse of functions to model and solve problems. 2 nd Six Weeks 1.01 Transform relations in two dimensions; describe algebraically and geometrically the results. Use the quadratic relations (parabola, circle, ellipse, hyperbola) to model and solve problems; justify results. (a) Solve using tables, graphs, and algebraic properties. (b) Interpret the constants and coefficients in the context of the 2.01 Use functions (polynomial, power, rational, exponential, logarithmic, logistic, piecewise, and greatest integer) to model and solve problems; justify results Solve using graphs and algebraic properties. Interpret the constants, coefficients, and bases in the context of the

4 Unit Titles/Competency and Objective Statements Supplementary Materials/Textbook Correlation Obj # (The Learner will be able to:) Use trigonometric and inverse trigonometric functions to model and solve problems; justify results. (a) Solve using graphs and algebraic properties. (b) Create and identify transformations with respect to period, amplitude, and vertical and horizontal shifts. (c) Develop and use the law of sines and the law of cosines. For sets of data, create and use calculator-generated models of linear, polynomial, exponential, trigonometric, power, logistic, and logarithmic functions. (a) Interpret the constants, coefficients, and bases in the context of the data. (b) Check models for goodness-of-fit; use the most appropriate model to draw conclusions or make predictions Use the composition and inverse of functions to model and solve problems. 3 rd Six Weeks 1.01 Transform relations in two dimensions; describe algebraically and geometrically the results. Use the quadratic relations (parabola, circle, ellipse, hyperbola) to model and solve problems; justify results. (a) Solve using tables, graphs, and algebraic properties. (b) Interpret the constants and coefficients in the context of the 2.02 Use trigonometric and inverse trigonometric functions to model and solve problems; justify results. (a) Solve using graphs and algebraic properties. (b) Create and identify transformations with respect to period, amplitude, and vertical and horizontal shifts. (c) Develop and use the law of sines and the law of cosines. For sets of data, create and use calculator-generated models of linear, polynomial, exponential, trigonometric, power, logistic, and logarithmic functions. (a) Interpret the constants, coefficients, and bases in the context of the data. (b) Check models for goodness-of-fit; use the most appropriate model to draw conclusions or make predictions Use polar equations to model and solve problems. (a) Solve using graphs and algebraic properties. (b) Interpret the constants and coefficients in the context of the

5 Unit Titles/Competency and Objective Statements Supplementary Materials/Textbook Correlation Obj # (The Learner will be able to:) Use parametric equations to model and solve problems Use recursively-defined functions to model and solve problems. (a) Find the sum of a finite sequence. (b) Find the sum of an infinite sequence. (c) Determine whether a given series converges or diverges. (d) Translate between recursive and explicit representations Explore the limit of a function graphically, numerically, and algebraically.

6 Days in Grading Period Pre-Calculus PACING GUIDE 1 st Grading Period Objectives Concept Key Concept Graphs and Equations Functions and Graphs Polynomial and Rational Functions Translate between algebraic, graphical and tabular representations of a function? Recognizing symmetry from the graph of a function Solve linear, quadratic, rational, absolute value and radical equations and inequalities. Recognizing basic functions (linear, identity, squaring, cubing, square rooting, reciprocal, absolute value, exponential, logarithmic, trigonometric) from their equations, graphs, and tables? Recognize the domain and range of a function from its graph and/or equation. Definition of continuity Definition of discontinuity (piece-wise functions) Recognize discontinuity on TI-83 Interpret the slope and y-intercept of a linear function in the context of a real-life situation Linear regression on data using TI-83 Calculate average rate of change Identify the critical behavior (i.e. increasing/ decreasing, minima/maxima, x-intercepts) of a function on a given interval? Find minima and maxima using TI-83 Find x-intercepts using TI-83 Recognize and perform transformations such as reflections, translations, stretches and compressions on the graphs of the basic functions Given a set of data, identify the appropriate type of regression equation. Use correlation coefficient on TI-83 Locate the vertical, horizontal and oblique asymptotes of a

7 Exponential and Logarithmic Functions 2 Remediation and Enrichment Unit Review and Mini-Assessment rational function. Recognize connection between asymptotes and domain and range. Identify the salient characteristics (x- and y-intercept asymptotes) of a graph of the equation of a rational function. Identify the salient characteristics (degree, real zeros, turning points, end behavior) of the graph of the equation of a polynomial. Locate the complex roots of a polynomial equation. Apply theorems and rules to analyze equations Find the inverse of a function. Relationship between the graphs of two inverse functions. Relationship between the domains and ranges of inverse functions. Use exponential and logarithmic equations to model real-world phenomena. Solve exponential and logarithmic equations using power rules and properties of logarithms.

8 Days in Grading Period Pre-Calculus PACING GUIDE 2 nd Grading Period Objectives Concept Key Concept Exponential and Logarithmic Functions Trigonometric Functions 1.5 Review and test Analytic Trigonometry Continue Convert between degrees (decimal and DMS) and radians. Find the exact values of the trigonometric functions for points on the unit circle. Recognize special triangles and understand the development of the unit circle. Given a trigonometric function for an angle and the quadrant the angle lies in, find the remaining trigonometric functions. Graph the six trigonometric functions. Perform transformations (phase shifts, vertical and horizontal stretches and compressions, vertical shifts) on the graphs of the trigonometric functions Fit a sine or cosine equation to real-world data and how do you interpret that equation. Find the relationship between linear and angular velocities. Find the exact and/or approximate values of the inverse trigonometric functions. Find principle angles and others Establish an identity. Find exact trigonometric function values for non-traditional angles. Apply sum, difference, double angle, half-angle formulas Solve trigonometric equation for all solutions in the first

9 Test Applications of Trigonometry revolution. Solve a triangle using right triangle trig, law of sines, or law of cosines. Find the area of a triangle given any three parts. Find and analyze an equation for an object in simple harmonic motion.

10 3 rd Grading Period Days in Objectives Concept Key Concept Grading Period Applications of Trigonometry Continue Polar Coordinates and Vectors Convert between polar and rectangular coordinates. Graph polar equations on polar coordinates. Identify the graph of a polar equation from its rule. Operate with vectors. Identify direction and magnitude. Add and subtract graphically and algebraically. Use vectors and their properties to solve real-world problems involving navigation and force. Analytic Geometry Determine the graph of the conic from the equation. Identify key features of graphs of conics (vertices, foci, axes, asymptotes). Use the TI-83 to graph parametric equations. Write x and y position equations in terms of a parameter (usually time) Sequences, Binomial Theorem Recursive and explicit formulas compare and contrast. Define a series of points that converges or diverges Limits Graphical, numerical and algebraic representations of limits of a function Review and Final Exam

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