Estimated Pre Calculus Pacing Timeline

Size: px
Start display at page:

Download "Estimated Pre Calculus Pacing Timeline"

Transcription

1 Estimated Pre Calculus Pacing Timeline School Year The timeframes listed on this calendar are estimates based on a fifty-minute class period. You may need to adjust some of them from time to time based on data to meet the needs of your students as some concepts may take less time and some may take more time. Estimated Timeframe for Instruction and Unit Name Assessment Unit 1: Prerequisite Information Chapter 0 (7 days) August 16 August 24 Unit 2: Functions Chapter 1 (12 days) August 25 - September 10 Unit 3: Power, Polynomial, and Rational Functions Chapter 2 (12 days) Optional Unit 4: Exponential and Logarithmic Functions Chapter 3 (7 days) Unit 5: Trigonometric Functions Chapter 4 (17 days) September 13 September 28 September 29 October 7 October 8 November 2 Note: Quarter 1 ends on October 15 Unit 6: Graphs of Trigonometric Functions Chapter 4 (10 days) November 3 November 17 Unit 7: Trigonometric Identities and Equations Chapter 5 (23 days) November 18 December 22 Includes review and exams Note: Quarter 2 ends on December 22 Unit 8: Conics and Parametric Equations Chapter 7 (15 days) January 10 January 31 Unit 9: Vectors Chapter 8 (15 days) February 1 February 22 Unit 10: Polar Coordinates and Complex Numbers Chapter 9 (17 days) February 23 March 25 Note: Quarter 3 ends on March 11 Unit 11: Sequences and Series Chapter 10 (20 days) March 28 April 22 Unit 12:Limits and Derivatives Chapter 12 (15 days) April 25 May 13 Review/Exams (11 days) May 17 June 1 Note: Quarter 4 ends on June 1 Page 1 of 26

2 Unit Title: (1) Preparing for Precalculus Chapter 0 Number of Days: 7 days Know: Understand: Do: Sets have notations to denote elements, subsets and components. The same operations that are used on real numbers can be used on complex numbers. Quadratic functions can be used to model data to analyze real life situations. There are specific rules for performing operations with exponents and radicals. Systems of equations and matrices can be used to model and solve real world equations. There are procedures to follow for solving equations and inequalities both algebraically and graphically. Use set notation to denote elements, subsets, and complements. Find intersections and unions of sets. Perform operations with imaginary numbers and complex numbers. Graph and solve quadratic equations. Simplify expressions in radical and exponential form. Solve systems of equations and inequalities. Perform operations and solve real life problems with matrices. Page 2 of 26

3 Unit Title: (1) Preparing for Precalculus Chapter 0 Number of Days: 7 days Key Learning: There are procedures to follow for solving equations and inequalities both algebraically and graphically. Unit Essential Question: What skills will prepare me for this course? Sets MA.912.S.3.2 MA.912.D How do I work with set notation and find intersections and unions of sets? set, subset, universal set, empty set, compliment Operations with Complex Numbers MA.912.A How do I perform operations with pure imaginary numbers and complex numbers? imaginary number, complex number, complex conjugates Quadratic Functions and Equations MA.912.A How do I solve and graph quadratic equations? parabola, quadratic equation, quadratic formula nth Roots and Real Exponents MA.912.A How do I simplify expressions in radical and exponential form? nth root, principal root Systems of Linear Equations and Inequalities MA.912.A How do I solve systems of equations and inequalities both algebraically and graphically? systems of equations, independent, dependent, inconsistent, system of inequalities Matrix Operations MA.912.D.8.1 MA.912.D How do I perform operations with matrices? matrix, element, dimensions, zero matrix, scalar Additional Information: Language Arts Benchmarks used in each concept: LA , LA , LA , LA , LA Glencoe McGraw-Hill, PRECALCULUS, 2011, is the Pasco County adopted textbook. Page 3 of 26

4 Unit Title: (2) Functions Chapter 1 Number of Days: 12 days Know: Understand: Do: Graphs of common functions can be shifted, reflected, and stretched and will help in sketching a wide variety of functions by hand. Combinations of functions can help model and analyze real world situations. Functions and their graphs can be analyzed to predict their future behavior. Write sets using set-builder and interval notation. Determine if relations are functions. Identify and evaluate functions and state their domains. Find domain, range, intercepts, and symmetry of a given relation. By analyzing the graph of a function the future behavior of a function can be indicated. Relations have inverses that can be found algebraically and graphically. Identify odd and even functions. Determine where a relation is continuous and discontinuous. Approximate zeros using the Intermediate Value Theorem. Determine the end behavior of a function. Apply end behavior to real world situations. Determine the intervals of which functions are increasing and decreasing. Identify extrema by hand and by using a graphing calculator. Page 4 of 26

5 Apply extrema to real world situations. Use real world situations to find the average rate of change. Describe and graph various transformations to a given parent function. Graph a piecewise-defined function. Perform various operations with functions. Compose and decompose functions. Determine whether or not an inverse function exists algebraically and graphically. Find and verify inverse functions algebraically and graphically. Page 5 of 26

6 Unit Title: (2) Functions Chapter 1 Number of Days: 12 days Key Learning: Functions and their graphs can be analyzed to predict their future behavior. Unit Essential Question: How do I analyze graphs to predict future function behavior? Functions and Their Graphs MA.912.A How do I identify and evaluate functions and state their domains? 2. How do I identify and graph functions? set-builder notation, interval notation, implied domain, piece-wise defined function, relevant domain, zeros, roots, even function, odd function Behaviors of Graphs and Limits MA.912.A.5.6 MA.912.C How do I use limits to determine the continuity of a function and determine end behavior of functions? 4. How do I find the average rate of change and determine whether the function is increasing, decreasing or constant? continuous, limit, discontinuous, infinite, jump, end behavior, increasing, decreasing, constant, maximum, minimum, extrema Parent Functions and Transformations MA.912.A How do I describe and graph transformations of functions? parent, step, greatest integer function Function Operations and Composition of Functions MA.912.A.2.7 MA.912.A How do I perform operations and find compositions of functions? composition Inverse Relations and Functions MA.912.A How do I solve problems involving functions and their inverses? inverse relation, inverse function, one-to-one Additional Information: Language Arts Benchmarks used in each concept: LA , LA , LA , LA , LA Glencoe McGraw-Hill, PRECALCULUS, 2011, is the Pasco County adopted textbook. Page 6 of 26

7 Unit Title: (3) Power, Polynomial, and Rational Functions Chapter 2 Number of Days: 12 days Know: Understand: Do: The graph of any function gives a good indication of the future behavior of a function. Polynomial and rational functions are useful in real life situations. Describe domain, range, intercepts, end behavior, continuity and where the function is increasing and decreasing. Solve radical and exponential equations. Polynomial division can help rewrite polynomials that are used to model real life problems. The zeros of polynomial functions yield important information to model real life problems. Apply the Leading Coefficient Test. Find the number of possible real zeros and the turning points. Graph higher-degree polynomial functions. Divide polynomials by long and synthetic division. Apply the Remainder Theorem in evaluating a polynomial. Apply the Factor Theorem to determine if one polynomial is a factor of another. Find all possible rational zeros of a function using the Rational Zero Theorem. Use the Fundamental Theorem of Algebra and the Linear Factorization Theorem to assist in finding zeros. Find all asymptotes of a rational function. Graph a rational function. Solve rational equations. Page 7 of 26

8 Unit Title: (3) Power, Polynomial, and Rational Functions Chapter 2 Number of Days: 12 days Key Learning: Polynomial and rational functions are useful in real life situations. Unit Essential Question: How are polynomial and rational functions used in real life? Exponential and Radical Functions MA.912.A How do I graph and analyze exponential and radical functions? 2. How do I solve exponential and radical equations? exponential function, radical function, extraneous solutions Polynomial Functions MA.912.A.4.5 MA.912.A How do I graph polynomial functions and use them to model real-world data? polynomial function, Leading Coefficient Test, multiplicity Zeros of Polynomial Functions & The Remainder Theorem MA.912.A.4.6 MA.912.A How do I use the Remainder Theorem to evaluate a polynomial? 5. How do I find real and complex zeros of a polynomial function? synthetic division, lower bound, upper bound Rational Functions MA.912.A.5.6 MA.912.C How do I analyze and graph rational functions? 7. How do I solve rational equations? rational function, asymptote, holes Additional Information: Language Arts Benchmarks used in each concept: LA , LA , LA , LA , LA Glencoe McGraw-Hill, PRECALCULUS, 2011, is the Pasco County adopted textbook. Page 8 of 26

9 Unit Title: (4) Exponential and Logarithmic Functions (Optional) Chapter 3 Number of Days: 7 days Know: Understand: Do: Exponential and logarithmic functions are inverses of one another. Real world situations can be solved using exponential and logarithmic functions. Sketch and analyze graphs of exponential and logarithmic functions. Properties of logarithms will help in solving exponential and logarithmic equations. Model real life data using exponential and logarithmic graphs. Evaluate logarithms using various methods. Solve exponential and logarithmic equations using Change of Base Formula and properties of logarithms. Solve real world problems using exponential and logarithmic equations. Page 9 of 26

10 Unit Title: (4) Exponential and Logarithmic Functions (Optional) Chapter 3 Number of Days: 7 days Key Learning: Real world situations can be solved using exponential and logarithmic functions. Unit Essential Question: How can real world situations be solved using exponential and logarithmic functions? Exponential and Logarithmic Functions (Optional) MA.912.A How do I evaluate, sketch and analyze exponential and logarithmic functions? , 3-2 exponential function, logarithmic function, natural base, natural log Using Properties of Logarithms in Solving Exponential and Logarithmic Equations (Optional) MA.912.A.8..2 MA.912.A How do I apply properties of logarithms to solve exponential and logarithmic equations? , 3-4 continuous compound interest Real World Applications (Optional) MA.912.A How do I solve real world problems using exponential and logarithmic equations? & additional resources Additional Information: This unit is optional. These benchmarks are not listed in the Precalculus State Benchmarks, however are necessary for preparation of Calculus. Language Arts Benchmarks used in each concept: LA , LA , LA , LA , LA Glencoe McGraw-Hill, PRECALCULUS, 2011, is the Pasco County adopted textbook. Page 10 of 26

11 Unit Title: (5) Trigonometric Functions Chapter 4 Number of Days: 17 days Know: Understand: Do: There are six trigonometric functions related to right triangles. Angles can be measured using degrees and radians. There are a variety of methods to solve for sides and angles of triangles and ways to find the area of triangles. Find the values of the six trigonometric ratios in any quadrant. Find the missing side lengths and angle measures of a right triangle. Use angle of elevation and depression to solve real life problems. There is a relationship between the unit circle and real numbers. Trigonometric functions are periodical. The Laws of Sines and Cosines are used to solve triangle measures. There are two additional methods of finding area in any triangle. Convert between DMS and decimal degree form. Convert between degrees and radians. Find and draw coterminal angles. Find arc length. Find angular and linear speed. Find the area of a sector. Evaluate a trig function given a point. Evaluate trig functions of a quadrantal angle. Find and use reference angles to find trig values. Find exact values using the unit circle. Apply the Law of Sines and the Law of Cosines. Find the area of oblique triangles. Page 11 of 26

12 Unit Title: (5) Trigonometric Functions Chapter 4 Number of Days: Key Learning: 17 days There are a variety of methods to solve for sides and angles of triangles and ways to find the area of triangles. Unit Essential Question: How do I solve for sides and angles of triangles and find their areas? Right Triangle Trigonometry MA.912.T.2.1 MA.912.T How do I find values of trigonometric functions in right triangles? trigonometric functions, inverse trigonometric functions, angles of elevation and depression Degrees and Radians MA.912.T How do I convert degree measures of angles to radian measure and vice versa? 3. How do I use angle measures to solve real world problems? initial side, terminal side, standard position, radian, coterminal angles, linear and angular velocity, sector Trigonometric Functions on the Unit Circle MA.912.T.1.2 MA.912.T How do I find values of trigonometric functions for any angle? 5. How do I find values of trigonometric functions using the unit circle? quadrantal angle, reference angle, unit circle, periodic function, period The Law of Sines and the Law of Cosines MA.912.T.2.3 MA.912.T How do I solve oblique triangles using Law of Sines and Law of Cosines? 7. How do I find the area of an oblique triangle? oblique triangle, Law of Sines and Cosines, ambiguous case, Heron s Formula Additional Information: Language Arts Benchmarks used in each concept: LA , LA , LA , LA , LA Glencoe McGraw-Hill, PRECALCULUS, 2011, is the Pasco County adopted textbook. Page 12 of 26

13 Unit Title: (6) Graphing Trigonometric Functions Chapter 4 Number of Days: 10 days Know: Understand: Do: Trigonometric functions are periodical. Trigonometric functions and their graphs can be used to model real life data. Each number in a trigonometric equation represents different transformations. Inverse functions can be evaluated using various methods. Trigonometric functions and their graphs can be used to model real life data. Find amplitude, period, frequency, x- intercepts and phase shift of sine and cosine functions. Find period, x-intercepts and asymptotes of tangent functions. Graph all trigonometric functions including reciprocal and inverse functions. Evaluate inverse functions. Use inverse trigonometric properties to find exact values. Evaluate compositions of trigonometric functions. Page 13 of 26

14 Unit Title: (6) Graphing Trigonometric Functions Chapter 4 Number of Days: 10 days Key Learning: Trigonometric functions and their graphs can be used to model real life data. Unit Essential Question: How do trigonometric functions and their graphs model real world data? Graphing Sine and Cosine Functions MA.912.T How do I graph sine and cosine functions? amplitude, frequency, phase shift, vertical shift, midline Graphing Other Trigonometric Functions MA.912.T.1.4 MA.912.T How do I graph tangent and reciprocal functions? damped trigonometric function Inverse Trigonometric Functions MA.912.T.2.3 MA.912.T How do I evaluate and graph inverse trigonometric functions? arcsine function, arccosine function, arctangent function Additional Information: Language Arts Benchmarks used in each concept: LA , LA , LA , LA , LA Glencoe McGraw-Hill, PRECALCULUS, 2011, is the Pasco County adopted textbook. Page 14 of 26

15 Unit Title: (7) Trigonometric Identities and Equations Chapter 5 Number of Days: 23 days Know: Understand: Do: Fundamental trigonometric identities can be used to simplify and rewrite trigonometric expressions. Techniques for solving algebraic equations can be applied to solve trigonometric equations. Identities can be used to rewrite trigonometric functions in more convenient forms. Rewriting equations using trigonometric identities helps to solve real-life problems. Derive and prove trigonometric identities. Simplify trigonometric expressions using the trigonometric identities. Use sum, difference, double-angle, and half-angle formulas to find exact values and to establish identities. Solve trigonometric equations using exact values and decimal approximations. Rewriting equations helps to solve real-life problems. Solve trigonometric equations using a graphing calculator. Page 15 of 26

16 Unit Title: (7) Trigonometric Identities and Equations Chapter 5 Number of Days: 23 days Key Learning: Rewriting equations using trigonometric identities helps to solve real-life problems. Unit Essential Question: How do I rewrite equations using trigonometric identities and solve real-life problems? Trigonometric Identities MA.912.T.1.8 MA.912.T How do I use basic trig identities to find trig values, simplify, and rewrite trig expressions? trigonometric identity, cofunction, odd-even identities Verifying Trigonometric Identities MA.912.T.1.8 MA.912.T How do I verify a trigonometric identity? verify an identity Solving Trigonometric Equations MA.912.T.1.8 MA.912.T How do I solve trig equations using identities or algebraic techniques? Sum and Difference Identities MA.912.T.3.2 MA.912.T How do I use sum and difference identities to evaluate and solve trigonometric equations? sum and difference identities Multiple Angle and Product-to-Sum Identities MA.912.T.3.3 MA.912.T How do I use half-angle and double-angle identities for sine, cosine and tangent functions? half-angle and doubleangle identities Additional Information: Language Arts Benchmarks used in each concept: LA , LA , LA , LA , LA Glencoe McGraw-Hill, PRECALCULUS, 2011, is the Pasco County adopted textbook. Page 16 of 26

17 Unit Title: (8) Conic Sections and Parametric Equations Chapter 7 Number of Days: 15 days Know: Understand: Do: Conic sections are the intersection of a plane and a double cone. Each conic section has its own equation. Conic sections and parametric equations can be used to model and solve many types of real life problems. Write an equation of a parabola. Identify the vertex, focus, directrix, and axis of symmetry and then graph the equation of a parabola. The equations can be used to graph the conic section and identify important features of the section. Graphs can be analyzed to find the equation of the conic section. Parametric functions consist of two functions, each of which is a function of another variable, the parameter. The parameter allows you to determine where an object was at a given time. These equations define a plane curve. Write an equation of a circle. Identify the center and radius and then graph an equation of a circle. Write the equation of an ellipse. Identify the center, vertices, covertices, foci, length of the major and minor axis, and then graph the equation of an ellipse. Write an equation of a hyperbola. Identify the center, vertices, foci, and asymptotes of a hyperbola and then graph the equation of a hyperbola. Graph parametric equations by hand and using a graphing calculator. Rewrite a rectangular equation into parametric form and vice versa. Solve real world problems using projectile motion. Page 17 of 26

18 Unit Title: (8) Conic Sections and Parametric Equations Chapter 7 Number of Days: 15 days Key Learning: Conic sections and parametric equations can be used to model and solve many types of real life problems. Unit Essential Question: How do I solve and model real life situations using conic sections and parametric equations? Parabolas MA.912.A.9.1 MA.912.A How do I analyze, graph and write equations of parabolas? conic, parabola, focus, directrix Ellipses and Circles MA.912.A.9.1 MA.912.A How do I analyze, graph and write equations of ellipses and circles? ellipse, foci, major axis, minor axis, center, vertices, covertices, eccentricity Hyperbolas MA.912.A.9.1 MA.912.A How do I analyze, graph and write equations of hyperbolas? 4. How do I identify the types of conic sections? hyperbola, transverse axis, conjugate axis Parametric Equations MA.912.D.10.1 MA.912.D How do I graph parametric equations and solve problems related to projectile motion? parametric equation, parameter, orientation, parametric curve Additional Information: Language Arts Benchmarks used in each concept: LA , LA , LA , LA , LA Glencoe McGraw-Hill, PRECALCULUS, 2011, is the Pasco County adopted textbook. Page 18 of 26

19 Unit Title: (9) Vectors - Chapter 8 Number of Days: 15 days Know: Understand: Do: Vectors represent a specific direction and magnitude. Vectors are used to analyze numerous aspects of every day life. Vectors are directed line segments that demonstrate the applications of physics. Graph vectors and find the position vector. Perform operations with two-dimensional and three-dimensional vectors including addition, subtraction, and scalar multiplication. Express a vector in component form. Vectors can be used in both twodimensions and three-dimensions. Find the magnitude and direction of a vector. Find a unit vector in the same direction as a given vector. Find the dot product of two vectors. Find the angle between the two vectors. Determine whether two vectors are parallel, orthogonal, or neither. Solve applied problems involving vectors. Find the cross product of two-dimensional and three-dimensional vectors. Plot points in three-dimensional space. Find the distance and midpoint between two points in space. Apply the geometric properties of cross products of vectors in space. Page 19 of 26

20 Unit Title: (9) Vectors Chapter 8 Number of Days: 15 days Key Learning: Vectors are directed line segments that demonstrate the applications of physics. Unit Essential Question: How are vectors used to demonstrate the application of physics problems? Introduction to Vectors MA.912.D.9.1 MA.912.D How do I represent and operate with vectors geometrically? 2. How do I solve vector problems? vector, initial point, terminal point, standard position, direction, magnitude, equivalent vectors, opposite vectors, resultant, zero vector, components, rectangular components Vectors in the Coordinate Plane MA.912.D.9.2 MA.912.D How do I represent and operate with vectors in the coordinate plane? 4. How do I write a vector as a linear combination of unit vectors? component form, unit vector, linear combination Dot Products and Vector Projections MA.912.D.9.1 MA.912.D How do I find the dot product of two vectors, and use the dot product to find the angle between them? dot product, orthogonal Vectors in Three- Dimensional Space MA.912.D.9.1 MA.912.D How do I plot points and vectors in the three-dimensional coordinate system? 7. How do I express algebraically and operate with vectors in space? three-dimensional coordinate system, z-axis, octant, ordered triple, Dot and Cross Products of Vectors in Space MA.912.D.9.1 MA.912.D How do I find dot products of an angle between vectors in space? 9. How do I find cross products of vectors in space, and use cross products to find area and volume? cross product, torque, parallelepiped, triple scalar product Additional Information: Language Arts Benchmarks used in each concept: LA , LA , LA , LA , LA Glencoe McGraw-Hill, PRECALCULUS, 2011, is the Pasco County adopted textbook. Page 20 of 26

21 Unit Title: (10) Polar Coordinates and Complex Numbers Chapter 9 Number of Days: 17 days Know: Understand: Do: Many types of graphs are simpler to graph in polar form than rectangular form. These graphs are identified with special names. Applications of polar equations of circles model real life problems. Polar equations, more so than a rectangular equation, allow us to graph illustrations of what we see in nature. Graph points on a polar grid. Find multiple representations of polar coordinates. Graph polar equations. Find the distance between polar coordinates. Methods for converting between polar and rectangular forms of points and equations offer a different mathematical perspective. Find symmetry, zeros and maximum r-values. Identify and graph classic curves. Convert between rectangular and polar form of coordinates and equations. Find the absolute value of a complex number. Convert between polar form and rectangular form of a complex number. Find the product and quotient of complex numbers in polar form. Apply De Moivre s Theorem. Page 21 of 26

22 Unit Title: (10) Polar Coordinates and Complex Numbers Chapter 9 Number of Days: Key Learning: 17 days Polar equations, more so than a rectangular equation, allow us to graph illustrations of what we see in nature. Unit Essential Question: When is it more appropriate to use polar equations rather than rectangular equations? Polar Coordinates MA.912.T.4.1 MA.912.T How do I graph points with polar coordinates? polar coordinate system, pole, polar axis, polar coordinates, polar equation, polar graph Graphs of Polar Equations MA.912.T How do I graph polar equations? 3. How do I identify and graph classical curves? limacon, cardioid rose, rose, lemniscates, spiral of Archimedes Polar and Rectangular Forms of Equations MA.912.T.4.2 MA.912.T How do I convert between polar and rectangular coordinates and equations? Complex Numbers and De Moivre s Theorem MA.912.T.4.4 MA.912.T How do I convert complex numbers from rectangular to polar form and vice versa? 6. How do I find products, quotients, powers and roots of complex numbers in polar form? complex plane, absolute value of a complex number, polar form of a complex number, trigonometric form of a complex number Additional Information: Language Arts Benchmarks used in each concept: LA , LA , LA , LA , LA Glencoe McGraw-Hill, PRECALCULUS, 2011, is the Pasco County adopted textbook. Page 22 of 26

23 Unit Title: (11) Sequences and Series Chapter 10 Number of Days: 20 Days Know: Understand: Do: Sequences and series are useful in identifying patterns. These patterns can be defined using formulas for arithmetic or geometric sequences. Using the formulas for sequences and series simplifies the solving of real life problems. Identify sequence and series notations and patterns. Find partial sums using sigma notation. Mathematical induction can be used to prove statements involving positive integers. Understand the use of factorial. Recognize, write, and find nth terms and partial sums of arithmetic and geometric sequences. Link arithmetic sequences to linear equations. Use arithmetic and geometric sequences to model and solve real life problems. Link geometric sequences to exponential functions. Find sums of finite and infinite geometric sequences and use to solve real life problems. Use mathematical induction to prove statements. Page 23 of 26

24 Unit Title: (11) Sequences and Series Chapter 10 Number of Days: 20 days Key Learning: Using the formulas for sequences and series simplifies the solving of real life problems. Unit Essential Question: How do I solve real world problems using the formulas for sequences and series? Sequences, Series, and Sigma Notation MA.912.D What different types of sequences exist? 2. How do I use sigma notation to represent and calculate sums of series? finite and infinite sequences, recursive sequence, explicit sequence, Fibonacci sequence, converge, diverge, finite and infinite series, partial sum, sigma notation Arithmetic Sequences and Series MA.912.D How do I find the nth term and arithmetic mean of arithmetic sequences and series? 4. How do I find the sum of n terms of an arithmetic series? arithmetic sequence, common difference, arithmetic means, arithmetic series Geometric Sequences and Series MA.912.D How do I find the nth term and geometric mean of geometric sequences and series? 6. How do I find the sum of n terms on a geometric series? geometric sequence, common ratio, geometric mean, geometric series Mathematical Induction MA.912.D How do I use mathematical induction? principal of mathematical induction, anchor step, inductive hypothesis, inductive step Additional Information: Language Arts Benchmarks used in each concept: LA , LA , LA , LA , LA Glencoe McGraw-Hill, PRECALCULUS, 2011, is the Pasco County adopted textbook. Page 24 of 26

25 Unit Title: (12) Limits and Derivatives Chapter 12 Number of Days: 15 days Know: Understand: Do: Limits provide useful information about the behavior of a function. Methods for finding the slopes of tangent lines can help describe the behavior of a function. Limits can be used to predict the values of a function as x gets infinitely large or infinitely small. Techniques for evaluating limits can be used to solve problems dealing with rates of change, cost, and area. Estimate limits of functions at fixed values and at infinity. Evaluate limits of polynomial and rational functions at selected points using the properties, substitution, factoring, and rationalizing. Evaluate limits of polynomials and rational functions at infinity. The continuity or types of discontinuity of a function on an interval or at a point provide important information about its behavior. Find limits of sequences. Find instantaneous rates of change by calculating slopes of tangent lines. Find average and instantaneous velocity. Page 25 of 26

26 Unit Title: (12) Limits and Derivatives Chapter 12 Number of Days: 15 days Key Learning: Techniques for evaluating limits can be used to solve problems dealing with rates of change, cost, and area. Unit Essential Question: How can evaluating limits be used to help solve problems involving rates of change, cost and area? Estimating Limits Graphically MA.912.C.1.1 MA.912.C.1.4 MA.912.C How do I estimate limits of functions at fixed values and at infinity? One-Sided Limit, Two- Sided Limit, Unbounded Behavior, Oscillating Behavior Evaluating Limits Algebraically MA.912.C.1.2 MA.912.C.1.3 MA.912.C How do I evaluate limits of polynomial and rational functions at selected points and at infinity? direct substitution, indeterminate form Derivatives MA.912.C How do I find the instantaneous rates of change by calculating derivatives? 4. How do I use the product and quotient rules to calculate derivatives? tangent line, instantaneous rate of change, difference quotient, instantaneous velocity Additional Information: Language Arts Benchmarks used in each concept: LA , LA , LA , LA , LA Glencoe McGraw-Hill, PRECALCULUS, 2011, is the Pasco County adopted textbook. Page 26 of 26

Thnkwell s Homeschool Precalculus Course Lesson Plan: 36 weeks

Thnkwell s Homeschool Precalculus Course Lesson Plan: 36 weeks Thnkwell s Homeschool Precalculus Course Lesson Plan: 36 weeks Welcome to Thinkwell s Homeschool Precalculus! We re thrilled that you ve decided to make us part of your homeschool curriculum. This lesson

More information

South Carolina College- and Career-Ready (SCCCR) Pre-Calculus

South Carolina College- and Career-Ready (SCCCR) Pre-Calculus South Carolina College- and Career-Ready (SCCCR) Pre-Calculus Key Concepts Arithmetic with Polynomials and Rational Expressions PC.AAPR.2 PC.AAPR.3 PC.AAPR.4 PC.AAPR.5 PC.AAPR.6 PC.AAPR.7 Standards Know

More information

Trigonometry Lesson Objectives

Trigonometry Lesson Objectives Trigonometry Lesson Unit 1: RIGHT TRIANGLE TRIGONOMETRY Lengths of Sides Evaluate trigonometric expressions. Express trigonometric functions as ratios in terms of the sides of a right triangle. Use the

More information

Advanced Algebra 2. I. Equations and Inequalities

Advanced Algebra 2. I. Equations and Inequalities Advanced Algebra 2 I. Equations and Inequalities A. Real Numbers and Number Operations 6.A.5, 6.B.5, 7.C.5 1) Graph numbers on a number line 2) Order real numbers 3) Identify properties of real numbers

More information

Precalculus REVERSE CORRELATION. Content Expectations for. Precalculus. Michigan CONTENT EXPECTATIONS FOR PRECALCULUS CHAPTER/LESSON TITLES

Precalculus REVERSE CORRELATION. Content Expectations for. Precalculus. Michigan CONTENT EXPECTATIONS FOR PRECALCULUS CHAPTER/LESSON TITLES Content Expectations for Precalculus Michigan Precalculus 2011 REVERSE CORRELATION CHAPTER/LESSON TITLES Chapter 0 Preparing for Precalculus 0-1 Sets There are no state-mandated Precalculus 0-2 Operations

More information

ALGEBRA & TRIGONOMETRY FOR CALCULUS MATH 1340

ALGEBRA & TRIGONOMETRY FOR CALCULUS MATH 1340 ALGEBRA & TRIGONOMETRY FOR CALCULUS Course Description: MATH 1340 A combined algebra and trigonometry course for science and engineering students planning to enroll in Calculus I, MATH 1950. Topics include:

More information

Algebra and Geometry Review (61 topics, no due date)

Algebra and Geometry Review (61 topics, no due date) Course Name: Math 112 Credit Exam LA Tech University Course Code: ALEKS Course: Trigonometry Instructor: Course Dates: Course Content: 159 topics Algebra and Geometry Review (61 topics, no due date) Properties

More information

Precalculus with Limits Larson Hostetler. `knill/mathmovies/ Assessment Unit 1 Test

Precalculus with Limits Larson Hostetler.  `knill/mathmovies/ Assessment Unit 1 Test Unit 1 Real Numbers and Their Properties 14 days: 45 minutes per day (1 st Nine Weeks) functions using graphs, tables, and symbols Representing & Classifying Real Numbers Ordering Real Numbers Absolute

More information

Higher Education Math Placement

Higher Education Math Placement Higher Education Math Placement Placement Assessment Problem Types 1. Whole Numbers, Fractions, and Decimals 1.1 Operations with Whole Numbers Addition with carry Subtraction with borrowing Multiplication

More information

pp. 4 8: Examples 1 6 Quick Check 1 6 Exercises 1, 2, 20, 42, 43, 64

pp. 4 8: Examples 1 6 Quick Check 1 6 Exercises 1, 2, 20, 42, 43, 64 Semester 1 Text: Chapter 1: Tools of Algebra Lesson 1-1: Properties of Real Numbers Day 1 Part 1: Graphing and Ordering Real Numbers Part 1: Graphing and Ordering Real Numbers Lesson 1-2: Algebraic Expressions

More information

Algebra II. Larson, Boswell, Kanold, & Stiff (2001) Algebra II, Houghton Mifflin Company: Evanston, Illinois. TI 83 or 84 Graphing Calculator

Algebra II. Larson, Boswell, Kanold, & Stiff (2001) Algebra II, Houghton Mifflin Company: Evanston, Illinois. TI 83 or 84 Graphing Calculator Algebra II Text: Supplemental Materials: Larson, Boswell, Kanold, & Stiff (2001) Algebra II, Houghton Mifflin Company: Evanston, Illinois. TI 83 or 84 Graphing Calculator Course Description: The purpose

More information

Prep for Calculus. Curriculum

Prep for Calculus. Curriculum Prep for Calculus This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet curricular

More information

GOALS AND OBJECTIVES. Goal: To provide students of Zane State College with instruction focusing on the following topics:

GOALS AND OBJECTIVES. Goal: To provide students of Zane State College with instruction focusing on the following topics: Phone: (740) 824-3522 ext. 1249 COURSE SYLLABUS Course Title: MATH 1350 Pre-Calculus Credit Hours: 5 Instructor: Miss Megan Duke E-mail: megan.duke@rvbears.org Course Description: Broadens the algebra

More information

TRIGONOMETRY GRADES THE EWING PUBLIC SCHOOLS 2099 Pennington Road Ewing, NJ 08618

TRIGONOMETRY GRADES THE EWING PUBLIC SCHOOLS 2099 Pennington Road Ewing, NJ 08618 TRIGONOMETRY GRADES 11-12 THE EWING PUBLIC SCHOOLS 2099 Pennington Road Ewing, NJ 08618 Board Approval Date: October 29, 2012 Michael Nitti Written by: EHS Mathematics Department Superintendent In accordance

More information

Chapter R - Basic Algebra Operations (69 topics, due on 05/01/12)

Chapter R - Basic Algebra Operations (69 topics, due on 05/01/12) Course Name: College Algebra 001 Course Code: R3RK6-CTKHJ ALEKS Course: College Algebra with Trigonometry Instructor: Prof. Bozyk Course Dates: Begin: 01/17/2012 End: 05/04/2012 Course Content: 288 topics

More information

Algebra 2 Chapter 1 Vocabulary. identity - A statement that equates two equivalent expressions.

Algebra 2 Chapter 1 Vocabulary. identity - A statement that equates two equivalent expressions. Chapter 1 Vocabulary identity - A statement that equates two equivalent expressions. verbal model- A word equation that represents a real-life problem. algebraic expression - An expression with variables.

More information

Class Notes for MATH 2 Precalculus. Fall Prepared by. Stephanie Sorenson

Class Notes for MATH 2 Precalculus. Fall Prepared by. Stephanie Sorenson Class Notes for MATH 2 Precalculus Fall 2012 Prepared by Stephanie Sorenson Table of Contents 1.2 Graphs of Equations... 1 1.4 Functions... 9 1.5 Analyzing Graphs of Functions... 14 1.6 A Library of Parent

More information

PRE-CALCULUS GRADE 12

PRE-CALCULUS GRADE 12 PRE-CALCULUS GRADE 12 [C] Communication Trigonometry General Outcome: Develop trigonometric reasoning. A1. Demonstrate an understanding of angles in standard position, expressed in degrees and radians.

More information

Montana Common Core Standard

Montana Common Core Standard Algebra 2 Grade Level: 10(with Recommendation), 11, 12 Length: 1 Year Period(s) Per Day: 1 Credit: 1 Credit Requirement Fulfilled: Mathematics Course Description This course covers the main theories in

More information

Table of Contents. Montessori Algebra for the Adolescent Michael J. Waski"

Table of Contents. Montessori Algebra for the Adolescent Michael J. Waski Table of Contents I. Introduction II. Chapter of Signed Numbers B. Introduction and Zero Sum Game C. Adding Signed Numbers D. Subtracting Signed Numbers 1. Subtracting Signed Numbers 2. Rewriting as Addition

More information

MTH304: Honors Algebra II

MTH304: Honors Algebra II MTH304: Honors Algebra II This course builds upon algebraic concepts covered in Algebra. Students extend their knowledge and understanding by solving open-ended problems and thinking critically. Topics

More information

Unit Overview. Content Area: Math Unit Title: Functions and Their Graphs Target Course/Grade Level: Advanced Math Duration: 4 Weeks

Unit Overview. Content Area: Math Unit Title: Functions and Their Graphs Target Course/Grade Level: Advanced Math Duration: 4 Weeks Content Area: Math Unit Title: Functions and Their Graphs Target Course/Grade Level: Advanced Math Duration: 4 Weeks Unit Overview Description In this unit the students will examine groups of common functions

More information

Text: A Graphical Approach to College Algebra (Hornsby, Lial, Rockswold)

Text: A Graphical Approach to College Algebra (Hornsby, Lial, Rockswold) Students will take Self Tests covering the topics found in Chapter R (Reference: Basic Algebraic Concepts) and Chapter 1 (Linear Functions, Equations, and Inequalities). If any deficiencies are revealed,

More information

4. Factor polynomials over complex numbers, describe geometrically, and apply to real-world situations. 5. Determine and apply relationships among syn

4. Factor polynomials over complex numbers, describe geometrically, and apply to real-world situations. 5. Determine and apply relationships among syn I The Real and Complex Number Systems 1. Identify subsets of complex numbers, and compare their structural characteristics. 2. Compare and contrast the properties of real numbers with the properties of

More information

Portable Assisted Study Sequence ALGEBRA IIA

Portable Assisted Study Sequence ALGEBRA IIA SCOPE This course is divided into two semesters of study (A & B) comprised of five units each. Each unit teaches concepts and strategies recommended for intermediate algebra students. The first half of

More information

Higher Education Math Placement

Higher Education Math Placement Higher Education Math Placement 1. Whole Numbers, Fractions, and Decimals 1.1 Operations with Whole Numbers Addition with carry (arith050) Subtraction with borrowing (arith006) Multiplication with carry

More information

NEW YORK STATE TEACHER CERTIFICATION EXAMINATIONS

NEW YORK STATE TEACHER CERTIFICATION EXAMINATIONS NEW YORK STATE TEACHER CERTIFICATION EXAMINATIONS TEST DESIGN AND FRAMEWORK September 2014 Authorized for Distribution by the New York State Education Department This test design and framework document

More information

Able Enrichment Centre - Prep Level Curriculum

Able Enrichment Centre - Prep Level Curriculum Able Enrichment Centre - Prep Level Curriculum Unit 1: Number Systems Number Line Converting expanded form into standard form or vice versa. Define: Prime Number, Natural Number, Integer, Rational Number,

More information

Algebra 2/ Trigonometry Extended Scope and Sequence (revised )

Algebra 2/ Trigonometry Extended Scope and Sequence (revised ) Algebra 2/ Trigonometry Extended Scope and Sequence (revised 2012 2013) Unit 1: Operations with Radicals and Complex Numbers 9 days 1. Operations with radicals (p.88, 94, 98, 101) a. Simplifying radicals

More information

EQ: How can regression models be used to display and analyze the data in our everyday lives?

EQ: How can regression models be used to display and analyze the data in our everyday lives? School of the Future Math Department Comprehensive Curriculum Plan: ALGEBRA II (Holt Algebra 2 textbook as reference guide) 2016-2017 Instructor: Diane Thole EU for the year: How do mathematical models

More information

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

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

More information

Common Curriculum Map. Discipline: Math Course: College Algebra

Common Curriculum Map. Discipline: Math Course: College Algebra Common Curriculum Map Discipline: Math Course: College Algebra August/September: 6A.5 Perform additions, subtraction and multiplication of complex numbers and graph the results in the complex plane 8a.4a

More information

College Algebra. Barnett, Raymond A., Michael R. Ziegler, and Karl E. Byleen. College Algebra, 8th edition, McGraw-Hill, 2008, ISBN: 978-0-07-286738-1

College Algebra. Barnett, Raymond A., Michael R. Ziegler, and Karl E. Byleen. College Algebra, 8th edition, McGraw-Hill, 2008, ISBN: 978-0-07-286738-1 College Algebra Course Text Barnett, Raymond A., Michael R. Ziegler, and Karl E. Byleen. College Algebra, 8th edition, McGraw-Hill, 2008, ISBN: 978-0-07-286738-1 Course Description This course provides

More information

Diploma Plus in Certificate in Advanced Engineering

Diploma Plus in Certificate in Advanced Engineering Diploma Plus in Certificate in Advanced Engineering Mathematics New Syllabus from April 2011 Ngee Ann Polytechnic / School of Interdisciplinary Studies 1 I. SYNOPSIS APPENDIX A This course of advanced

More information

Georgia Department of Education Kathy Cox, State Superintendent of Schools 7/19/2005 All Rights Reserved 1

Georgia Department of Education Kathy Cox, State Superintendent of Schools 7/19/2005 All Rights Reserved 1 Accelerated Mathematics 3 This is a course in precalculus and statistics, designed to prepare students to take AB or BC Advanced Placement Calculus. It includes rational, circular trigonometric, and inverse

More information

Prentice Hall Mathematics: Algebra 2 2007 Correlated to: Utah Core Curriculum for Math, Intermediate Algebra (Secondary)

Prentice Hall Mathematics: Algebra 2 2007 Correlated to: Utah Core Curriculum for Math, Intermediate Algebra (Secondary) Core Standards of the Course Standard 1 Students will acquire number sense and perform operations with real and complex numbers. Objective 1.1 Compute fluently and make reasonable estimates. 1. Simplify

More information

Thinkwell s Homeschool Algebra 2 Course Lesson Plan: 34 weeks

Thinkwell s Homeschool Algebra 2 Course Lesson Plan: 34 weeks Thinkwell s Homeschool Algebra 2 Course Lesson Plan: 34 weeks Welcome to Thinkwell s Homeschool Algebra 2! We re thrilled that you ve decided to make us part of your homeschool curriculum. This lesson

More information

Construction of the Real Line 2 Is Every Real Number Rational? 3 Problems Algebra of the Real Numbers 7

Construction of the Real Line 2 Is Every Real Number Rational? 3 Problems Algebra of the Real Numbers 7 About the Author v Preface to the Instructor xiii WileyPLUS xviii Acknowledgments xix Preface to the Student xxi 1 The Real Numbers 1 1.1 The Real Line 2 Construction of the Real Line 2 Is Every Real Number

More information

ALGEBRA II Billings Public Schools Correlation and Pacing Guide Math - McDougal Littell High School Math 2007

ALGEBRA II Billings Public Schools Correlation and Pacing Guide Math - McDougal Littell High School Math 2007 ALGEBRA II Billings Public Schools Correlation and Guide Math - McDougal Littell High School Math 2007 (Chapter Order: 1, 2, 3, 4, 5, 6, 7, 8, 9, 13, 14, 10) BILLINGS PUBLIC SCHOOLS II 2009 Eleventh Grade-McDougal

More information

ALGEBRA I / ALGEBRA I SUPPORT

ALGEBRA I / ALGEBRA I SUPPORT Suggested Sequence: CONCEPT MAP ALGEBRA I / ALGEBRA I SUPPORT August 2011 1. Foundations for Algebra 2. Solving Equations 3. Solving Inequalities 4. An Introduction to Functions 5. Linear Functions 6.

More information

BookTOC.txt. 1. Functions, Graphs, and Models. Algebra Toolbox. Sets. The Real Numbers. Inequalities and Intervals on the Real Number Line

BookTOC.txt. 1. Functions, Graphs, and Models. Algebra Toolbox. Sets. The Real Numbers. Inequalities and Intervals on the Real Number Line College Algebra in Context with Applications for the Managerial, Life, and Social Sciences, 3rd Edition Ronald J. Harshbarger, University of South Carolina - Beaufort Lisa S. Yocco, Georgia Southern University

More information

Calculus C/Multivariate Calculus Advanced Placement G/T Essential Curriculum

Calculus C/Multivariate Calculus Advanced Placement G/T Essential Curriculum Calculus C/Multivariate Calculus Advanced Placement G/T Essential Curriculum UNIT I: The Hyperbolic Functions basic calculus concepts, including techniques for curve sketching, exponential and logarithmic

More information

Mercer County Public Schools PRIORITIZED CURRICULUM. Mathematics Content Maps Algebra II Revised August 07

Mercer County Public Schools PRIORITIZED CURRICULUM. Mathematics Content Maps Algebra II Revised August 07 Mercer County Public Schools PRIORITIZED CURRICULUM Mathematics Content Maps Algebra II Revised August 07 Suggested Sequence: C O N C E P T M A P ALGEBRA I I 1. Solving Equations/Inequalities 2. Functions

More information

Course Name: Course Code: ALEKS Course: Instructor: Course Dates: Course Content: Textbook: Dates Objective Prerequisite Topics

Course Name: Course Code: ALEKS Course: Instructor: Course Dates: Course Content: Textbook: Dates Objective Prerequisite Topics Course Name: MATH 1204 Fall 2015 Course Code: N/A ALEKS Course: College Algebra Instructor: Master Templates Course Dates: Begin: 08/22/2015 End: 12/19/2015 Course Content: 271 Topics (261 goal + 10 prerequisite)

More information

MATHEMATICS (CLASSES XI XII)

MATHEMATICS (CLASSES XI XII) MATHEMATICS (CLASSES XI XII) General Guidelines (i) All concepts/identities must be illustrated by situational examples. (ii) The language of word problems must be clear, simple and unambiguous. (iii)

More information

Birmingham City Schools

Birmingham City Schools Activity 1 Classroom Rules & Regulations Policies & Procedures Course Curriculum / Syllabus LTF Activity: Interval Notation (Precal) 2 Pre-Assessment 3 & 4 1.2 Functions and Their Properties 5 LTF Activity:

More information

Math 4 Review Problems

Math 4 Review Problems Topics for Review #1 Functions function concept [section 1. of textbook] function representations: graph, table, f(x) formula domain and range Vertical Line Test (for whether a graph is a function) evaluating

More information

Overview of Math Standards

Overview of Math Standards Algebra 2 Welcome to math curriculum design maps for Manhattan- Ogden USD 383, striving to produce learners who are: Effective Communicators who clearly express ideas and effectively communicate with diverse

More information

TOMS RIVER REGIONAL SCHOOLS MATHEMATICS CURRICULUM

TOMS RIVER REGIONAL SCHOOLS MATHEMATICS CURRICULUM Content Area: Mathematics Course Title: Precalculus Grade Level: High School Right Triangle Trig and Laws 3-4 weeks Trigonometry 3 weeks Graphs of Trig Functions 3-4 weeks Analytic Trigonometry 5-6 weeks

More information

Algebra II Pacing Guide First Nine Weeks

Algebra II Pacing Guide First Nine Weeks First Nine Weeks SOL Topic Blocks.4 Place the following sets of numbers in a hierarchy of subsets: complex, pure imaginary, real, rational, irrational, integers, whole and natural. 7. Recognize that the

More information

Identify examples of field properties: commutative, associative, identity, inverse, and distributive.

Identify examples of field properties: commutative, associative, identity, inverse, and distributive. Topic: Expressions and Operations ALGEBRA II - STANDARD AII.1 The student will identify field properties, axioms of equality and inequality, and properties of order that are valid for the set of real numbers

More information

Curriculum Map Precalculus Saugus High School Saugus Public Schools

Curriculum Map Precalculus Saugus High School Saugus Public Schools Curriculum Map Precalculus Saugus High School Saugus Public Schools The Standards for Mathematical Practice The Standards for Mathematical Practice describe varieties of expertise that mathematics educators

More information

BERKELEY HEIGHTS PUBLIC SCHOOLS BERKELEY HEIGHTS, NEW JERSEY. Curriculum Guide. September 2013

BERKELEY HEIGHTS PUBLIC SCHOOLS BERKELEY HEIGHTS, NEW JERSEY. Curriculum Guide. September 2013 BERKELEY HEIGHTS PUBLIC SCHOOLS BERKELEY HEIGHTS, NEW JERSEY GOVERNOR LIVINGSTON HIGH SCHOOL MATHEMATICS DEPARTMENT MATH ANALYSIS/MATH ANALYSIS HONORS #MAY1210/#MAY1220 Curriculum Guide September 2013

More information

MATH BOOK OF PROBLEMS SERIES. New from Pearson Custom Publishing!

MATH BOOK OF PROBLEMS SERIES. New from Pearson Custom Publishing! MATH BOOK OF PROBLEMS SERIES New from Pearson Custom Publishing! The Math Book of Problems Series is a database of math problems for the following courses: Pre-algebra Algebra Pre-calculus Calculus Statistics

More information

HIGH SCHOOL: GEOMETRY (Page 1 of 4)

HIGH SCHOOL: GEOMETRY (Page 1 of 4) HIGH SCHOOL: GEOMETRY (Page 1 of 4) Geometry is a complete college preparatory course of plane and solid geometry. It is recommended that there be a strand of algebra review woven throughout the course

More information

Prep for College Algebra

Prep for College Algebra Prep for College Algebra This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet

More information

PRECALCULUS Semester I Exam Review Sheet

PRECALCULUS Semester I Exam Review Sheet PRECALCULUS Semester I Exam Review Sheet Chapter Topic P.1 Real Numbers {1, 2, 3, 4, } Natural (aka Counting) Numbers {0, 1, 2, 3, 4, } Whole Numbers {, -3, -2, -2, 0, 1, 2, 3, } Integers Can be expressed

More information

Lecture 1 (Review of High School Math: Functions and Models) Introduction: Numbers and their properties

Lecture 1 (Review of High School Math: Functions and Models) Introduction: Numbers and their properties Lecture 1 (Review of High School Math: Functions and Models) Introduction: Numbers and their properties Addition: (1) (Associative law) If a, b, and c are any numbers, then ( ) ( ) (2) (Existence of an

More information

MATH 2 Course Syllabus Spring Semester 2007 Instructor: Brian Rodas

MATH 2 Course Syllabus Spring Semester 2007 Instructor: Brian Rodas MATH 2 Course Syllabus Spring Semester 2007 Instructor: Brian Rodas Class Room and Time: MC83 MTWTh 2:15pm-3:20pm Office Room: MC38 Office Phone: (310)434-8673 E-mail: rodas brian@smc.edu Office Hours:

More information

Math Analysis. A2. Explore the "menu" button on the graphing calculator in order to locate and use functions.

Math Analysis. A2. Explore the menu button on the graphing calculator in order to locate and use functions. St. Mary's College High School Math Analysis Introducing the Graphing Calculator A. Using the Calculator for Order of Operations B. Using the Calculator for simplifying fractions, decimal notation and

More information

Algebra 1 Course Title

Algebra 1 Course Title Algebra 1 Course Title Course- wide 1. What patterns and methods are being used? Course- wide 1. Students will be adept at solving and graphing linear and quadratic equations 2. Students will be adept

More information

Administrative - Master Syllabus COVER SHEET

Administrative - Master Syllabus COVER SHEET Administrative - Master Syllabus COVER SHEET Purpose: It is the intention of this to provide a general description of the course, outline the required elements of the course and to lay the foundation for

More information

Algebra 2 Year-at-a-Glance Leander ISD 2007-08. 1st Six Weeks 2nd Six Weeks 3rd Six Weeks 4th Six Weeks 5th Six Weeks 6th Six Weeks

Algebra 2 Year-at-a-Glance Leander ISD 2007-08. 1st Six Weeks 2nd Six Weeks 3rd Six Weeks 4th Six Weeks 5th Six Weeks 6th Six Weeks Algebra 2 Year-at-a-Glance Leander ISD 2007-08 1st Six Weeks 2nd Six Weeks 3rd Six Weeks 4th Six Weeks 5th Six Weeks 6th Six Weeks Essential Unit of Study 6 weeks 3 weeks 3 weeks 6 weeks 3 weeks 3 weeks

More information

Developmental Math Course Outcomes and Objectives

Developmental Math Course Outcomes and Objectives Developmental Math Course Outcomes and Objectives I. Math 0910 Basic Arithmetic/Pre-Algebra Upon satisfactory completion of this course, the student should be able to perform the following outcomes and

More information

INTERNATIONAL BACCALAUREATE (IB) MATH STANDARD LEVEL, YEARS 1 AND 2 Grades 11, 12

INTERNATIONAL BACCALAUREATE (IB) MATH STANDARD LEVEL, YEARS 1 AND 2 Grades 11, 12 INTERNATIONAL BACCALAUREATE (IB) MATH STANDARD LEVEL, YEARS 1 AND 2 Grades 11, 12 Unit of Credit: 1 Year for Year 1 and 1 Year for Year 2 Pre-requisite: Algebra 2 for Year 1 IB Math Standard Level Year

More information

Math 1280/1300, Pre-Calculus

Math 1280/1300, Pre-Calculus Math 1280/1300, Pre-Calculus Instructor: Office: Office Hours: Phone: E-mail: MyMathLab Course Code: Text and Materials: ISBN: 1269594060 Author: Blitzer Title: Precalculus, Books a la Carte Edition Package

More information

http://www.aleks.com Access Code: RVAE4-EGKVN Financial Aid Code: 6A9DB-DEE3B-74F51-57304

http://www.aleks.com Access Code: RVAE4-EGKVN Financial Aid Code: 6A9DB-DEE3B-74F51-57304 MATH 1340.04 College Algebra Location: MAGC 2.202 Meeting day(s): TR 7:45a 9:00a, Instructor Information Name: Virgil Pierce Email: piercevu@utpa.edu Phone: 665.3535 Teaching Assistant Name: Indalecio

More information

PURE MATHEMATICS AM 27

PURE MATHEMATICS AM 27 AM Syllabus (015): Pure Mathematics AM SYLLABUS (015) PURE MATHEMATICS AM 7 SYLLABUS 1 AM Syllabus (015): Pure Mathematics Pure Mathematics AM 7 Syllabus (Available in September) Paper I(3hrs)+Paper II(3hrs)

More information

PURE MATHEMATICS AM 27

PURE MATHEMATICS AM 27 AM SYLLABUS (013) PURE MATHEMATICS AM 7 SYLLABUS 1 Pure Mathematics AM 7 Syllabus (Available in September) Paper I(3hrs)+Paper II(3hrs) 1. AIMS To prepare students for further studies in Mathematics and

More information

Math SYLLABUS (1 st ~ 8 th Grade, Advance, SAT/ACT)

Math SYLLABUS (1 st ~ 8 th Grade, Advance, SAT/ACT) Math SYLLABUS (1 st ~ 8 th Grade, Advance, SAT/ACT) Math -- 1 st Grade 1. Kindergarteners or 1 st graders in regular school 2. At least 5 years old Syllabus 1. Numeration (0 through 99) 2. Addition (2

More information

Pre-Algebra - MA1100. Topic Lesson Objectives. Variables and Expressions

Pre-Algebra - MA1100. Topic Lesson Objectives. Variables and Expressions Variables and Expressions Problem Solving: Using a Problem-Solving Plan Use a four-step plan to solve problems. Choose an appropriate method of computation. Numbers and Expressions Use the order of operations

More information

PreCalculus Curriculum Guide

PreCalculus Curriculum Guide MOUNT VERNON CITY SCHOOL DISTRICT A World Class Organization PreCalculus Curriculum Guide THIS HANDBOOK IS FOR THE IMPLEMENTATION OF THE NYS MATH b CURRICULUM IN MOUNT VERNON. THIS PROVIDES AN OUTLINE

More information

Official Math 112 Catalog Description

Official Math 112 Catalog Description Official Math 112 Catalog Description Topics include properties of functions and graphs, linear and quadratic equations, polynomial functions, exponential and logarithmic functions with applications. A

More information

Precalculus Workshop - Functions

Precalculus Workshop - Functions Introduction to Functions A function f : D C is a rule that assigns to each element x in a set D exactly one element, called f(x), in a set C. D is called the domain of f. C is called the codomain of f.

More information

MyMathLab ecourse for Developmental Mathematics

MyMathLab ecourse for Developmental Mathematics MyMathLab ecourse for Developmental Mathematics, North Shore Community College, University of New Orleans, Orange Coast College, Normandale Community College Table of Contents Module 1: Whole Numbers and

More information

MATH. ALGEBRA I HONORS 9 th Grade 12003200 ALGEBRA I HONORS

MATH. ALGEBRA I HONORS 9 th Grade 12003200 ALGEBRA I HONORS * Students who scored a Level 3 or above on the Florida Assessment Test Math Florida Standards (FSA-MAFS) are strongly encouraged to make Advanced Placement and/or dual enrollment courses their first choices

More information

Mathematics Standards

Mathematics Standards 1 Table of Contents Mathematics Standards Subject Pages Algebra 1-2 2-4 Algebra 3-4 5-6 AP Calculus AB and BC Standards 7 AP Statistics Standards 8 Consumer Math 9 Geometry 1-2 10-11 Honors Differential

More information

STUDENT LEARNING OUTCOMES FOR THE SANTIAGO CANYON COLLEGE MATHEMATICS DEPARTMENT (Last Revised 8/20/14)

STUDENT LEARNING OUTCOMES FOR THE SANTIAGO CANYON COLLEGE MATHEMATICS DEPARTMENT (Last Revised 8/20/14) STUDENT LEARNING OUTCOMES FOR THE SANTIAGO CANYON COLLEGE MATHEMATICS DEPARTMENT (Last Revised 8/20/14) Department SLOs: Upon completion of any course in Mathematics the student will be able to: 1. Create

More information

COURSE SYLLABUS Pre-Calculus A/B Last Modified: April 2015

COURSE SYLLABUS Pre-Calculus A/B Last Modified: April 2015 COURSE SYLLABUS Pre-Calculus A/B Last Modified: April 2015 Course Description: In this year-long Pre-Calculus course, students will cover topics over a two semester period (as designated by A and B sections).

More information

IB Mathematics SL :: Checklist. Topic 1 Algebra The aim of this topic is to introduce students to some basic algebraic concepts and applications.

IB Mathematics SL :: Checklist. Topic 1 Algebra The aim of this topic is to introduce students to some basic algebraic concepts and applications. Topic 1 Algebra The aim of this topic is to introduce students to some basic algebraic concepts and applications. Check Topic 1 Book Arithmetic sequences and series; Sum of finite arithmetic series; Geometric

More information

Prentice Hall Mathematics: Algebra 1 2007 Correlated to: Michigan Merit Curriculum for Algebra 1

Prentice Hall Mathematics: Algebra 1 2007 Correlated to: Michigan Merit Curriculum for Algebra 1 STRAND 1: QUANTITATIVE LITERACY AND LOGIC STANDARD L1: REASONING ABOUT NUMBERS, SYSTEMS, AND QUANTITATIVE SITUATIONS Based on their knowledge of the properties of arithmetic, students understand and reason

More information

MATH 095, College Prep Mathematics: Unit Coverage Pre-algebra topics (arithmetic skills) offered through BSE (Basic Skills Education)

MATH 095, College Prep Mathematics: Unit Coverage Pre-algebra topics (arithmetic skills) offered through BSE (Basic Skills Education) MATH 095, College Prep Mathematics: Unit Coverage Pre-algebra topics (arithmetic skills) offered through BSE (Basic Skills Education) Accurately add, subtract, multiply, and divide whole numbers, integers,

More information

COURSE OUTLINE. MATHEMATICS 101 Intermediate Algebra

COURSE OUTLINE. MATHEMATICS 101 Intermediate Algebra Degree Applicable I. Catalog Statement COURSE OUTLINE MATHEMATICS 101 Intermediate Algebra Glendale Community College October 2013 Mathematics 101 is an accelerated course of Intermediate Algebra. Topics

More information

Chapter 1 Quadratic Equations in One Unknown (I)

Chapter 1 Quadratic Equations in One Unknown (I) Tin Ka Ping Secondary School 015-016 F. Mathematics Compulsory Part Teaching Syllabus Chapter 1 Quadratic in One Unknown (I) 1 1.1 Real Number System A Integers B nal Numbers C Irrational Numbers D Real

More information

Chapter 111. Texas Essential Knowledge and Skills for Mathematics. Subchapter C. High School

Chapter 111. Texas Essential Knowledge and Skills for Mathematics. Subchapter C. High School High School 111.C. Chapter 111. Texas Essential Knowledge and Skills for Mathematics Subchapter C. High School Statutory Authority: The provisions of this Subchapter C issued under the Texas Education

More information

Math Course Descriptions & Student Learning Outcomes

Math Course Descriptions & Student Learning Outcomes Math Course Descriptions & Student Learning Outcomes Table of Contents MAC 100: Business Math... 1 MAC 101: Technical Math... 3 MA 090: Basic Math... 4 MA 095: Introductory Algebra... 5 MA 098: Intermediate

More information

2312 test 2 Fall 2010 Form B

2312 test 2 Fall 2010 Form B 2312 test 2 Fall 2010 Form B 1. Write the slope-intercept form of the equation of the line through the given point perpendicular to the given lin point: ( 7, 8) line: 9x 45y = 9 2. Evaluate the function

More information

Trigonometry Notes Sarah Brewer Alabama School of Math and Science. Last Updated: 25 November 2011

Trigonometry Notes Sarah Brewer Alabama School of Math and Science. Last Updated: 25 November 2011 Trigonometry Notes Sarah Brewer Alabama School of Math and Science Last Updated: 25 November 2011 6 Basic Trig Functions Defined as ratios of sides of a right triangle in relation to one of the acute angles

More information

Middle Grades Mathematics 5 9

Middle Grades Mathematics 5 9 Middle Grades Mathematics 5 9 Section 25 1 Knowledge of mathematics through problem solving 1. Identify appropriate mathematical problems from real-world situations. 2. Apply problem-solving strategies

More information

Math Course: Algebra II Grade 10

Math Course: Algebra II Grade 10 MATH 401 Algebra II 1/2 credit 5 times per week (1 st Semester) Taught in English Math Course: Algebra II Grade 10 This is a required class for all 10 th grade students in the Mexican and/or U.S. Diploma

More information

Exam 2 Review. 3. How to tell if an equation is linear? An equation is linear if it can be written, through simplification, in the form.

Exam 2 Review. 3. How to tell if an equation is linear? An equation is linear if it can be written, through simplification, in the form. Exam 2 Review Chapter 1 Section1 Do You Know: 1. What does it mean to solve an equation? To solve an equation is to find the solution set, that is, to find the set of all elements in the domain of the

More information

Algebra II and Trigonometry

Algebra II and Trigonometry Algebra II and Trigonometry Textbooks: Algebra 2: California Publisher: McDougal Li@ell/Houghton Mifflin (2006 EdiHon) ISBN- 13: 978-0618811816 Course descriphon: Algebra II complements and expands the

More information

Items related to expected use of graphing technology appear in bold italics.

Items related to expected use of graphing technology appear in bold italics. - 1 - Items related to expected use of graphing technology appear in bold italics. Investigating the Graphs of Polynomial Functions determine, through investigation, using graphing calculators or graphing

More information

Rockhurst High School Algebra 1 Topics

Rockhurst High School Algebra 1 Topics Rockhurst High School Algebra 1 Topics Chapter 1- Pre-Algebra Skills Simplify a numerical expression using PEMDAS. Substitute whole numbers into an algebraic expression and evaluate that expression. Substitute

More information

Math Placement Test Study Guide. 2. The test consists entirely of multiple choice questions, each with five choices.

Math Placement Test Study Guide. 2. The test consists entirely of multiple choice questions, each with five choices. Math Placement Test Study Guide General Characteristics of the Test 1. All items are to be completed by all students. The items are roughly ordered from elementary to advanced. The expectation is that

More information

The standards in this course continue the work of modeling situations and solving equations.

The standards in this course continue the work of modeling situations and solving equations. Algebra II Overview View unit yearlong overview here Building on the understanding of linear, quadratic and exponential functions from Algebra I, this course will extend function concepts to include polynomial,

More information

Math 131 College Algebra Fall 2015

Math 131 College Algebra Fall 2015 Math 131 College Algebra Fall 2015 Instructor's Name: Office Location: Office Hours: Office Phone: E-mail: Course Description This course has a minimal review of algebraic skills followed by a study of

More information

Math Department Student Learning Objectives Updated April, 2014

Math Department Student Learning Objectives Updated April, 2014 Math Department Student Learning Objectives Updated April, 2014 Institutional Level Outcomes: Victor Valley College has adopted the following institutional outcomes to define the learning that all students

More information

Pre-Calculus Semester 1 Course Syllabus

Pre-Calculus Semester 1 Course Syllabus Pre-Calculus Semester 1 Course Syllabus The Plano ISD eschool Mission is to create a borderless classroom based on a positive student-teacher relationship that fosters independent, innovative critical

More information