Prentice Hall Algebra Correlated to: Hawaii Mathematics Content and Performances Standards (HCPS) II (Grades 9-12)

Transcription

1 NUMBER AND OPERATIONS STANDARD 1: Students understand numbers, ways of representing numbers, relationships among numbers, and number systems Recognize and use real and complex numbers and infinity. Represent real and complex numbers variously (e.g.., number line, coordinate plane, rational exponents, and logarithms). Model situations appropriately with vectors or matrices. 1. Writes solutions to problem 5 notation which indicates recognition of type of answer, real or complex (a + bi notation). 2. Uses the concept of infinity in a number of ways (e.g., unbounded behavior of functions, sequences, as a limit for a variable). 3. Represents real or complex numbers in various ways (e.g., graph, rational exponents, logarithms). SE: 1-1 Properties of Real Numbers, 1-5 Absolute Value Equations and Inequalities, 5-6 Complex Numbers, 5-7 Completing the Square, 6-5 Theorems About Roots of Polynomial Equations, 6-6 The Fundamental Theorem of Algebra, 8-3 Logarithmic Functions as Inverses, 5-10, 33-38, , , , , , 355, 357, 438, , 451 SE: Extension: End Behavior, 11-5 Geometric Series, 306, , SE: 1-1 Properties of Real Numbers, Investigation: Exploring π, 1-4 Solving Inequalities, 1-5 Absolute Value Equations and Inequalities, 5-6 Complex Numbers, 7-1 Roots and Radical Expressions, 7-2 Multiplying and Dividing Radical Expressions, 7-3 Binomial Radical Expressions, 7-4 Rational Exponents, 8-3 Logarithmic Functions as Inverses, 8-4 Properties of Logarithms, 8-6 Natural Logarithms, 6-9, 11, 26-32, 35-38, 49-50, 262, 271, , 296, , , , , 416, 418, 439, 442, , 462,

2 4. Uses vectors or matrix operations to solve problems. STANDARD 2: Students understand the meaning of operations and how they relate to each other SE: 4-1 Organizing Data Into Matrices, , 225 Add, subtract and scalar multiply SE: 4-2 Adding and Subtracting Matrices, vectors. 1. Adds, subtracts, and scalar multiplies Technology: Working with Matrices, 4-3 Represent and operate with matrices no matrices. Matrix Multiplication, 4-5 2x2 Matrices, larger that 3x3. Determinants, and Inverses, 4-6 3x3 Matrices, Determinants, and Inverses, Extension: Networks, 4-8 Augmented Matrices and Systems, , 177, , , , , , Uses inverses of matrices to solve problems. SE: 4-5 2x2 Matrices, Determinants, and Inverses, 4-6 3x3 Matrices, Determinants, and Inverses, 4-7 Inverse Matrices and Systems, , , , STANDARD 3: Students use computational tools and strategies fluently and when appropriate, use estimation. Recognize conditions governing use of formulas (e.g., discriminant in the quadratic formula). Identify computational limitation of calculators and computers (e.g., dividing by small numbers). 1. In the use of formulas, indicates conditions when a given formula can be used (e.g., when the discriminant of a quadratic formula is negative, solutions will be complex). SE: 5-8 The Quadratic Formula,

3 Understand the effects of measurement error on computed values. Analyze effects of rounding in various situations. Use vectors or matrices to solve problems. MEASUREMENT 2. Explains or provides examples of the limitations of calculators and computers in solving problems. 3. Explains that rounding answers in certain real world situations may lead to major problems (e.g., a rocket missing the moon, a bridge collapsing). 4. Use vector or matrix operations to solve problems. SE: 4-2 Adding and Subtracting Matrices, 4-3 Matrix Multiplication, 4-4 Geometric Transformations with Matrices, 4-5 2x2 Matrices, Determinants, and Inverses, 4-6 3x3 Matrices, Determinants, and Inverses, 4-7 Inverse Matrices and Systems, 4-8 Augmented Matrices and Systems, Real- World Snapshots: As the Ball Flies, , , , , 204, , , , 359 STANDARD 1: Students understand attributes, units, systems of units in measurement; and develop and use techniques, tools, and formulas for measuring. Explain rate of change as a quotient of two different measures (e.g., velocity = change in displacement/change in time). Use degree measures in problem situations. Determine precision, accuracy and measurement errors; identify sources and 1. Expresses rates of change as a ratio of two different measures, where units are included in the ratio. SE: 2-2 Linear Equations, 69 3

4 (Continued) magnitudes of possible errors in a measurement setting; describe how errors can propagate within computations; and determine how much imprecision is reasonable in various measurements. Experimentally determine and use formulas for the volume of a sphere, cylinder, and cone. Apply limit concepts to develop concepts of area under a curve and instantaneous rate of change. Combine measurements using multiplication or ratios to produce measurements such as force, work, velocity, acceleration, density, pressure, or trigonometric ratios. 2. Solves problems involving degree measures. 3. Completes an error analysis for measurement data by (a) determining precision, accuracy and measurement errors; and (b) identifying sources and magnitudes of possible errors. 4. Describes how errors can compound with multiple computations in a problem. 5. Determines how much imprecision is reasonable. SE: 1-3 Solving Equations, 3-2 Solving Systems Algebraically, 13-2 Angles and the Unit Circle, 13-3 Radian Measure, 13-4 The Sine Function, Technology: Graphing Trigonometric Functions, 13-6 The Tangent Function, 13-8 Reciprocal Trigonometric Functions, 14-2 Solving Trigonometric Equations Using Inverses, 14-3 Right Triangles and Trigonometric Ratios, 14-4 Area and the Law of Sines, Extension: The Ambiguous Case, 15-5 The Law of Cosines, 14-6 Angle Identities, 14-7 Double-Angle and Half-Angle Identities, 22-23, 126, , , 720, 724, 727, 728, , , , 760, 770, 774, , , 793, , , ,

5 6. Solves problems using formulas for the volume of a sphere, cylinder and cone. 7. Estimates area under a curve by summing the areas of inscribed and/or circumscribed rectangles as the number of rectangles increase. 8. Estimates instantaneous rate of change by calculating average rate of change over smaller and smaller intervals. SE: 1-3 Solving Equations, 2-1 Relations and Functions, 5-4 Factoring Quadratic Expressions, 6-1 Polynomial Functions, 6-4 Solving Polynomial Equations, 7-5 Solving Radical Equations, Geometry Review: Expressions in Formulas, 7-7 Inverse Relations and Functions, 9-4 Rational Expressions, Skills Handbook: Area and Volume, 21, 60, 260, 304, 325, 388, 391, 404, 502, 847 SE: 11-6 Area Under a Curve, ,

6 9. Solves problems involving formulas used in science, business, or math applications (e.g., force, work, velocity, acceleration, density, pressure, or trigonometric ratios). SE: 1-1 Properties of Real Numbers, 1-2 Algebraic Expressions, 1-3 Solving Equations, 4-7 Inverse Matrices and Systems, 4-8 Augmented Matrices and Systems, 5-2 Properties of Parabolas, 5-5 Quadratic Equations, 6-8 The Binomial Theorem, Real-World Snapshots: As the Ball Flies, 7-2 Multiplying and Dividing Radical Expressions, 7-4 Rational Exponents, 7-5 Solving Radical Equations, Geometry Review: Expressions in Formulas, 7-8 Graphing Radical Functions, 8-2 Properties of Exponential Functions, 8-5 Exponential and Logarithmic Equations, 8-6 Natural Logarithms, 9-1 Inverse Variation, 9-2 Graphing Inverse Variations, 9-4 Rational Expressions, 9-5 Adding and Subtracting Rational Expressions, 9-6 Solving Rational Equations, Real-World Snapshots: Martian Math, 14-2 Solving Trigonometric Equations Using Inverses, 14-5 The Law of Cosines, 14-6 Angle Identities, 14-7 Double-Angle and Half- Angle Identities, 9, 15, 22-23, 214, 221, 244, , , , 371, , , 391, 412, , , , 480, 489, 502, , 509, , 518, 585, , , , 793, , , ,

7 GEOMETRY AND SPATIAL SENSE STANDARD 1: Students analyze properties of objects and relationships among the properties Make and evaluate conjectures about, and solve problems involving classes of (None for this course) two- and three-dimensional objects (e.g., Are all squares rectangles? STANDARD 2: Students use transformations and symmetry to analyze mathematical situations. Represent transformations of objects in the plane with coordinates, vectors, or matrices; describe the effects of a given transformation. Apply transformations to threedimensional objects. 1. Represents transformations of objects in the plane (e.g., translations, rotations, reflections, and dilations) by using sketches with coordinates, vectors, functional notations, or matrices. SE: 2-6 Vertical and Horizontal Translations, 4-4 Geometric Transformations with Matrices, 5-3 Translating Parabolas, 7-8 Graphing Radical Functions, 8-2 Properties of Exponential Functions, 8-3 Logarithmic Functions as Inverses, 9-2 Graphing Inverse Variations, 10-3 Circles, 10-6 Translating Conic Sections, 13-7 Translating Sine and Cosine Functions, 91-98, , 201, 207, 226, 228, , , 432, , 441, 443, , 550, 552, ,

8 STANDARD 3: Students use visualization and spatial reasoning to solve problems both within and outside of mathematics. Sketch three-dimensional objects and spaces from different perspective and (None for this course) interpret two- and three-dimensional drawings of objects. Analyze and describe cross-sections, truncations, and compositions/decompositions of threedimensional objects. STANDARD 4: Students select and use different representational systems, including coordinate geometry. Solve problems involving two- and three-dimensional figures. Analyze and apply coordinate systems on a sphere (distance and place on the earth s surface, positions of stars in 1. Solves problems involving two- and three dimensional figures using coordinate geometry. heavens). 2. Uses given spherical coordinates to find the arc length between two points on a sphere. SE: 3-5 Graphs in Three Dimensions,

9 PATTERNS, FUNCTIONS, AND ALGEBRA STANDARD 1: Students understand various types of patterns and functional relationships. Describe and use relations and functions (e.g., absolute value, piecewise defined, step, trigonometric, logarithmic, exponential, polynomial). Analyze and use linear relations among three variables. Analyze and use quadratic relations between two variables. 1. Performs operations on functions (e.g., addition, subtraction, multiplication, division, composition, inverse). SE: 7-6 Function Operations, 7-7 Inverse Relations and Functions, 8-2 Properties of Exponential Functions, 14-2 Solving Trigonometric Equations, , , , 440, Determines properties of relations and functions that may include some or all of the following: domain, range, symmetry, asymptotes, points of discontinuity, relative maximum/minimum values, zeroes, intercepts, concavity, points of inflection). SE: 2-2 Linear Equations, Extension: Piecewise Functions, 2-3 Direct Variation, 2-5 Absolute Value Functions and Graphs, 2-6 Vertical and Horizontal Translations, 2-7 Two Variable Inequalities, 5-2 Properties of Parabolas, 5-5 Quadratic Equations, 5-7 Completing the Square, 5-8 the Quadratic Formula, 6-1 Polynomial Functions, 6-2 Polynomials and Linear Factors, 6-3 Dividing Polynomials, 6-4 Solving Polynomial Equations, Extension: Descartes s Rule of Signs, 6-5 Theorems About Roots of Polynomial Equations, 6- The Fundamental Theorem of Algebra, 7-8 Graphing Radical Functions, 9

10 (Continued) 2. Determines properties of relations and functions that may include some or all of the following: domain, range, symmetry, asymptotes, points of discontinuity, relative maximum/minimum values, zeroes, intercepts, concavity, points of inflection). 3. Graphs relations and functions using their properties. (Continued) SE: 8-1 Exploring Exponential Models, 8-2 Properties of Exponential Functions,9-1 Inverse Variation, 9-2 Graphing Inverse Variations, 9-3 Rational Functions and Their Graphs, 13-1 Exploring Periodic Data, 13-4 The Sine Function, 13-5 The Cosine Function, 13-6 the Tangent Function, 13-8 Reciprocal Trigonometric Functions, 14-2 Solving Trigonometric Equations, 63-69, 71, 72-76, 86-90, , , , , , 293, , , , , 328, , , , , , , , , , , 710, , , , , , SE: 2-6 Vertical and Horizontal Translations, 2-7 Two Variable Inequalities, 5-2 Properties of Parabolas, 7-7 Inverse Relations and Functions, Technology: Graphing Inverses, 7-8 Graphing Radical Functions, 8-1 Exploring Exponential Functions, 8-2 Properties of Exponential Functions, Technology: Graphing Rational Functions, 10

11 (Continued) 3. Graphs relations and functions using their properties. 4. Uses relations and functions to solve problems. (Continued) SE: 9-2 Graphing Inverse Variations, 9-3 Rational Functions and Their Graphs, 13-4 The Sine Function, 13-5 The Cosine Function, 13-6 The Tangent Function, 13-8 Reciprocal Trigonometric Functions, 91-97, , , 294, , 407, , , , 484, , , , , SE: 2-3 Direct Variation, 2-4 Using Linear Models, 2-7 Two Variable Inequalities, 3-1 Graphing Systems of Equations, 3-2 Solving Systems Algebraically, 3-3 Systems of Inequalities, 3-4 Linear Programming, Technology: Linear Programming, 5-2 Properties of Parabola, 5-5 Quadratic Equations, 5-7 Completing the Square, 5-8 The Quadratic Formula, 6-2 Polynomials and Linear Factors, 6-4 Solving Polynomial Equations, 7-5 Solving Radical Equations, 8-1 Exploring Exponential Models, 8-2 Properties of Exponential Functions, 8-5 Exponential and Logarithmic Equations, 8-6 Natural Logarithms, 9-2 Graphing Inverse Functions, 9-3 Rational Functions and Their Graphs, 9-6 Solving Rational Equations, 13-4 The Sine Function, 13-5 The Cosine Function, 13-6 The Tangent Function, 11

12 (Continued) 4. Uses relations and functions to solve problems. 5. Represents and uses arithmetic, geometric and other sequences and series. 6. Uses linear relations with three variables. 7. Analyzes quadratic relations between two variables (Continued) SE: 63-69, 78-84, 97, 100, , , , , , 141, , 160, , , , , , , , , , , , , , , , , , , , 727, 733, , SE: 11-1 Mathematical Patterns, 11-2 Arithmetic Sequences, Extension: The Fibonacci Sequence, 11-3 Geometric Sequences, 11-4 Arithmetic Series, Investigation: Geometry and Infinite Series, 11-5 Geometric Series, , , 599, , , 613, SE: Technology: Parametric Equations, 3-5 Graphs in Three Dimensions, 3-6 Systems with Three Variables, 122, , , SE: 5-1 Modeling Data with Quadratic Functions, 5-2 Properties of Parabolas, 10-2 Parabolas, 10-3 Circles, 10-4 Ellipses, 10-5 Hyperbolas, , , 293, , , ,

13 8. Uses quadratic relations with two variables to solve problems. STANDARD 2: Students use symbolic forms to represent, model, and analyze mathematical situations. SE: 5-5 Quadratic Equations, Extension: Quadratic Inequalities, 5-7 Completing the Square, 5-8 The Quadratic Formula, 10-1 Exploring Conic Sections, 10-4 Ellipses, 10-5 Hyperbolas, 10-6 Translating Conic Sections, Extension: Solving Quadratic Systems, , 269, , , , , 557, 561, 565, , 572, , 577, Represent relations and functions with graphs, tables, and symbolic rules and translate among these representations. Model phenomena with a variety of functions and explain how and why a particular function can model many different situations. Approximate and interpret accumulation and rates of change for functions representing a variety of situations (e.g., compound interest). 1. Represents relations and functions with graph, tables of values, and symbolic rules and translates among these representations. 2. Determines which function best fits a given situation and justifies that choice of function. SE: 2-1 Relations and Functions, 2-2 Linear Equations, 2-3 Direct Variation, 2-5 Absolute Value Functions and Graphs, 2-6 Vertical and Horizontal Translations, 2-7 Two Variable Inequalities, 5-2 Properties of Parabolas, 5-3 Translating Parabolas, 7-7 Inverse Relations and Functions, 7-8 Graphing Radical Functions, 8-1 Exploring Exponential Models, 9-1 Inverse Variation, 10-1 Exploring Conic Sections, 55-61, 62-69, 72, 74-76, 86-90, 91-98, , , , , , 404, , 422, 469, , 485, 527, 528, 530, SE: Real-World Snapshots: Bridges, Beams, and Tension, 9-1 Inverse Variation, 113, 479, 481, 527,

14 3. Describes several different situations that can be represented by the same type of function and justifies the function used. 4. Chooses an appropriate function to represent (or fit) given data, given a situation involving accumulation (or change). 5. Uses the function to predict intermediate values (interpolation), given a situation involving accumulation (or change). DATA ANALYSIS, STATISTICS, AND PROBABILITY SE: 8-1 Exploring Exponential Models, SE: 8-1 Exploring Exponential Models, 8-5 Exponential and Logarithmic Equations, , SE: 8-1 Exploring Exponential Models, 8-5 Exponential and Logarithmic Equations, 8-6 Natural Logarithms, , , , STANDARD 1: Students pose questions and collect, organize, and represent data to answer those questions. Design and carry out investigations or experiments with two variables. 1. Identifies purpose of investigation of Select appropriate methods for experiment by stating hypothesis or posing collecting, recording, organizing, and questions. representing data; and describe how a 2. Identifies two variables in an investigation change in representation affects the or experiment. likely interpretation of the information. 3. Creates a survey instrument, if applicable, where: a. The sample population is identified. b. The sampling method is described. 14

15 4. Outlines a plan for organizing and representing data. 5. Collects and organizes data (e.g., makes tables, graphs). 6. Describes potentially misleading interpretations that may by due to different types of representation. STANDARD 2: Students interpret data using methods of exploratory data analysis. Compute, identify and interpret measures of center and spread (including standard deviation) Look for patterns in data and understand their use in interpretation of the data. Explain how sample size or transformations of data affect shape, center, and spread. Explain trends and use technology to determine how well different models fit data (e.g., line of best fit). 1. Computes and identifies measures of center and spread (including standard deviation). 2. Describes the population using measures of central tendency and spread. 3. Describes trends in data and uses them to interpret data (e.g., positive or negative correlation). 4. Explains how sample size or transformations of data affect shape, center and spread. 5. Uses technology to find the line or curve of best fit for data collected. SE: 12-3 Probability and Statistics, 12-4 Standard Deviation, , , , 719 SE: 12-3 Probability and Statistics, 12-7 Normal Distributions, , SE: 2-4 Using Linear Models, SE: 1-6 Probability, 12-3 Analyzing Data, 12-5 Working with Samples, 39, , , 689 SE: Technology: Finding a Line of Best Fit, 5-1 Modeling Data with Quadratic Functions, Technology: Modeling Using Residuals, 6-1 Polynomial Functions, Technology: Fitting Exponential Curves to Data, 8-5 Exponential and Logarithmic Equations, Real-World Snapshots: A Crowded House, 85, , 240, , 430, 455,

16 STANDARD 3: Students develop and evaluate inferences, predictions, and arguments that are based on data. Identify good models for phenomena (e.g., exponential model for population growth). Apply models to predict unobserved outcomes. Evaluate conclusions based on data and support inferences with valid arguments. 1. Identifies what best fits the data provided (e.g., linear (amount of sales tax), quadratic (height of bouncing ball), exponential (growth of certificates of deposit), sinusoidal (tides, number of daylight hours throughout the year)). 2. Identifies functions and interpolates or extrapolates data to predict unobserved outcomes. 3. Justifies predictions, inferences, or conclusions. SE: Extension: Linear and Exponential Models, 461 SE: 5-1 Modeling Data with Quadratic Functions, 6-1 Polynomial Functions, 8-5 Exponential and Logarithmic Equations, Real-World Snapshots: A Crowded House, , , , 475 STANDARD 4: Students understand and apply basic notions of chance and probability. Identify relationships among events (e.g., inclusion, disjoint, complementary, independent, and dependent). Compute probabilities of two events under different relationships unions and intersections. 1. Identifies relationships among events (e.g., inclusion, disjoint, complementary, independent, and dependent). 2. Calculates probabilities of two events under union and intersection. SE: 9-7 Probability of Multiple Events, , SE: 1-6 Probability, 9-7 Probability of Multiple Events, 12-2 Conditional Probability, 42-43, , , ,

17 (Continued) Use fundamental counting principle permutations, and combinations as counting techniques to solve problems. Compute the theoretical probabilities of repeated experiments with replacement and repeated experiments without replacement. Recognize random variables in real situations (e.g., insurance, life expectancy) and estimate and compute expectations. 3. Applies permutations, combinations, and the fundamental counting principle to calculate probabilities of events. 4. Calculates theoretical probabilities of repeated experiments with and without replacement. 5. Examines real life situations and determines if any random variable plays a major role. SE: 6-7 Permutations and Combinations, 12-6 Binomial Distributions, , 355, , 689 SE: 9-7 Probability of Multiple Events, Estimates and calculates expected values. SE: 12-7 Normal Distributions, 680,