Subject Area Mathematics Senior High Course Name Advanced Algebra 2B Date June 2010 Advanced Algebra 2B and Algebra 2B courses parallel each other in content and time. The Advanced Algebra 2B class is taught at a slightly more rigorous pace. Students are expected to work at a higher level and are assigned more advanced problems for homework and formal assessments. Students are also given more assessments in addition to tests and quizzes. Timeli ne 10 Content Standards Addressed Skills/Benchmarks Essential Questions Assessments Exponential and Logarithmic Models: #Exploring exponential models #Properties of exponential models #Log functions as inverses #Properties of logs #Exponential and Log equations #Using Natural Logs Represent and solve problems using exponential functions such as: investment growth, depreciation, and population growth. Sketch the graph of an exponential function. Translate between graphs, tables and symbolic representations. Use graphing technology to graph Represent relationships in various contexts using equations of exponential Solve equations involving exponential functions graphically or numerically. Know how to use graphing utilities to solve exponential model exponential growth and decay. identify the role of the constants in the exponential equation. use e as a base. write, evaluate, and graph log expressions and use the properties of logs. solve exponential and log equations. 1. How is exponential growth and decay different from linear growth and decay? 2. How are exponential and log functions related? 3. What real life situations can be modeled by exponential and log functions? Quizzes and Tests NCAA basketball tourney activity A Crowded House Activity on population growth ( text p. 484) evaluate and solve natural log expressions and equations. 10 Rational Identify symbolically and 1. How is inverse variation
Functions: #Inverse Variation #Reciprocal Functions #Rational Functions and their Graphs #Rational Expressions #Adding and Subtracting Rational Expressions #Solving Rational Equations #Probability of Multiple Events graphically asymptotes for Exponential Identify symbolically and graphically asymptotes for Reciprocals of linear functions Sketch graphs and translations of the reciprocal of a linear function. Know how to use graphing technology to graph these Add, subtract, multiply and divide algebraic fractions. Apply intersections and unions to calculate probabilities to solve problems. Apply complements of events to calculate probabilities to solve problems. Apply independence to calculate probabilities to solve problems. Understand the relationship between these concepts and the words AND, OR and NOT. Understand basic probability formula involving intersections, unions and complements. use inverse, joint, and other variations. graph reciprocal functions and translations of such identify properties of rational functions and be able to graph them. simplify rational expressions. perform the four basic operations on rational expressions. simplify complex fractions. use and solve rational equations in solving problems. different from direct variation? 2. What real life situations can be modeled with inverse or joint variation? 3. What is the connection between extraneous solutions and the graph of a rational function. 4. What real life situations can be modeled with rational expressions. 5. How are basic operations performed on rational expressions? 6. How is a probability of an intersection and a union calculated? Quizzes and Tests Extraneous Solution Activity Page 521 in text Number cube activity page 531 find the probability of the event A and B. find the probability of the event A or B. 10 Quadratic Know the equation for the graph of a circle with radius r graph and identify the four 1. How are the four conic sections formed from a cone
Relations and Conic Sections #Exploring Conic Sections #Circles #Parabolas #Ellipses #Hyperbolas and center (h, k). Justify this equation using Pythagorean Theorem and properties of translations. conic sections. write the equation of and graph parabolas. write the equation of and graph circles. find the center and radius of a circle. and a plane? 2. What applications of parabolas are found in real life? 3. How does the distance formula help develop the formulas for the conic sections? 4. How does the equation of a conic change when the graph is translated? Quizzes and Tests Graphing Activity page 554 in text Find photos of conic sections from magazines or other publications or personal photos write the equation of and graph ellipses. find the foci of an ellipse. graph hyperbolas. find and use the foci of an hyperbola. write an equation of a translated conic section. 10 Sequences and Series #Mathematical Express terms of a geometric sequence recursively and explicitly. Express partial sums of a geometric series recursively. 10. Students will be able to identify a conic section from an equation. identify mathematical patterns. 1. How are arithmetic and geometric sequences formed? 2. What applications of sequences and series can be Tests and Quizzes
Patterns #Arithmetic Sequences and Series #Geometric Sequences and Series Recognize and solve problems that can be modeled using finite geometric sequences and series (home mortgage, etc). Know how to use spreadsheets and calculators to explore geometric sequences and series. use a formula to find the nth term of a sequence. identify and generate arithmetic sequences. identify and generate geometric sequences. found in real life? 3. What is the difference between recursive and explicit formulas for different kinds of series? Geometric sequences from a triangle Geometric interpretation of an infinite series page 625 in text use summation notation to find sums of arithmetic sequences. evaluate finite and infinite geometric series. 15 Probability and Statistics #Probability Distributions #Conditional Probability #Analyzing Data #Standard Deviation #Working with Samples #Binomial Distribution #Normal Distribution Describe a data set using appropriate data displays. Describe and compare data sets using summary statistics including measures of center & location (mean, median, mode, quartile, and percentile). Describe and compare data sets using summary statistics including measures of spread(standard deviation, range & interquartile range. Know how to use calculators, spreadsheets or other technology to display and calculate. Analyze the effects on summary statistics of changes make and use a probability distribution. find conditional probabilities. use formulas and tree diagrams. calculate measures of central tendency. construct and interpret a box plot. 1. How are measures of center and spread calculated and used to describe a data set? 2. What type of display is best for a particular data set? 3. How does standard deviation help us interpret a normal distribution? 4. How do we best interpret a published study and understand the statistics in the study? 5. What effect does sample size have on the margin of error? Daily homework and in class Tests and Quizzes Graphing project on personal data Simulation using Random Number generator and/or other manipulatives
in data sets (inserting or deleting). Use mean and standard deviation to fit a data set to a normal distribution. Estimate population percentages using a normal distribution. Recognize that not all data sets are normally distributed. Use technology to estimate the area under the normal curve. Evaluate reports based on data published in the media. Identify the source of the data. Identify the design of the study. Identify the way the data are analyzed and displayed. Show how graphs and data can be distorted to support different points of view. Know how to use technology to recognize and analyze distortions in data displays. Identify and explain misleading uses of data. Explain the impact of sampling methods, bias, and questions phrasing during data collection. Select and apply counting procedures to determine size of sample space to calculate probabilities. Calculate experimental probabilities by performing simulations. Understand the Law of Large Numbers. find the standard deviation of a data set. use standard deviation in a real world situation. find margin or error the sample proportion.. find binomial probabilities and use binomial distributions. 10. Students will be able to use a normal distribution.
15 Periodic Functions and Trigonometry #Exploring Periodic Data #Angles and the Unit Circle #Radian Measure #The Sine Function #The Cosine Function #The Tangent Function #Translating Sine and Cosine Functions #Reciprocal Trig. Functions Understand how properties of right triangles allow the defining of trigonometric ratios. Determine the sine, cosine and tangent of an acute angle in a right triangle. Apply trigonometric ratios to solve problems, such as determining length and area in triangles and figures that can be decomposed into right triangles. Know how to use calculators, tables or other technology to evaluate trigonometric ratios. Use calculators, tables, or other technology in conjunction with trigonometric ratios to find angle measures in right triangles. identify cycles and periods of periodic find the amplitude of a function. be able to work with angles in standard position. find the coordinates of points on the unit circle. measure angles in radians. find the length of an arc in a circle. 1. What is meant by a periodic function? 2. How do the graph of a trig function and the unit circle work together? 3. How is solving a trig equation similar to and different from solving other equations? 4. How are the formulas for arc length and sector area in radians developed? 5. What applications lead to periodic functions? Tests and quizzes Sunrise/Sunset project Ferris wheel project identify properties of and graph the sine function graph and write cosine solve trig equations. 10. Students will be able to graph the tangent function. 1 graph and write equations of translated trig
1 evaluate and graph reciprocal trig 15 Trigonometric Identities and Equations #Trig Identities #Solving trig equations using inverses #Right triangles and trig ratios #Area and the Sine Law #Cosine Law #Angle Identities Know and apply properties of right triangles including 45-45-90 triangles. Know and apply properties of right triangles including 30-60-90 triangles. verify trig identities. evaluate inverses of trig identities. solve trig equations using inverses. find the length of missing sides and the measure of missing angles in any triangle. find the area of any triangle and use the Sine Law. 1. What applications lead to solving a triangle? 2. Why doesn t every triangle have a unique solution? 3. How does the formula for finding the area of a triangle lead to the development of the Sine Law? 4. How the Cosine Law compare to the Pythagorean Theorem? 5. How do you determine which method to use for solving a triangle? Tests and quizzes Ambiguous case for SSA Bow Tie in the Unit Circle use the Cosine Law. verify and use angle identities. Content -- big ideas, broad topics, major subcategories and underlying concepts Standards Addressed -- state and/or local standards Skills/Benchmarks -- tells what the student will be able to do as a result of instruction Essential Questions -- what overarching questions will guide instruction and produce higher levels of thinking? Assessments -- evidence that the student understands the concepts, demonstration of skills