1 st Semester AKS/Topics Geometric concepts review. 1 week Handouts, review packets, Loaded on MOCC McDougal Littell Geometry Textbook MA2G1 Students will identify and use special right triangles.(20) a. determine the lengths of sides of 30 60 90 triangle.(21) b. Determine the lengths of sides of a 45 45 90 triangle. (22) MA2G2 Students will define and apply sine, cosine and tangent ratios to right triangles a. Use and apply the relationship of the trigonometric ratios for similar triangles (23) b. Explain the relationship between the trigonometric ratios of complementary angles (24) 1 week Math 2: 5-1 to 5-4 (p.150-180) You may also want to use McDougal Littell Geometry textbook as an extra resource MA2G2 Students will define and apply sine, cosine and tangent ratio s to right triangles c. Solve application problems using trigonometric ratios (25) 1 week Exemplar/Buried Treasure Exemplar/How Tall is the Building Old Blue Geometry Book Ch 9 Loaded on MOCC 3 days work then 1 day test over MA2G1 and MA2G2 Page 1 of 7
MA2G3 Students will investigate the relationship between lines and circles. a. Find equations of circles (26) b. Graph a circle given an equation in general form (27) MA2G3 Students will investigate the relationship between lines and circles. c. Find the equation of a tangent line to a circle at a given point.(28) d. Solve a system of equations involving a circle and a line.(29) e. Solve a system of equations involving two circles.(30) MA2G5 Students will investigate planes and spheres. a. Plot the point (x,y,z) and understand it as a vertex of a rectangular prism. (35) b. Apply the distance formula in three dimensional space.(36) c. Recognize and understand equations of planes and spheres(37) MA2D1. Using sample data, students will make informal inferences about population means and standard deviations. a. Pose a question and collect sample data from at least two different populations.(75) b. Understand and calculate the means and standard deviations of sets of data.(76) c. Use means and standard deviations to compare data sets.(77) d. Compare the means and standard deviations of random samples with the corresponding population parameters. Observe that the different sample means vary from one sample to the next. Observe that the distribution of the sample means has less variability than the population distribution.(78) 2 weeks Math 3 Book p.180 Old Blue Geometry Chapter 9 Exemplar Distance formula vs Pythagorean Theorem 1 week Math 3 Section 5-7 p.205 Holt Geometry Book p.402 Exemplar Matrices Math 3 Start pg. 38 1 week Math 2 chapter 7 Sections 4-6 Consult AP Stat teacher for resources 2 days work 1 day quiz p.183 HW Look at McDougal Littell Geometry CD Supplement 3 days work 1 day quiz Old Blue Geometry p.602 #56 Must supplement MA2G3C Loaded on MOCC 1 day review and 1 day test over MA2G3 4 days of work and 1 day quiz Assessment from Holt Geometry book is good 2 days on exemplar and 1 day test over MA2G5 4 days work and 1 day quiz Page 2 of 7
MA2D2. Students will create probability histograms of discrete random variables, using both experimental and theoretical probabilities.(79) MA2D3. Students will solve problems involving probabilities by interpreting a normal distribution as a probability histogram for a continuous random variable (z-scores are used for a general normal distribution)(80) a. Determine intervals about the mean that include a given percent of data.(81) b. Determine the probability that a given value falls within a specified interval.(82) c. Estimate how many items in a population fall within a specified interval.(83) 1 week Math 2 chapter 7 Section 4 Math 3 chapter 6 Sections 1-3 Chapter 12 MA2D4. Students will understand the differences between experimental and observational studies by posing questions and collecting, analyzing, and interpreting data.(84) 1 week Math 3 chapter 6 Sections 3-5 Finish up all (MAA2_D2008-75 through 84) days work 1 day test 9 week Interim assessment End of 1 st Quarter MA2A1. Students will explore exponential functions. a. Understand and recognize geometric sequences as exponential functions with domains that are sets of whole numbers.(43) b. Interpret the constant ratio in a geometric sequence as the base of the associated exponential function.(44) 2 weeks You may want to add Geometric sums and infinite Geometric sums. Use book as resource Review Arithmetic sequences and series at this time. Page 3 of 7
MA2A2 Students will explore inverses of Functions. a. Analyze the characteristics of functions and their inverses, including one-to-oneness, domain and range.(45) b. Determine inverses of linear, quadratic, and power functions including use of restricted domains.(46) c. Analyze the graphs of functions and their inverses.(47) d. Use composition to verify that functions are inverses of each other.(48) MA2A1 Students will explore exponential functions a. Extend properties of exponents to include all integer exponents(38) b. Investigate and explain characteristics of exponential functions, including domain and range, asymptotes, zero s, intercepts, intervals of increase and decrease, rates of change and end behavior(39) x c. Graph functions as transformations of f ( x) a (40) d. Solve simple exponential equations and inequalities analytically, graphically, and by using appropriate technology.(41) e. Understand and use basic exponential functions as models of real phenomena.(42) 3 weeks Math 2 4.1-4.6 p.106-132 Additional : Holt Alg II Chapter 2 Exemplars 3 weeks Math 2 4.4 and 4.5 p.120-131 Additional : Holt Alg II Chapter 6.1 to 6.2 p.354-369 Exemplar Review and quiz 4 days work and 1 day test over MA2A2 Concentrate on linear and quadratic 4 days work and 1 day quiz Review and Final Exams End of 1 st Semester Page 4 of 7
2 nd Semester AKS/Topics MA2A4. Students will explore logarithmic functions as inverses of exponential functions. th a. Define and understand the properties of n roots.(53) b. Extend properties of exponents to include rational exponents.(54) c. Define logarithmic functions as inverses of exponential functions.(55) d. Understand and use properties of logarithms by extending laws of exponents.(56) e. Investigate and explain characteristics of exponential and logarithmic functions including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, and rate of change.(57) f. Graph functions as transformations of x x f ( x) a, f ( x) log a x, f ( x) e, f ( x) ln x (58) g. Explore real phenomena related to exponential and logarithmic functions including half life and doubling time.(59) 3 weeks Math 3 chapter 3 Sections 1,2 Chapter 4 sections 1-6 Chapter 6 and 2 Pre-Calculus with limits Chapter 3 MA2A3 Students will analyze graphs of polynomial functions of higher degree a. Graph simple polynomial functions as translations of the function n f ( x) ax.(49) b. Describe the effects of the following on the graph of a polynomial function: degree, lead coefficient, and multiplicity of real zeros.(50) c. Determine whether a polynomial function has symmetry and whether it is even, odd or neither. (51) d. Investigate and explain characteristics of polynomial functions, including domain and range, intercepts, zeros, relative and absolute extrema, intervals of increase and decrease, and end behavior.(52) 3 weeks Math 3 chapter 2 sections 1,2,7,8. Chapter 7 all sections Test Test Page 5 of 7
MA2A5. Students will solve a variety of equations and inequalities. a. Find the real and complex roots of higher degree polynomial equations using the factor theorem, remainder theorem, rational root theorem, and fundamental theorem of algebra, incorporating complex and radical conjugates.(60) b. Solve polynomial, exponential, and logarithmic equations analytically, graphically, and using technology.(61) c. Solve polynomial, exponential, and logarithmic inequalities analytically, graphically, and using appropriate technology. Represent solution sets of inequalities using interval notation.(62) d. Solve a variety of types of equations by appropriate means choosing among mental calculation, pencil and paper, or appropriate technology.(63) 3 weeks Math 3 chapter 2 Sections 3-7. Chapter 4 sections 1,3 and 7 Chapters 6, 7 and 8 9 week Interim assessment End of 3 rd Quarter MA2A6 Students will perform basis operations with matrices a. Add, Subtract, multiply and Invert matrices, when possible, choosing appropriate methods, including technology(64) b. Find the determinants and inverses of two by two and three by three matrices using pencil and paper, and find inverses of larger matrices using technology.(65) 1 week Math 3 p.38-62 Holt Alg 2 Chapter 4 Page 6 of 7
MA2A7 Students will use matrices to formulate and solve problems a. Represent a system of linear equations as a matrix equation.(67) b. Solve matrix equations using inverse matrices.(68) c. Represent and solve realistic problems using systems of linear equations(69) d. Examine the properties of matrices, contrasting them with the properties of real numbers(66) 2 weeks Math 3 p.38-62 Exemplars Test over MA2A6 and MA2A7 MA2A8 Students will solve linear programming problems in two variables a. Solve systems of inequalities in two variables, showing the solutions graphically.(70) b. Represent and solve realistic problems using linear programming(71) MA2A9 Students will understand and apply matrix representations of vertex edge graphs.(72) a. Use graphs to represent realistic situations(73) b. Use matrices to represent graphs, and solve problems that can be represented by graphs.(74) 2 weeks Math 3 1.4-1.7 p.17-37 Additional : Holt Alg II Section 3.5 p.187 4 days work 1 day test MA2G4. Students will recognize, analyze, and graph the equations of the conic sections (parabolas, circles, ellipses, and hyperbolas).(31) a. Convert equations of conics by completing the square.(32) b. Graph conic sections, indentifying fundamental characteristics.(33) c. Write equations of conic sections given appropriate information.(34) 3 weeks Math 3 chapter 5 Sections 1 to 5 Chapter 9 1 week Review and final exam Page 7 of 7