Hartselle High School

Advanced Algebra II with Statistics Syllabus 2024-2025

Mrs. Sonie Wilson

sonie.wilson@hartselletigers.org 

Course Description: Algebra II with Statistics builds essential concepts necessary for students to meet their postsecondary goals (whether they pursue additional study or enter the workforce), function as effective citizens, and recognize the wonder, joy, and beauty of mathematics (NCTM, 2018). In particular, it builds foundational knowledge of algebra and functions needed for students to take the specialized courses which follow it. This course also focuses on inferential statistics, which allows students to draw conclusions about populations and cause-and-effect based on random samples and controlled experiments.

 In Algebra II with Statistics, students incorporate knowledge and skills from several mathematics content areas, leading to a deeper understanding of fundamental relationships within the discipline and building a solid foundation for further study. In the content area of Algebra and Functions, students explore an expanded range of functions, including polynomial, trigonometric (specifically sine and cosine), logarithmic, reciprocal, radical, and general piecewise functions. Students also solve equations associated with these classes of functions. In the content area of Data Analysis, Statistics, and Probability, students learn how to make inferences about a population from a random sample drawn from the population and how to analyze cause-and-effect by conducting randomized experiments. Students are introduced to the study of matrices in the Number and Quantity content area.

Prerequisites:  Algebra I and Geometry

Materials Needed:

• An organized math notebook for notes, assignments, and graded work
• Pencils, lead, colored pencils, and erasers
• College ruled paper (small pack)
• Graph paper--I will provide this when needed
• Ruler
• Page Protectors--I will provide 
• Graphing Calculator--TI 84 Plus CE is preferred (We use the graphing calculator most days)

Classroom Policies:

• Be on time and prepared to learn. Your timeliness affects you and your classmates. You are expected to be in class and ready to learn when the bell rings. You should have a sharpened pencil, an organized notebook and needed supplies daily.
• Seek help when needed. If you are having trouble with the material, please seek help. Ask your classmates, ask me, come in early for help, and/or utilize the internet. Khan Academy is a great resource and it’s free (https://www.khanacademy.org/) and don’t forget to look at You-Tube videos. I will upload the notes from class each day in Google Classroom. I will also post videos of each lesson daily.
• Always show your work. The process of working through a problem is just as important as the final result. All work must be shown to receive full credit.
• Make-up and turn in missed assignments. You are responsible for all notes and assignments missed when absent. Notes and the pages needed will be uploaded into Google Classroom daily.  
• Late work. Late work is accepted, but will be an alternate assignment, and as long as it is turned in while working on the same unit. Once we’ve moved on to the next unit, late work will not be accepted. You will need to come in before school to do the alternate assignment.
• Use digital devices in class ONLY when given permission. There will be times in class when the use of cell phones and/or other devices is relevant to the curriculum and content; however, until given permission, you are to put your cell phones in the “cell jail” in the back of the room.

• No food or drinks are allowed in the classroom, with the exception of water.

• We do not have free days. Our class time is valuable and we have a lot to learn. So please don’t ask if we are doing something, the answer will always be yes.

• Respect yourself, others, and classroom property.

Grading Procedures:  Grades will be based on test/quizzes, classwork, and homework.  Test/quizzes will count 60%, class work, homework and practice will count 40% each nine weeks.  Tests will be comprehensive throughout the semester. A comprehensive exam will be given in December and will count 20% of first semester grade.  Another comprehensive exam will be given in May and it will count for 20% of the second semester grade.

Course Content:

• Identify numbers written in the form a + bi, where a and b are real numbers and i^ 2 = –1, as complex numbers. 
• Use matrices to represent and manipulate data
• Multiply matrices by scalars to produce new matrices. 
• Add, subtract, and multiply matrices of appropriate dimensions.  
• Describe the roles that zero and identity matrices play in matrix addition and multiplication, recognizing that they are similar to the roles of 0 and 1 in the real numbers
• Factor polynomials using common factoring techniques, and use the factored form of a polynomial to reveal the zeros of the function it defines.
• Prove polynomial identities and use them to describe numerical relationships.
• Explain why extraneous solutions to an equation may arise and how to check to be sure that a candidate solution satisfies an equation. Extend to radical equations. 
• For exponential models, express as a logarithm the solution to abct = d, where a, c, and d are real numbers and the base b is 2 or 10; evaluate the logarithm using technology to solve an exponential equation. 
• Create equations and inequalities in one variable and use them to solve problems. Extend to equations arising from polynomial, trigonometric (sine and cosine), logarithmic, radical, and general piecewise functions. 
• Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x).  
• Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Extend to polynomial, trigonometric (sine and cosine), logarithmic, radical, and general piecewise functions
• Identify the effect on the graph of replacing 𝑓(𝑥) by 𝑓(𝑥) + 𝑘, 𝑘 · 𝑓(𝑥), 𝑓(𝑘 · 𝑥), and 𝑓(𝑥 + 𝑘) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Extend to polynomial, trigonometric (sine and cosine), logarithmic, reciprocal, radical, and general piecewise functions.
• For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Note: Key features include intercepts; intervals where the function is increasing, decreasing, positive, or negative; maximums and minimums; symmetries (including even and odd); end behavior; and periodicity. Extend to polynomial, trigonometric (sine and cosine), logarithmic, reciprocal, radical, and general piecewise functions. 
• Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Extend to polynomial, trigonometric (sine and cosine), logarithmic, reciprocal, radical, and general piecewise functions. 
• Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Extend to polynomial, trigonometric (sine and cosine), logarithmic, reciprocal, radical, and general piecewise functions. 
• Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Extend to polynomial, trigonometric (sine and cosine), logarithmic, reciprocal, radical, and general piecewise functions.
• Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle, building on work with non-right triangle trigonometry. 
• Use the mathematical modeling cycle to solve real-world problems involving polynomial, trigonometric (sine and cosine), logarithmic, radical, and general piecewise functions, from the simplification of the problem through the solving of the simplified problem, the interpretation of its solution, and the checking of the solution’s feasibility. 
• Use mathematical and statistical reasoning about normal distributions to draw conclusions and assess risk; limit to informal arguments. 
• Design and carry out an experiment or survey to answer a question of interest, and write an informal persuasive argument based on the results. 
• From a normal distribution, use technology to find the mean and standard deviation and estimate population percentages by applying the empirical rule. 
•  Describe the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. 
• Distinguish between a statistic and a parameter and use statistical processes to make inferences about population parameters based on statistics from random samples from that population.
• Describe differences between randomly selecting samples and randomly assigning subjects to experimental treatment groups in terms of inferences drawn regarding a population versus regarding cause and effect.
• Explain the consequences, due to uncontrolled variables, of non-randomized assignment of subjects to groups in experiments. 
• Evaluate where bias, including sampling, response, or nonresponse bias, may occur in surveys, and whether results are representative of the population of interest.
• Evaluate the effect of sample size on the expected variability in the sampling distribution of a sample statistic.
• Produce a sampling distribution by repeatedly selecting samples of the same size from a given population or from a population simulated by bootstrapping (resampling with replacement from an observed sample). Do initial examples by hand, then use technology to generate a large number of samples. 
• Use data from a randomized experiment to compare two treatments; limit to informal use of simulations to decide if an observed difference in the responses of the two treatment groups is unlikely to have occurred due to randomization alone, thus implying that the difference between the treatment groups is meaningful. 
• Define the radian measure of an angle as the constant of proportionality of the length of an arc it intercepts to the radius of the circle; in particular, it is the length of the arc intercepted on the unit circle. 
• Choose trigonometric functions (sine and cosine) to model periodic phenomena with specified amplitude, frequency, and midline. 
• Prove the Pythagorean identity sin2 (θ) + cos2 (θ) = 1 and use it to calculate trigonometric ratios.
• Derive and apply the formula A = ½·ab·sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side, extending the domain of sine to include right and obtuse angles.
• Derive and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles. Extend the domain of sine and cosine to include right and obtuse angles.  

Personal Statement:  

If you are having difficulties with any of the topics covered in this course, see me as soon as possible.  I am always available before school to help you.  I am generally in my room by 7:40am and will help you as much and often as you need me to.  In addition, keep the following thoughts in mind:

When you worry, “I can’t do it”, tell yourself, “I can do it and I just need to figure it out.”

You can ALWAYS ask for help.

Set goals every week and recognize your accomplishments.

Bring a positive attitude and a smile to class.

• Sonie Wilson ☺
• Sonie.wilson@hartselletigers.org

Google Classroom: Enter this code to enter the classroom...

1st period: tainkpm 

I will use Google Classroom daily to make announcements, assignments, and post videos of the lessons. Each Sunday, I will post the weekly Lesson Plan in GC. The plan could change a little bit throughout the week, but very little. Each day, I will post the worksheets, a video of the notes, and answers to the notes. I also post homework and the homework is to be submitted back to me in GC by 8am the following day. If the assignment is not submitted on time, then an alternate assignment will be assigned and must be completed in my classroom, before school. I am at school by 7:40am each day.