Unit 1 - Mathematical Practices & Introduction (8 Days)
1. Write a function that describes a relationship between two quantities given a graph, a description of a relationship, or two input-output pairs and solve problems in the context of the data.
2. 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).
3. Calculate the average rate of change.
4. Find inverse functions.
Unit 2 - Quadratics & Complex (25 Days)
5. Factor a quadratic expression to reveal the zeros and solve quadratic equations with that have real solutions.
6. Complete the square to reveal the maximum or minimum value and connect the equation of a quadratic to its focus and directrix.
7. Know there is a complex number and be able to add, subtract, multiply, and divide them.
8. Solve quadratic equations with real coefficients that have complex solutions.
Revisit: The average rate of change.
Revisit: Inverse functions.
Unit 3 - Systems (5 Days)
9. Solve systems of linear equations exactly and approximately.
10. Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.
Revisit: 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).
Unit 4 - Rationals & Radicals (15 Days)
11. Solve simple radical equations in one variable, and give examples showing how extraneous solutions may arise.
12. Solve simple rational equations in one variable, and give examples showing how extraneous solutions may arise.
Revisit: Inverse functions.
Unit 5 - Polynomials (20 Days)
13. Be able to add, subtract, multiply, and divide polynomials.
14. Know and apply the Remainder Theorem and identify zeros of polynomials.
15. Graph given polynomial functions and construct a rough graph of the function defined by key features and then state maximums, minimums, and end behavior.
Unit 6 - Exponentials & Logarithms (15 Days)
16. Use the properties of exponents to interpret expressions for exponential functions and classify them as representing exponential growth or decay.
17. For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers.
18. Graph exponential and logarithmic functions, showing intercepts and end behavior.
Unit 7 - Trigonometry (20 Days)
19. Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
20. Explain the unit circle in the coordinate plane.
21. Find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.
22. Model periodic phenomena with specified amplitude and frequency.
Unit 8 - Sequences & Series (10 Days)
23. Write arithmetic and geometric sequences both recursively and with an explicit formula and use them to model situations and find these formulas given a context.
24. Use the formula for the sum of a finite geometric series and use the formula to solve problems.
Unit 9 - Statistics (10 Days)
25. Recognize the purposes of and differences among sample surveys, experiments, and observational studies.
26. Use data from a sample survey to estimate a population mean.
27. Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages.
Unit 10 - Probability (10 Days)
28. Understand and find the conditional probability of A given B.
29. Construct and interpret two-way frequency tables and use the two-way table to approximate conditional probabilities.
30. Describe events as subsets of a sample space using characteristics such as unions, intersections, or complements.
There are no field trips or special projects planned!