Essential Learning Outcomes for Algebra 2
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1 ALGEBRA 2 ELOs 1 Essential Learning Outcomes for Algebra 2 The following essential learning outcomes (ELOs) represent the 12 skills that students should be able to demonstrate knowledge of upon completion of the Algebra 2 course offered at SDA. The number of skills has been limited to 12 so that 6 may be taught, adequately practiced, and applied per quarter. A description of each skill is provided along with sample problems. These sample problems are included only to provide some color for each skill and are not intended to serve as a model for what an assessment of the learning outcome might resemble. The ELOs outlined in this document address the key California academic content standards in Algebra II. They have been selected so that students can construct the knowledge reflected in the ELOs from prior knowledge attained in the Algebra I and Geometry courses. They are also intended to provide the skills required to make a seamless transition into the Math Analysis and Chemistry classes offered at SDA.
2 ALGEBRA 2 ELOs 2 1. Be able to solve equations and inequalities that contain absolute value notation. 2. Be able to solve a system of equations and inequalities graphically, by substitution, and by linear combination methods. Students should be able to do this for systems of up to 3 equations with three unknowns. 3. Be able to apply the properties of exponents and radicals to simplify exponential and radical expressions. This skill should be performed without the use of a calculator to ensure understanding of the properties. Express the quotient in scientific notation: 4. Be able to solve exponential equations. Students should be able to solve these equations by deriving a common base.
3 ALGEBRA 2 ELOs 3 5. Be able to graph quadratics from intercept and vertex forms. As part of this learning outcome students should also be able to identify the vertex, intercepts, and whether the vertex is a maximum or minimum. Graph the parabola from standard form. Put the vertex in the middle of the data table in the dark boxes. Input (x) Output (y) Graph the parabola from vertex form. Put the vertex in the middle of the data table in the dark boxes and fill in the blank sections Input (x) Output (y) Equation for the Axis of Symmetry: Y intercept: ( 0, )
4 ALGEBRA 2 ELOs 4 6. Be able to solve quadratic equations. This skill includes solving equations where the coefficient of the quadratic term is not 1. As part of this learning outcome, students should also be able to solve equations by expressing them in vertex form and using square roots. Students should be able to produce both real and complex solutions. 7. Be able to add, subtract, multiply, and divide polynomials and complex numbers. 8. Be able to find the zeros of a polynomial function and use them to graph the function. Students should be able to do this by grouping, using the sum and difference of perfect cubes formulas, and by division when one zero is provided. Students should also be able to apply this skill in reverse by writing a polynomial function that passes through given zeros. Find the zeros of the following functions. If -2 is a zero of the following function, find the other zeros and graph the function of the coordinate plane.
5 ALGEBRA 2 ELOs 5 9. Be able to add, subtract, multiply, divide, and reduce rational expressions. Students should also be able to solve equations containing rational expressions. Solve for x: 10. Be able to use the properties of logarithms, including expanding and condensing, to evaluate logarithmic expressions and solve logarithmic and exponential equations. These skills should be performed without the use of a calculator to ensure understanding of logarithmic notation. Evaluate each expression without using a calculator. Show all of your work. Express your answer in simplest form. Expand: Solve for x:
6 ALGEBRA 2 ELOs Be able to solve problems involving probabilities. Students should also be able to incorporate the use of probabilities with graphic organizers (tables and tree diagrams) to make decisions and solve problems, including problems involving expected value. Find the theoretical probabilities of the following events and express them as a fraction in simplest form: Flipping heads on three consecutive coin tosses. Rolling a sum of 9 on a two dice roll. What is the expected value of drawing twice from a bag containing two $10 bills and three $1 bills? If you are offered $8 every week, or a weekly opportunity to draw twice from the bag, which should you choose and why? 12. Be able to use the fundamental counting principal to find the number of combinations and permutations of a set, including the number of distinguishable permutations. Students should also be able to solve problems by appropriately choosing a permutation or combination strategy. Find the number of Permutations or Combinations: Find the number of distinguishable permutations of the letters in the word ASSESS. In how many ways could you choose a committee of 4 people from a group of 52? In how many ways could you choose a president, vice president, secretary, and treasurer from a class of 88 students?
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