Below is the Worktext for Section 2.
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Vocabulary in Section 2
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EQ's and Standards that are taught in this Section.
1. How do you form algebraic equations? MAFS. 912A-CED.1.1 2. How do you use properties of equality when solving linear equations? MAFS.912.A-REI.1.1 3. How do you solve equations using the Zero Product Property? MAFS. 912A-REI 1.1, MAFS 912A-CED1.3, MAFS 912A-REI 2.3 4. How do you solve algebraic equations? MAFS. 912A-REI 2.3, MAFS.912A-REI 1.1 5/6.. How do you solve algebraic inequalities? MAFS. 912A-REI 2.3, MAFS.912A-REI 1.1 7. How do you solve compound inequalities? MAFS.912A-CED 1.3, MAFS.912A-REI 2.3 8. How do you solve absolute value equations and inequalities? MAFS 912A-REI 1.1, MAFS912A. CED 2.3 9. How do you rearrange formulas to solve for a variable? MAFS. 912A-CED 1.4 10. How do you form solution sets to equations with two variables? MAFS.912.A-REI.4.10 MAFS.912.A-SSE.1.2 - Use the structure of an expression to identify ways to rewrite it. MAFS.912.A-REI.1.1- Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. MAFS.912.A-REI.2.3 - Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. MAFS.912.A-CED.1.1 - Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational exponential functions. MAFS.912.A-CED.1.2 - Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales MAFS.912.A-CED.1.4 - Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. MAFS.912.A-REI.4.10 - Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). |
Zero Product PropertyThe zero product property is when you solve each binomial to have it equal to zero. When you multiply any number by 0, the solution must equal to 0 as well.
Below is a video on the zero product property from Virtual Nerd. www.virtualnerd.com/algebra-1/polynomials-and-factoring/factoring-strategy-solving-equations/solving-equations/zero-product-property-definition |
Solving One Step, Two Step, and Multi Step EquationsThe key to solving linear equations is to keep the equations balanced like scales. If you subtract a number from the left hand side of the equal sign, you must subtract also on the right hand side of the equal sign. This goes for adding, multiplying, and dividing.
Properties of Equality: These properties are used to identify each step when solving an equation. Addition Property of Equality Subtraction Property of Equality Multiplication Property of Equality Division Property of Equality Below is a video on the "scale" representation with two step equations. www.khanacademy.org/math/algebra/one-variable-linear-equations/alg1-two-steps-equations-intro/v/why-we-do-the-same-thing-to-both-sides-two-step-equations |
Solving Inequalities
Below is a video on compound inequalities. www.khanacademy.org/math/algebra/one-variable-linear-inequalities/compound-inequalities/v/compound-inequalities |
Solving Absolute Value Inequalities and Equations
1. When solving for an absolute value equation, the most important component to remember is to set one equation to a positive value and the other equation to a negative value.
2. Absolute value means "how many spots away from 0 is the number" so if your value inside of the absolute value bars is negative...the final answer will be positive because of the definition of absolute value.
3. When solving absolute value inequalities, you will need to have two inequalities (just like the equations), one positive and one negative, BUT the inequality sign must flip.
4. ***Before you set up a positive and negative inequality, make sure every value around the absolute value bars is moved to the other side of the inequality/equation sign using the properties of inequality/equality.
1. When solving for an absolute value equation, the most important component to remember is to set one equation to a positive value and the other equation to a negative value.
2. Absolute value means "how many spots away from 0 is the number" so if your value inside of the absolute value bars is negative...the final answer will be positive because of the definition of absolute value.
3. When solving absolute value inequalities, you will need to have two inequalities (just like the equations), one positive and one negative, BUT the inequality sign must flip.
4. ***Before you set up a positive and negative inequality, make sure every value around the absolute value bars is moved to the other side of the inequality/equation sign using the properties of inequality/equality.
Solving for a Variable
Rearranging formulas for a specific variable will help in future math and science class. Instead of memorizing the formulas, students can manipulate the variables around according to properties of equality.
Rearranging formulas for a specific variable will help in future math and science class. Instead of memorizing the formulas, students can manipulate the variables around according to properties of equality.
Types of Functions and Solution Sets
1. Discrete Function: Functions that have specific solutions in their sets.
1. Discrete Function: Functions that have specific solutions in their sets.