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Student Edition algca_(s) |
| 1.0 |
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Students identify and use the arithmetic properties of subsets of integers and rational, irrational, and real numbers, including closure properties for the four basic arithmetic operations where applicable: |
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1-4, 1-3, 1-4, 2-3, 2-4, 2-5, 2-6, 3-2, 4-1, 4-3, 14-1, 14-4 |
| 1.1 |
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Students use properties of numbers to demonstrate whether assertions are true or false. |
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1-3, 1-4, 2-1, 2-4 |
| 2.0* |
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Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents. |
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2-3, 2-4, 4-3, 8-2, 8-3, 8-5, 8-6 |
| 3.0* |
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Students solve equations and inequalities involving absolute values. |
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3-7, 12-6 |
| 4.0* |
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Students simplify expressions before solving linear equations and inequalities in one variable, such as 3(2x - 5) + 4(x - 2) = 12. |
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, 1-3, 1-4, 3-4, 3-6, 4-1, 4-4, 4-5, 4-6, 4-7, 12-2, 12-3, 12-4 |
| 5.0* |
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Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step. |
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3-4, 3-6, 3-7, 4-5, 4-6, 4-7, 5-1, 12-2, 12-4 |
| 6.0* |
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Students graph a linear equation and compute the x-and y-intercepts (e.g., graph 2x + 6y = 4). They are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2x + 6y < 4). |
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7-5, 7-6, 12-7 |
| 7.0* |
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Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations by using the point-slope formula. |
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6-2, 7-2, 7-3 |
| 8.0* |
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Students understand the concepts of parallel lines and perpendicular lines and how those slopes are related. Students are able to find the equation of a line perpendicular to a given line that passes through a given point. |
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7-7 |
| 9.0* |
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Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solution sets. |
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13-1, 13-2, 13-3, 13-4, 13-5, 13-7 |
| 10.0* |
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Students add, subtract, multiply, and divide monomials and polynomials. Students solve multistep problems, including word problems, by using these techniques. |
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1-4, 4-1, 8-2, 9-2, 9-3, 9-4, 9-5, 15-3 |
| 11.0 |
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Students apply basic factoring techniques to second-and simple third-degree polynomials. These techniques include finding a common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect squares of binomials. |
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10-2, 10-3, 10-4, 10-5 |
| 12.0 |
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Students simplify fractions with polynomials in the numerator and denominator by factoring both and reducing them to the lowest terms. |
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15-1 |
| 13.0 |
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Students add, subtract, multiply, and divide rational expressions and functions. Students solve both computationally and conceptually challenging problems by using these techniques. |
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15-2, 15-3, 15-4, 15-5, 15-6 |
| 14.0 |
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Students solve a quadratic equation by factoring or completing the square. |
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11-4,11-5 |
| 15.0* |
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Students apply algebraic techniques to solve rate problems, work problems, and percent mixture problems. |
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5-4, 6-5, 6-6, 13-3, 13-5 |
| 16.0 |
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Students understand the concepts of a relation and a function, determine whether a given relation defines a function, and give pertinent information about given relations and functions. |
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6-1, 6-2, 6-4 |
| 17.0 |
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Students determine the domain of independent variables and the range of dependent variables defined by a graph, a set of ordered pairs, or a symbolic expression. |
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6-1, 6-2, 6-4 |
| 18.0 |
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Students determine whether a relation defined by a graph, a set of ordered pairs, or a symbolic expression is a function and justify the conclusion. |
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6-4 |
| 19.0 |
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Students know the quadratic formula and are familiar with its proof by completing the square. |
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11-6 |
| 20.0 |
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Students use the quadratic formula to find the roots of a second-degree polynomial and to solve quadratic equations. |
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11-6 |
| 21.0 |
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Students graph quadratic functions and know that their roots are the x-intercepts. |
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11-3 |
| 22.0 |
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Students use the quadratic formula or factoring techniques or both to determine whether the graph of a quadratic function will intersect the x-axis in zero, one, or two points. |
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11-4, 11-6 |
| 23.0 |
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Students apply quadratic equations to physical problems, such as the motion of an object under the force of gravity. |
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11-3, 11-4, 11-5, 11-6 |
| 24.3 |
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Students use counterexamples to show that an assertion is false and recognize that a single counterexample is sufficient to refute an assertion. |
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1-3, 1-4, 12-3, 14-1 |
| 25.0 |
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Students use properties of the number system to judge the validity of results, to justify each step of a procedure, and to prove or disprove statements: |
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1-2, 1-3, 1-4, 12-3 |
| 25.1 |
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Students use properties of numbers to construct simple, valid arguments (direct and indirect) for, or formulate counterexamples to, claimed assertions. |
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1-2, 1-3, 1-4, 4-3, 4-5, 7-3, 9-1, 12-3, 14-1 |
| 25.2 |
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Students judge the validity of an argument according to whether the properties of the real number system and the order of operations have been applied correctly at each step. |
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1-2, 1-3, 1-4, 8-2, 8-3 |
| 25.3 |
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Given a specific algebraic statement involving linear, quadratic, or absolute value expressions or equations or inequalities, students determine whether the statement is true sometimes, always, or never. |
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2-1, 4-1, 4-6, 11-6, 12-2 |
* CAHSEE Standard
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Extra Examples—
