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# California Academic Content Standards

### Use the links below to find resources that support standards adopted by the California State Board of Education

for English-language arts, mathematics, history-social science, science, and visual and performing arts.

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California Academic Content Standards1641507 9317

Strand Algebra I1265 217

- Symbolic reasoning and calculations with symbols are central in algebra. Through the study of algebra, a student develops an understanding of the symbolic language of mathematics and the sciences. In addition, algebraic skills and concepts are developed and used in a wide variety of problem-solving situations.
- Substrand 1.0Students 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:1 7
- Substrand 2.0Students 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.11 22
- Substrand 3.0Students solve equations and inequalities involving absolute values.11 9
- Substrand 4.0Students simplify expressions before solving linear equations and inequalities in one variable, such as 3(2x-5) + 4(x-2) = 12.21 19
- Substrand 5.0Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step.11 40
- Substrand 6.0Students 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).21 59
- Substrand 7.0Students 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.11 23
- Substrand 8.0Students 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.11 17
- Substrand 9.0Students 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.11 32
- Substrand 10.0Students add, subtract, multiply, and divide monomials and polynomials. Students solve multistep problems, including word problems, by using these techniques.11 11
- Substrand 11.0Students 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.1 11
- Substrand 12.0Students simplify fractions with polynomials in the numerator and denominator by factoring both and reducing them to the lowest terms.1 8
- Substrand 13.0Students add, subtract, multiply, and divide rational expressions and functions. Students solve both computationally and conceptually challenging problems by using these techniques.1 6
- Substrand 14.0Students solve a quadratic equation by factoring or completing the square.1 6
- Substrand 15.0Students apply algebraic techniques to solve rate problems, work problems, and percent mixture problems.11 28
- Substrand 16.0Students 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.1 14
- Substrand 17.0Students 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.1 7
- Substrand 18.0Students determine whether a relation defined by a graph, a set of ordered pairs, or a symbolic expression is a function and justify the conclusion.1 10
- Substrand 19.0Students know the quadratic formula and are familiar with its proof by completing the square.1 3
- Substrand 20.0Students use the quadratic formula to find the roots of a seconddegree polynomial and to solve quadratic equations.1 6
- Substrand 21.0Students graph quadratic functions and know that their roots are the x-intercepts.1 28
- Substrand 22.0Students 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.1 9
- Substrand 23.0Students apply quadratic equations to physical problems, such as the motion of an object under the force of gravity.1 12
- Substrand 24.0Students use and know simple aspects of a logical argument:3 6
- Substrand 25.0Students 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:3 15