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Grade 9 Math Courses - Texas Curriculum

Discover Texas Grade 9 Math, focusing on Algebra I. Explore linear and quadratic functions, polynomials, and more. Prepare for success with our comprehensive curriculum aligned to state standards.

Texas Grade 9 Math Curriculum - Algebra I

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ID
Strand & Expectation
StudyPug Topic
TX.A1.2.A
Linear Functions, Equations, and Inequalities: Determine the domain and range of a linear function in mathematical problems; determine reasonable domain and range values for real-world situations
Relationship between two variables
Domain and range of a function
Understanding graphs of linear relationships
Understanding tables of values of linear relationships
Applications of linear relationships
TX.A1.2.B
Linear Functions, Equations, and Inequalities: Write linear equations in two variables in various forms, given one point and the slope and given two points
Slope intercept form: y = mx + b
Point-slope form: y - y_1 = m(x - x_1)
General form: Ax + By + C = 0
Graphing linear functions using a single point and slope
TX.A1.2.C
Linear Functions, Equations, and Inequalities: Write linear equations in two variables given a table of values, a graph, and a verbal description
Graphing from slope-intercept form y=mx+b
Graphing linear functions using x- and y-intercepts
Word problems of graphing linear functions
TX.A1.2.D
Linear Functions, Equations, and Inequalities: Write and solve equations involving direct variation
Introduction to linear equations
Direct variation
TX.A1.2.E
Linear Functions, Equations, and Inequalities: Write the equation of a line that contains a given point and is parallel to a given line
Parallel line equation
Parallel and perpendicular lines in linear functions
TX.A1.2.F
Linear Functions, Equations, and Inequalities: Write the equation of a line that contains a given point and is perpendicular to a given line
Perpendicular line equation
TX.A1.2.G
Linear Functions, Equations, and Inequalities: Write an equation of a line that is parallel or perpendicular to the X or Y axis and determine whether the slope of the line is zero or undefined
Combination of both parallel and perpendicular line equations
Special case of linear equations: Horizontal lines
Special case of linear equations: Vertical lines
TX.A1.2.H
Linear Functions, Equations, and Inequalities: Write linear inequalities in two variables given a table of values, a graph, and a verbal description
Express linear inequalities graphically and algebraically
TX.A1.2.I
Linear Functions, Equations, and Inequalities: Write systems of two linear equations given a table of values, a graph, and a verbal description
Determining number of solutions to linear equations
TX.A1.3.A
Linear Functions, Equations, and Inequalities: Determine the slope of a line given a table of values, a graph, two points on the line, and an equation written in various forms
Slope equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}m=x2​−x1​y2​−y1​​
TX.A1.3.B
Linear Functions, Equations, and Inequalities: Calculate the rate of change of a linear function represented tabularly, graphically, or algebraically in context of mathematical and real-world problems
Rate of change
Applications of linear relations
TX.A1.3.C
Linear Functions, Equations, and Inequalities: Graph linear functions on the coordinate plane and identify key features
Graphing linear functions using table of values
Understand relations between x- and y-intercepts
TX.A1.3.D
Linear Functions, Equations, and Inequalities: Graph the solution set of linear inequalities in two variables on the coordinate plane
Graphing systems of linear inequalities
Graphing linear inequalities in two variables
TX.A1.3.E
Linear Functions, Equations, and Inequalities: Determine the effects on the graph of the parent function f(x) = x when f(x) is replaced by af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d
Transformations of functions: Horizontal translations
Transformations of functions: Vertical translations
Reflection across the y-axis: y = f(-x)
Reflection across the x-axis: y = -f(x)
Transformations of functions: Horizontal stretches
Transformations of functions: Vertical stretches
TX.A1.3.F
Linear Functions, Equations, and Inequalities: Graph systems of two linear equations in two variables on the coordinate plane and determine the solutions if they exist
Solving systems of linear equations by graphing
TX.A1.3.G
Linear Functions, Equations, and Inequalities: Estimate graphically the solutions to systems of two linear equations with two variables in real-world problems
Solving systems of linear equations by elimination
TX.A1.3.H
Linear Functions, Equations, and Inequalities: Graph the solution set of systems of two linear inequalities in two variables on the coordinate plane
Graphing systems of quadratic inequalities
TX.A1.4.A
Linear Functions, Equations, and Inequalities: Calculate, using technology, the correlation coefficient between two quantitative variables and interpret this quantity as a measure of the strength of the linear association
Regression analysis
Bivariate, scatter plots and correlation
TX.A1.4.C
Linear Functions, Equations, and Inequalities: Write, with and without technology, linear functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems
Equation of the best fit line
TX.A1.5.A
Linear Functions, Equations, and Inequalities: Solve linear equations in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides
Solving linear equations using multiplication and division
Solving two-step linear equations: ax + b = c, x/a + b = c
Solving linear equations using distributive property: a(x + b) = c
Solving linear equations with variables on both sides
TX.A1.5.B
Linear Functions, Equations, and Inequalities: Solve linear inequalities in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides
Solving one-step linear inequalities
Solving multi-step linear inequalities
TX.A1.5.C
Linear Functions, Equations, and Inequalities: Solve systems of two linear equations with two variables for mathematical and real-world problems
Solving systems of linear equations by substitution
TX.A1.6.A
Quadratic Functions and Equations: Determine the domain and range of quadratic functions and represent the domain and range using inequalities
Characteristics of quadratic functions
TX.A1.6.B
Quadratic Functions and Equations: Write equations of quadratic functions given the vertex and another point on the graph, write the equation in vertex form (f(x) = a(x - h)^2 + k), and rewrite the equation from vertex form to standard form (f(x) = ax^2 + bx + c)
Quadratic function in general form: y = ax^2 + bx + c
Converting from general to vertex form by completing the square
Quadratic function in vertex form: y = a(x-p)^2 + q
TX.A1.6.C
Quadratic Functions and Equations: Write quadratic functions when given real solutions and graphs of their related equations
Finding the quadratic functions for given parabolas
TX.A1.7.A
Quadratic Functions and Equations: Graph quadratic functions on the coordinate plane and use the graph to identify key attributes
Graphing quadratic functions: General form VS. Vertex form
TX.A1.7.B
Quadratic Functions and Equations: Describe the relationship between the linear factors of quadratic expressions and the zeros of their associated quadratic functions
Nature of roots of quadratic equations: The discriminant
TX.A1.7.C
Quadratic Functions and Equations: Determine the effects on the graph of the parent function f(x) = x^2 when f(x) is replaced by af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d
Transformations of quadratic functions
TX.A1.8.A
Quadratic Functions and Equations: Solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula
Solving quadratic equations by factoring
Solving quadratic equations by completing the square
Using quadratic formula to solve quadratic equations
TX.A1.8.B
Quadratic Functions and Equations: Write, using technology, quadratic functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems
Applications of quadratic functions
TX.A1.9.A
Exponential Functions and Equations: Determine the domain and range of exponential functions of the form f(x) = ab^x and represent the domain and range using inequalities
Graphing exponential functions
TX.A1.9.B
Exponential Functions and Equations: Interpret the meaning of the values of a and b in exponential functions of the form f(x) = ab^x in real-world problems
Graphing transformations of exponential functions
TX.A1.9.C
Exponential Functions and Equations: Write exponential functions in the form f(x) = ab^x (where b is a rational number) to describe problems arising from mathematical and real-world situations
Finding an exponential function given its graph
Exponential growth and decay by percentage
TX.A1.9.D
Exponential Functions and Equations: Graph exponential functions that model growth and decay and identify key features
Exponential growth and decay by a factor
TX.A1.9.E
Exponential Functions and Equations: Write, using technology, exponential functions that provide a reasonable fit to data and make predictions for real-world problems
Finance: Compound interest
TX.A1.10.A
Number and Algebraic Methods: Add and subtract polynomials of degree one and degree two
Adding and subtracting polynomials
TX.A1.10.B
Number and Algebraic Methods: Multiply polynomials of degree one and degree two
Multiplying monomial by binomial
Multiplying binomial by binomial
Multiplying monomial by monomial
Multiplying polynomial by polynomial
TX.A1.10.C
Number and Algebraic Methods: Determine the quotient of a polynomial of degree one and polynomial of degree two when divided by a polynomial of degree one and polynomial of degree two when the degree of the divisor does not exceed the degree of the dividend
Polynomial long division
Polynomial synthetic division
TX.A1.10.D
Number and Algebraic Methods: Rewrite polynomial expressions of degree one and degree two in equivalent forms using the distributive property
Common factors of polynomials
Characteristics of polynomials
Equivalent expressions of polynomials
TX.A1.10.E
Number and Algebraic Methods: Factor, if possible, trinomials with real factors in the form ax^2 + bx + c, including perfect square trinomials of degree two
Factoring polynomials: ax^2 + bx + c
Factoring polynomials: x^2 + bx + c
Applications of polynomials: x^2 + bx + c
Solving polynomials with the unknown "b" from ax^2 + bx + c
Factoring perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2
TX.A1.10.F
Number and Algebraic Methods: Decide if a binomial can be written as the difference of two squares and, if possible, use the structure of a difference of two squares to rewrite the binomial
Find the difference of squares: (a - b)(a + b) = (a^2 - b^2)
TX.A1.11.A
Number and Algebraic Methods: Simplify numerical radical expressions involving square roots
Square and square roots
Operations with radicals
TX.A1.11.B
Number and Algebraic Methods: Simplify numeric and algebraic expressions using the laws of exponents, including integral and rational exponents
Combining the exponent rules
Quotient rule of exponents
Power of a product rule
Power of a quotient rule
Power of a power rule
Negative exponent rule
Scientific notation
Convert between radicals and rational exponents
Exponent rules
Product rule of exponents
TX.A1.12.A
Number and Algebraic Methods: Decide whether relations represented verbally, tabularly, graphically, and symbolically define a function
Identifying functions
TX.A1.12.B
Number and Algebraic Methods: Evaluate functions, expressed in function notation, given one or more elements in their domains
Function notation
TX.A1.12.C
Number and Algebraic Methods: Identify terms of arithmetic and geometric sequences when the sequences are given in function form using recursive processes
Arithmetic sequences
Geometric sequences
TX.A1.12.D
Number and Algebraic Methods: Write a formula for the nth term of arithmetic and geometric sequences, given the value of several of their terms
Arithmetic series
Geometric series
TX.A1.12.E
Number and Algebraic Methods: Solve mathematic and scientific formulas, and other literal equations, for a specified variable
Solving literal equations

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