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- When possible, students will apply mathematics to problems arising in everyday life, society, and the workplace. Students will use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a...
- Students will use mathematical relationships to generate solutions and make connections and predictions. Students will analyze mathematical relationships to connect and communicate mathematical ideas. Students will display, explain, or justify...
- The student applies the mathematical process standards when using graphs of linear functions, key features, and related transformations to represent in multiple ways and solve, with and without technology, equations, inequalities, and systems of equations. The student applies the mathematical process standards to formulate statistical relationships and evaluate their reasonableness based on real-world data. The student is expected to: A calculate, using technology, the correlation coefficient between two quantitative variables and interpret this quantity as a measure of the strength of the linear association; B compare and contrast association and causation in real-world problems; and C write, with and without technology, linear functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems.
- The student applies the mathematical process standards to solve, with and without technology, linear equations and evaluate the reasonableness of their solutions. The student is expected to: A 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; B 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; and C solve systems of two linear equations with two variables for mathematical and real-world problems. The student applies the mathematical process standards when using properties of quadratic functions to write and represent in multiple ways, with and without technology, quadratic equations. The student applies the mathematical process standards when using graphs of quadratic functions and their related transformations to represent in multiple ways and determine, with and without technology, the solutions to equations.
- The student applies the mathematical process standards to solve, with and without technology, quadratic equations and evaluate the reasonableness of their solutions. The student formulates statistical relationships and evaluates their reasonableness based on real-world data. The student is expected to: A solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula; and B write, using technology, quadratic functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems.
- The student applies the mathematical process standards when using properties of exponential functions and their related transformations to write, graph, and represent in multiple ways exponential equations and evaluate, with and without technology, the reasonableness of their solutions. The student applies the mathematical process standards and algebraic methods to rewrite in equivalent forms and perform operations on polynomial expressions. The student applies the mathematical process standards and algebraic methods to rewrite algebraic expressions into equivalent forms. The student is expected to: A simplify numerical radical expressions involving square roots; and B simplify numeric and algebraic expressions using the laws of exponents, including integral and rational exponents.
Pearson Texas Algebra 1 Student Text And Homework Helper Answers
The student applies the mathematical process standards and algebraic methods to write, solve, analyze, and evaluate equations, relations, and functions. The student is expected to: A decide whether relations represented verbally, tabularly, graphically, and symbolically define a function; B evaluate functions, expressed in function notation, given one or more elements in their domains; C identify terms of arithmetic and geometric sequences when the sequences are given in function form using recursive processes; D write a formula for the nth term of arithmetic and geometric sequences, given the value of several of their terms; and E solve mathematic and scientific formulas, and other literal equations, for a specified variable.- Students shall be awarded one-half to one credit for successful completion of this course. Prerequisite: Algebra I. Students will broaden their knowledge of quadratic functions, exponential functions, and systems of equations. Students will study logarithmic, square root, cubic, cube root, absolute value, rational functions, and their related equations.
- Students will connect functions to their inverses and associated equations and solutions in both mathematical and real-world situations. In addition, students will extend their knowledge of data analysis and numeric and algebraic methods. The student applies mathematical processes to understand that functions have distinct key attributes and understand the relationship between a function and its inverse. The student applies mathematical processes to formulate systems of equations and inequalities, use a variety of methods to solve, and analyze reasonableness of solutions. The student is expected to: A formulate systems of equations, including systems consisting of three linear equations in three variables and systems consisting of two equations, the first linear and the second quadratic; B solve systems of three linear equations in three variables by using Gaussian elimination, technology with matrices, and substitution; C solve, algebraically, systems of two equations in two variables consisting of a linear equation and a quadratic equation; D determine the reasonableness of solutions to systems of a linear equation and a quadratic equation in two variables; E formulate systems of at least two linear inequalities in two variables; F solve systems of two or more linear inequalities in two variables; and G determine possible solutions in the solution set of systems of two or more linear inequalities in two variables.
- The student applies mathematical processes to understand that quadratic and square root functions, equations, and quadratic inequalities can be used to model situations, solve problems, and make predictions. The student applies mathematical processes to understand that exponential and logarithmic functions can be used to model situations and solve problems. The student applies mathematical processes to understand that cubic, cube root, absolute value and rational functions, equations, and inequalities can be used to model situations, solve problems, and make predictions. The student applies mathematical processes to simplify and perform operations on expressions and to solve equations. The student is expected to: A add, subtract, and multiply complex numbers; B add, subtract, and multiply polynomials; C determine the quotient of a polynomial of degree three and of degree four when divided by a polynomial of degree one and of degree two; D determine the linear factors of a polynomial function of degree three and of degree four using algebraic methods; E determine linear and quadratic factors of a polynomial expression of degree three and of degree four, including factoring the sum and difference of two cubes and factoring by grouping; F determine the sum, difference, product, and quotient of rational expressions with integral exponents of degree one and of degree two; G rewrite radical expressions that contain variables to equivalent forms; H solve equations involving rational exponents; and I write the domain and range of a function in interval notation, inequalities, and set notation.
- The student applies mathematical processes to analyze data, select appropriate models, write corresponding functions, and make predictions. The student is expected to: A analyze data to select the appropriate model from among linear, quadratic, and exponential models; B use regression methods available through technology to write a linear function, a quadratic function, and an exponential function from a given set of data; and C predict and make decisions and critical judgments from a given set of data using linear, quadratic, and exponential models.
- Geometry, Adopted One Credit. Within the course, students will begin to focus on more precise terminology, symbolic representations, and the development of proofs. Students will explore concepts covering coordinate and transformational geometry; logical argument and constructions; proof and congruence; similarity, proof, and trigonometry; two- and three-dimensional figures; circles; and probability. Students will connect previous knowledge from Algebra I to Geometry through the coordinate and transformational geometry strand.
- In the logical arguments and constructions strand, students are expected to create formal constructions using a straight edge and compass. Though this course is primarily Euclidean geometry, students should complete the course with an understanding that non-Euclidean geometries exist. In proof and congruence, students will use deductive reasoning to justify, prove and apply theorems about geometric figures. Throughout the standards, the term "prove" means a formal proof to be shown in a paragraph, a flow chart, or two-column formats. Proportionality is the unifying component of the similarity, proof, and trigonometry strand.
- Students will use their proportional reasoning skills to prove and apply theorems and solve problems in this strand. The two- and three-dimensional figure strand focuses on the application of formulas in multi-step situations since students have developed background knowledge in two- and three-dimensional figures. Using patterns to identify geometric properties, students will apply theorems about circles to determine relationships between special segments and angles in circles. Due to the emphasis of probability and statistics in the college and career readiness standards, standards dealing with probability have been added to the geometry curriculum to ensure students have proper exposure to these topics before pursuing their post-secondary education. These standards are not meant to limit the methodologies used to convey this knowledge to students.
- Though the standards are written in a particular order, they are not necessarily meant to be taught in the given order. In the standards, the phrase "to solve problems" includes both contextual and non-contextual problems unless specifically stated. The student uses the process skills to understand the connections between algebra and geometry and uses the one- and two-dimensional coordinate systems to verify geometric conjectures.
- The student is expected to: A determine the coordinates of a point that is a given fractional distance less than one from one end of a line segment to the other in one- and two-dimensional coordinate systems, including finding the midpoint; B derive and use the distance, slope, and midpoint formulas to verify geometric relationships, including congruence of segments and parallelism or perpendicularity of pairs of lines; and C determine an equation of a line parallel or perpendicular to a given line that passes through a given point. The student uses the process skills to generate and describe rigid transformations translation, reflection, and rotation and non-rigid transformations dilations that preserve similarity and reductions and enlargements that do not preserve similarity.
- The student is expected to: A describe and perform transformations of figures in a plane using coordinate notation; B determine the image or pre-image of a given two-dimensional figure under a composition of rigid transformations, a composition of non-rigid transformations, and a composition of both, including dilations where the center can be any point in the plane; C identify the sequence of transformations that will carry a given pre-image onto an image on and off the coordinate plane; and D identify and distinguish between reflectional and rotational symmetry in a plane figure.
- The student uses the process skills with deductive reasoning to understand geometric relationships. The student is expected to: A distinguish between undefined terms, definitions, postulates, conjectures, and theorems; B identify and determine the validity of the converse, inverse, and contrapositive of a conditional statement and recognize the connection between a biconditional statement and a true conditional statement with a true converse; C verify that a conjecture is false using a counterexample; and D compare geometric relationships between Euclidean and spherical geometries, including parallel lines and the sum of the angles in a triangle.
- The student uses constructions to validate conjectures about geometric figures. The student is expected to: A investigate patterns to make conjectures about geometric relationships, including angles formed by parallel lines cut by a transversal, criteria required for triangle congruence, special segments of triangles, diagonals of quadrilaterals, interior and exterior angles of polygons, and special segments and angles of circles choosing from a variety of tools; B construct congruent segments, congruent angles, a segment bisector, an angle bisector, perpendicular lines, the perpendicular bisector of a line segment, and a line parallel to a given line through a point not on a line using a compass and a straightedge; C use the constructions of congruent segments, congruent angles, angle bisectors, and perpendicular bisectors to make conjectures about geometric relationships; and D verify the Triangle Inequality theorem using constructions and apply the theorem to solve problems.
- The student uses the process skills with deductive reasoning to prove and apply theorems by using a variety of methods such as coordinate, transformational, and axiomatic and formats such as two-column, paragraph, and flow chart. The student uses the process skills in applying similarity to solve problems. The student is expected to: A apply the definition of similarity in terms of a dilation to identify similar figures and their proportional sides and the congruent corresponding angles; and B apply the Angle-Angle criterion to verify similar triangles and apply the proportionality of the corresponding sides to solve problems. The student is expected to: A prove theorems about similar triangles, including the Triangle Proportionality theorem, and apply these theorems to solve problems; and B identify and apply the relationships that exist when an altitude is drawn to the hypotenuse of a right triangle, including the geometric mean, to solve problems.
- The student uses the process skills to understand and apply relationships in right triangles. The student uses the process skills to recognize characteristics and dimensional changes of two- and three-dimensional figures. The student is expected to: A identify the shapes of two-dimensional cross-sections of prisms, pyramids, cylinders, cones, and spheres and identify three-dimensional objects generated by rotations of two-dimensional shapes; and B determine and describe how changes in the linear dimensions of a shape affect its perimeter, area, surface area, or volume, including proportional and non-proportional dimensional change. The student uses the process skills in the application of formulas to determine measures of two- and three-dimensional figures. The student is expected to: A apply the formula for the area of regular polygons to solve problems using appropriate units of measure; B determine the area of composite two-dimensional figures comprised of a combination of triangles, parallelograms, trapezoids, kites, regular polygons, or sectors of circles to solve problems using appropriate units of measure; C apply the formulas for the total and lateral surface area of three-dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solve problems using appropriate units of measure; and D apply the formulas for the volume of three-dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solve problems using appropriate units of measure.
- The student uses the process skills to understand geometric relationships and apply theorems and equations about circles. The student uses the process skills to understand probability in real-world situations and how to apply independence and dependence of events. The student is expected to: A develop strategies to use permutations and combinations to solve contextual problems; B determine probabilities based on area to solve contextual problems; C identify whether two events are independent and compute the probability of the two events occurring together with or without replacement; D apply conditional probability in contextual problems; and E apply independence in contextual problems. The course approaches topics from a function point of view, where appropriate, and is designed to strengthen and enhance conceptual understanding and mathematical reasoning used when modeling and solving mathematical and real-world problems.
- Students systematically work with functions and their multiple representations. The study of Precalculus deepens students' mathematical understanding and fluency with algebra and trigonometry and extends their ability to make connections and apply concepts and procedures at higher levels. Students investigate and explore mathematical ideas, develop multiple strategies for analyzing complex situations, and use technology to build understanding, make connections between representations, and provide support in solving problems. The student uses process standards in mathematics to explore, describe, and analyze the attributes of functions. The student makes connections between multiple representations of functions and algebraically constructs new functions.
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