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TEKS Number STAARsort descending Student Expectation
2A(5)(B)

sketch graphs of conic sections to relate simple parameter changes in the equation to corresponding changes in the graph;

Resource ID Author Select Subject(s) Grade Title
A2M3L16 IPSI Mathematics 9–12

Using the Method of Completing the Square

Given a pictorial model or a quadratic equation or expression, students will use the method of completing the square to solve a problem, or will identify an appropriate next-step if they were to use the method of completing the square in order to solve a problem.

2A(5)(C)

identify symmetries from graphs of conic sections;

2A(5)(D)

identify the conic section from a given equation; and

2A(5)(E)

use the method of completing the square.

2A(6)(A)

determine the reasonable domain and range values of quadratic functions, as well as interpret and determine the reasonableness of solutions to quadratic equations and inequalities;

2A(6)(B)

relate representations of quadratic functions, such as algebraic, tabular, graphical, and verbal descriptions; and

2A(6)(C)

determine a quadratic function from its roots or a graph.

2A(7)(A)

use characteristics of the quadratic parent function to sketch the related graphs and connect between the y = ax² + bx + c and the y = a(x - h)² + k symbolic representations of quadratic functions; and

2A(7)(B)

use the parent function to investigate, describe, and predict the effects of changes in a, h, and k on the graphs of y = a(x - h)² + k form of a function in applied and purely mathematical situations.

2A(8)(A)

analyze situations involving quadratic functions and formulate quadratic equations or inequalities to solve problems;

2A(8)(B)

analyze and interpret the solutions of quadratic equations using discriminants and solve quadratic equations using the quadratic formula;

2A(8)(C)

compare and translate between algebraic and graphical solutions of quadratic equations; and

2A(8)(D)

solve quadratic equations and inequalities using graphs, tables, and algebraic methods.

2A(9)(A)

use the parent function to investigate, describe, and predict the effects of parameter changes on the graphs of square root functions and describe limitations on the domains and ranges;

Resource ID Author Select Subject(s) Grade Title
A2M3L3 IPSI Mathematics 9–12

Transformations of Square Root and Rational Functions

Given a square root function in the form f(x) = a√(x − h) + k, or a rational function in the form f(x) = a/(x − h) + k, the student will describe the effect of changes in a, h, and k using graphs, tables, and verbal descriptions as compared to the parent function.

2A(9)(B)

relate representations of square root functions, such as algebraic, tabular, graphical, and verbal descriptions;

Resource ID Author Select Subject(s) Grade Title
A2M6L2A IPSI Mathematics 9–12

Solving Square Root Equations Using Tables and Graphs

Given a square root equation, the student will solve the equation using tables or graphs - connecting the two methods of solution.

2A(9)(C)

determine the reasonable domain and range values of square root functions, as well as interpret and determine the reasonableness of solutions to square root equations and inequalities;

2A(9)(D)

determine solutions of square root equations using graphs, tables, and algebraic methods;

2A(9)(E)

determine solutions of square root inequalities using graphs and tables;

2A(9)(F)

analyze situations modeled by square root functions, formulate equations or inequalities, select a method, and solve problems; and

2A(9)(G)

connect inverses of square root functions with quadratic functions.

2A(10)(A)

use quotients of polynomials to describe the graphs of rational functions, predict the effects of parameter changes, describe limitations on the domains and ranges, and examine asymptotic behavior;

Resource ID Author Select Subject(s) Grade Title
A2M7L0 IPSI Mathematics 9–12

Rational Functions: Predicting the Effects of Parameter Changes

Given parameter changes for rational functions, students will be able to predict the resulting changes on important attributes of the function, including domain and range and asymptotic behavior.

2A(10)(B)

analyze various representations of rational functions with respect to problem situations;

2A(10)(C)

determine the reasonable domain and range values of rational functions, as well as interpret and determine the reasonableness of solutions to rational equations and inequalities;

2A(10)(D)

determine the solutions of rational equations using graphs, tables, and algebraic methods;

2A(10)(E)

determine solutions of rational inequalities using graphs and tables;

2A(10)(F)

analyze a situation modeled by a rational function, formulate an equation or inequality composed of a linear or quadratic function, and solve the problem; and

2A(10)(G)

use functions to model and make predictions in problem situations involving direct and inverse variation.

2A(11)(A)

develop the definition of logarithms by exploring and describing the relationship between exponential functions and their inverses;

2A(11)(B)

use the parent functions to investigate, describe, and predict the effects of parameter changes on the graphs of exponential and logarithmic functions, describe limitations on the domains and ranges, and examine asymptotic behavior;

2A(11)(C)

determine the reasonable domain and range values of exponential and logarithmic functions, as well as interpret and determine the reasonableness of solutions to exponential and logarithmic equations and inequalities;

2A(11)(D)

determine solutions of exponential and logarithmic equations using graphs, tables, and algebraic methods;

2A(11)(E)

determine solutions of exponential and logarithmic inequalities using graphs and tables; and

2A(11)(F)

analyze a situation modeled by an exponential function, formulate an equation or inequality, and solve the problem.

G(1)(A)

develop an awareness of the structure of a mathematical system, connecting definitions, postulates, logical reasoning, and theorems;

G(1)(B)

recognize the historical development of geometric systems and know mathematics is developed for a variety of purposes; and

G(1)(C)

compare and contrast the structures and implications of Euclidean and non-Euclidean geometries.

G(2)(A)

use constructions to explore attributes of geometric figures and to make conjectures about geometric relationships; and

G(2)(B)

make conjectures about angles, lines, polygons, circles, and three-dimensional figures and determine the validity of the conjectures, choosing from a variety of approaches such as coordinate, transformational, or axiomatic.

G(3)(A)

determine the validity of a conditional statement, its converse, inverse, and contrapositive;

G(3)(B)

construct and justify statements about geometric figures and their properties;

G(3)(C)

use logical reasoning to prove statements are true and find counter examples to disprove statements that are false;

Resource ID Author Select Subject(s) Grade Title
GM1L19 IPSI Mathematics 9–12

Using Logical Reasoning to Prove Conjectures about Circles

Given conjectures about circles, the student will use deductive reasoning and counter examples to prove or disprove the conjectures.

G(3)(D)

use inductive reasoning to formulate a conjecture; and

G(3)(E)

use deductive reasoning to prove a statement.

G(4)(A)

The student is expected to select an appropriate representation (concrete, pictorial, graphical, verbal, or symbolic) in order to solve problems.

G(5)(A)

use numeric and geometric patterns to develop algebraic expressions representing geometric properties;

G(5)(B)

use numeric and geometric patterns to make generalizations about geometric properties, including properties of polygons, ratios in similar figures and solids, and angle relationships in polygons and circles;

Resource ID Author Select Subject(s) Grade Title
GM2L3 IPSI Mathematics 9–12

Generalizing Geometric Properties of Ratios in Similar Figures

Given conjectures about circles, the student will use deductive reasoning and counterexamples to prove or disprove the conjectures.

G(5)(C)

use properties of transformations and their compositions to make connections between mathematics and the real world, such as tessellations; and

G(5)(D)

identify and apply patterns from right triangles to solve meaningful problems, including special right triangles (45-45-90 and 30-60-90) and triangles whose sides are Pythagorean triples.

G(6)(A)

describe and draw the intersection of a given plane with various three-dimensional geometric figures;

G(6)(B)

use nets to represent and construct three-dimensional geometric figures; and

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