# Texas Assessment of Math Knowledge and Skills-Answer Key

Refer to the  TAKS information Booklet  Mathematics Grades 8-11 for a more complete
description of the objectives measured.

Objective 1:The students will describe functional relationship in a variety of ways.

A(b)(1) Foundations for functions .The student understands that a function re presents a dependence
of one quantity on another and can be described in a variety of ways.

(A) The student describes independent and dependent quantities in functional relationships.

(B) The student [gathers and record data, or] uses data sets, to determine functional
(systematic) relationships between quantities.

(C) The student describes functional relationships for given problem situations and writes
equations or inequalities to answer questions arising from the situations.

(D) The student represents relationships among quantities using [concrete] models, tables,
graphs, diagrams, verbal descriptions, equations, and inequalities.

(E) The student interprets and makes inferences from functional relationships.

Objective 2:The students will demonstrate an understanding of the properties and attributes of
functions.

A(b)(2)Foundations for functions . The student uses the properties and attributes of functions.

(A) The student identifies [and sketches] the general forms of linear (y = x) and quadratic
(y = x2 ) parent functions.

(B) For a variety of situations, the student identifies the mathematical domains and ranges and
determines reasonable domain and range values for given situations.

(C) The student interprets situations in terms of given graphs [or creates situations that fit given
graphs].

(D) In solving problems, the student [collects and] organizes data, [makes and] interprets
scatterplots, and models, predicts, and makes decisions and critical judgments.

A(b)(3) Foundations for functions . The student understands how algebra can be used to express
generalizations and recognizes and uses the power of symbols to represent situations.

(A) The student uses symbols to represent unknowns and variables .

(B) Given situations, the student looks for patterns and represents generalizations algebraically.

A(b)(4) Foundations for functions . The student understands the importance of the skills required to
manipulate symbols in order to solve problems and uses the necessary algebraic skills required to
simplify algebraic expressions and solve equations and inequalities in problem situations.

(A) The student finds specific function values, simplifies polynomial expressions, transforms and
solves equations, and factors as necessary in problem situations.

(B) The student uses the commutative, associative, and distributive properties to simplify
algebraic expressions.

Objective 3:The student will demonstrate an understanding of linear functions .

A(c)(1) Linear functions. The student understands that linear functions can be represented in different
ways and translates among their various representations.

(A) The student determines whether or not given situations can be presented by linear functions.

(C) The student translates among and uses algebraic, tabular, graphical, or verbal descriptions
of linear functions.

A(c)(2)  Linear functions. The student understands the meaning of the slope and intercepts of linear
functions and interprets and describes the effects of changes in parameters of linear functions in
real-world and mathematical situations.

(A) The student develops the concepts of slope as a rate of change and determines slopes from
graphs, tables, and algebraic expressions.

(B) The student interprets the meaning of slope and intercepts in situations using data, symbolic
representations, or graphs.

(C) The student investigates, describes, and predicts the effects of changes in m and b on the
graph of y = mx + b.

(D) The student graphs and writes equations of lines given characteristics such as two points , a
point and a slope, or a slope and -intercept.

(E) The student determines the intercepts of linear functions from graphs, tables, and algebraic
representations.

(F) The student interprets and predicts the effects of changing slope and -intercept in applied
situations.

(G) The student relates direct variation to linear functions and solves problems involving
proportional change.

Objective 4: The student will formulate and use linear equations and inequalities.

A(c)(3)  Linear functions. The student formulates equations and inequalities based on linear functions,
uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.

(A) The student analyzes situations involving linear functions and formulates linear equations or
inequalities to solve problems.

(B) The student investigates methods for solving linear equations and inequalities using
[concrete] models, graphs, and the properties of equality, selects a method, and solves the
equations and inequalities.

(C) For given contexts, the student interprets and determines the reasonableness of solutions to
linear equations and inequalities.

A(c)(4)  Linear functions.  The student formulates systems of linear equations from problem situations,
uses a variety of methods to solve them, and analyzes the solutions in terms of the situation.

(A) The student analyzes situations and formulates systems of linear equations to solve
problems.

(B) The student solves systems of linear equations using [concrete] models, graphs, tables, and
algebraic methods.

(C) For given contexts, the student interprets and determines the reasonableness of solutions to
systems of linear equations.

Objective 5:

The student will demonstrate an understanding of quadratic and other nonlinear
functions.

A(d)(1) Quadratic and other nonlinear functions. The student understands that the graphs of
quadratic functions are affected by the parameters of the function and can interpret and describe
the effects of changes in the parameters of quadratic functions.

(B) The student investigates, describes, and predicts the effects of changes in on the graph
of y = ax2.

(C) The student investigates, describes, and predicts the effects of changes in on the graph
of y = x2 + c.

(D) For problem situations, the student analyzes graphs of quadratic functions and draws
conclusions.

A(d)(2) Quadratic and other nonlinear functions. The student understands there is more than one
way to solve a quadratic equation and solves them using appropriate methods.

(A) The student solves quadratic equations using [concrete] models, tables, graphs, and
algebraic methods.

(B) The student relates the solutions of quadratic equations to the roots of their functions .

A(d)(3) Quadratic and other nonlinear functions. The student understands there are situations
modeled by functions that are neither linear nor quadratic and models the situations.

(A) The student uses [patterns to generate] the laws of exponents and applies them in problemsolving
situations.

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