III e Grade11 Taksobj

8/3/2019 III e Grade11 Taksobj

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Grade 11 Exit Level TAKS Mathematics—Objective 1

Understanding functional relationships is critical for algebra and geometry. Students need tounderstand that functions represent pairs of numbers in which the value of one number is dependenton the value of the other. This basic idea has major significance in areas such as science, socialstudies, and economics. From their understanding of functions, students should be able tocommunicate information using models, tables, graphs, diagrams, verbal descriptions, and algebraicequations or inequalities. Making inferences and drawing conclusions from functional relationshipsare also important skills for students because these skills will allow students to understand howfunctions relate to real-life situations and how real-life situations relate to functions. Mastering theknowledge and skills in Objective 1 at eleventh grade will help students master the knowledge andskills in other TAKS objectives in eleventh grade.

Objective 1 groups together the basic ideas of functional relationships included within the TEKS.The concepts of patterns, relationships, and algebraic thinking found in the lower grades form thefoundation for Objective 1.

TAKS Objectives and TEKS Student Expectations

Objective 1

The student will describe functional relationships in a variety of ways.

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

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

(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 writesequations 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.

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Objective 1—For Your Information

For the eleventh-grade exit level test, students should be able to

work with linear and quadratic functions;

describe a functional relationship by selecting an equation or inequality that describes onevariable in terms of another variable given in the problem;

match a representation of a functional relationship with an interpretation of the results for agiven situation;

translate functional relationships among numerous forms; and

recognize linear equations in different forms, such as slope-intercept, standard, etc.

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1 For Saturday’s debate tournament, Sarahordered 3 cookies for each student participantand a tray of 30 cookies for the sponsors’hospitality room. This relationship can be

expressed by the function f ( s) = 3 s + 30, where s is the number of student participants. Whichis the dependent quantity in this functionalrelationship?

A* The number of cookies ordered

B The number of trays ordered

C The number of student participants

D The number of sponsors

Students should be able to identify ordescribe the dependent and independentquantities.

Objective 1 Sample Items

2 Mr. Henry decided to invest money earnedfrom selling some land. He invested $5000 of the money at an annual rate of 4% and therest of the money, x, at an annual rate of

6.25%. Which equation describes y, the totalamount of interest earned from bothinvestments during the first year?

A* y = 0.04(5000) + 0.0625 x

B y = 4(5000) + 6.25 x

C y = (5000 + x)(0.04 + 0.0625)

D y = (5000 + x)(4 + 6.25)



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3 Which graph best represents the inequality − x + y ≥ 3?

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Understanding the properties and attributes of functions is critical for algebra and geometry.Recognizing the similarities and differences between linear and quadratic functions is useful whenevaluating and analyzing statistical data. The ability to work with and solve algebraic equations isuseful for creating effective personal and business budgets that include shopping, fuel efficiency, car payments, etc. Mastering the knowledge and skills in Objective 2 at eleventh grade will help studentsmaster the knowledge and skills in other TAKS objectives in eleventh grade.

Objective 2 groups together the properties and attributes of functions found within the TEKS. Theconcepts of patterns, relationships, and algebraic thinking found in the lower grades form thefoundation for Objective 2.


Objective 2

The student 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 = x 2) 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] interpretsscatterplots, and models, predicts, and makes decisions and critical judgments.

A(b)(3) Foundations for functions. The student understands how algebra can be used to expressgeneralizations 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 generalizationsalgebraically.

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

(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.



work with linear and quadratic functions;

identify a valid decision or judgment based on a given set of data;

write an expression or equation describing a pattern; and

recognize linear equations in numerous forms, such as slope-intercept, standard, etc.

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1 Which best describes the range represented inthe graph?

A −3 ≤ y ≤ 3

B −3 ≤ x ≤ 3

C x ≤ 2

D* y ≤ 2

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2 The pattern of dots shown below continuesinfinitely, with more dots being added at eachstep.

Which expression can be used to determinethe number of dots in the nth step?

A 2n

B n(n + 2)

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3 What is the area of the shaded region of therectangle, reduced to simplest terms?

A 8 x 2 + 25 x

B 6 x 2 + 24 x

C* 4 x 2 + 23 x

D 2 x 2 + x

x + 4

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6 x





Understanding linear functions is critical for algebra and geometry. Students should understand thatlinear functions are pairs of numbers that can be represented by the graph of a line. Linear functionsare an integral part of science, geography, and economics. The concept of rate of change between data points is used in everyday situations such as calculating taxicab or telephone-billing rates. Masteringthe knowledge and skills in Objective 3 at eleventh grade will help students master the knowledgeand skills in other TAKS objectives in eleventh grade.

Objective 3 groups together concepts of linear functions found within the TEKS. The concepts of patterns, relationships, and algebraic thinking found in the lower grades form the foundation for Objective 3.


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 indifferent 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 verbaldescriptions 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 functionsin real-world and mathematical situations.

(A) The student develops the concepts of slope as a rate of change and determines slopesfrom 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 onthe 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 y-intercept.

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

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

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



translate linear relationships among various forms;

recognize linear equations in numerous forms, such as slope-intercept, standard, etc.;

work with both x- and y-intercepts; and

solve problems involving linear functions and proportional change, with or without the keywords “varies directly” in the item.

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1 Two lines are shown on the grid. The two linespass through (−4, 6). One line passes throughthe origin, and the other passes through thepoint (5, −3).

Which pair of equations below identifies theselines?

A y = − x + 2 and y = x −

B y = x and y = x − 2

C y = − x and y = − x

D* y = − x + 2 and y = − x32

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2 The amount of garbage produced in theUnited States varies directly with the numberof people who produce it. It is estimated thaton average 200 people produce 50 tons of

garbage annually. Approximately how manytons of garbage are produced each year by100,000 people?

A 800 tons

B* 25,000 tons

C 125,000 tons

D 400,000 tons

3 The cost of a long-distance telephone call is afunction of the length of the call. The cost of 4calls is shown in the table.

If the data are graphed with minutes on thehorizontal axis and cost on the vertical axis,what does the slope represent?

A* A rate of $0.12 per minute

B The total cost per call

C An average time of 8 minutes per call

D A total time of 10 minutes between calls

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Minutes Cost

5 $0.60

15 $1.80

25 $3.00

60 $7.20





Understanding how to formulate and use linear equations and inequalities is critical for algebraand geometry. The ability to organize contextual problems into equations and inequalities or systemsof equations and inequalities allows students to find and evaluate reasonable solutions in dailysituations. For example, as students become more knowledgeable consumers, they may want to use asystem of equations to determine which car-insurance company offers a better rate. Mastering theknowledge and skills in Objective 4 at eleventh grade will help students master the knowledge andskills in other TAKS objectives in eleventh grade.

Objective 4 groups together the ideas of how to formulate and use linear equations and

inequalities found within the TEKS. The concepts of patterns, relationships, and algebraic

thinking found in the lower grades form the foundation for Objective 4.


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 thesituation.

(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 solvesthe 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 problemsituations, 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.

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recognize linear equations in numerous forms, such as slope-intercept, standard, etc.;

select an equation or inequality that can be used to find the solution;

find a solution expressed as a number or a range of numbers; and

look at solutions in terms of a given context and determine whether the solution is reasonable.

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1 Mrs. Olsen rented a car on Monday at the rateof $29 per day plus $0.15 per mile driven. Herbill for Monday was $44 for rental andmileage charges. Mrs. Olsen rented a car on

Wednesday at the same rate and drove exactly3 times as many miles as she drove onMonday. What was the amount of her billWednesday for rental and mileage charges?

Record your answer and fill in the bubbles onyour answer document. Be sure to use thecorrect place value.

This item asks for a dollar amount. Ongriddable items, students do not grid thedollar sign ($). It is acceptable, although

not necessary, to bubble in the zeros infront of the seven and/or after thedecimal. These zeros will not affect thevalue of the correct answer.

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2 The equations of two lines are

4 x − 5 y = −15 and y = x − 6

Which of the following describes their point of intersection?

A (5, −2)

B (−5, 1)

C (10, −5)

D* No intersection

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3 Some students read a magazine article thatsaid a person’s height is a function of thelength of the person’s foot. The students usedthe equation h = 8 f − 7 to represent the

function, with h for height and f for footlength. The students recorded their heightsand foot lengths in a table.

Which is a valid statement about the accuracyof this equation for this set of data?

A* It gives a reasonably accurate measureonly for Joanne.

B It does not give a reasonably accuratemeasure for any of the 4 students.

C It gives an exact measure for at least 1 of these students.

D It gives a reasonably accurate measure foreveryone except Mark.

Foot Length(inches)

StudentHeight

(inches)

Mark 10 6712

Tyson 101

268

Joanne 9 6514

Melinda 734

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Understanding quadratic and other nonlinear functions is critical for algebra and geometry.Students should understand that quadratic functions can be represented by the graph of a parabola.Graphs of quadratic functions can be used to represent data, such as population growths in biology, projectile movements in physics, and compound interest rates in economics. In these and other examples, students should understand how changes in the functional situation affect the graph of the parabola. Understanding the correct use of exponents is essential in scientific fields, such asmedicine, astronomy, and microbiology. Mastering the knowledge and skills in Objective 5 ateleventh grade will help students master the knowledge and skills in other TAKS objectives ineleventh grade.

Objective 5 groups together the concepts of quadratic and other nonlinear functions found withinthe TEKS. The concepts of patterns, relationships, and algebraic thinking found in the lower grades form the foundation for Objective 5.


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 anddescribe the effects of changes in the parameters of quadratic functions.

(B) The student investigates, describes, and predicts the effects of changes in a on thegraph of y = ax 2.

(C) The student investigates, describes, and predicts the effects of changes in c on thegraph of y = x 2 + c.

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

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, andalgebraic methods.

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

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A(d)(3) Quadratic and other nonlinear functions. The student understands there are situationsmodeled 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 problem-solving situations.



recognize how the graph of the parabola is modified when the quadratic equation changes; and

determine reasonable solutions to quadratic equations based on the given context of the problem.

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1 What is the effect on the graph of the equation y = 2 x 2 when the equation is changed to y = −2 x 2?

A The x values for any given y are fartherfrom the y-axis.

B* The graph of y = − 2 x 2 is a reflection of y = 2 x 2 across the x-axis.

C The graph is rotated 90° about the origin.

D The x values for any given y are closer tothe y-axis.

3 A ball that was hit had an initial upwardvelocity of 96 feet per second. The functionthat describes the position of the ball at anytime after it was hit is h = 96t − 16t 2, where

t is the time in seconds and h is the height infeet. The graph of this function is shownbelow.

Which is the best conclusion about the ball’saction?

A The ball traveled more than 300 feet inless than 6 seconds.

B* The ball reached its maximum height inabout 3 seconds.

C The ball returned to the ground in lessthan 5 seconds.

D The ball traveled more slowly as itapproached the ground.

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2 A rocket was shot upward with an initialvelocity of 144 feet per second. The height of the rocket is a function of t, the time inseconds since the rocket left the ground. Theheight can be expressed by the equationh(t) = 144t − 16t 2. How many seconds will ittake for the rocket to return to the ground?

A 4.5 sec

B 6.5 sec

C 8.0 sec

D* 9.0 sec




Understanding geometric relationships and spatial reasoning is important because the structure of the world is based on geometric properties. The concepts covered in this objective are an integral partof many fields, such as physics, navigation, geography, and construction. These concepts buildspatial-reasoning skills that help develop an understanding of distance, location, and area. Theknowledge and skills contained in Objective 6 will allow students to understand how the basicconcepts of geometry are related to the real world. Mastering the knowledge and skills in Objective 6at eleventh grade will help students master the knowledge and skills in other TAKS objectives ineleventh grade.

Objective 6 groups together the fundamental concepts of geometric relationships and spatial

reasoning found within the TEKS. The concepts of geometry and spatial reasoning found in thelower grades form the foundation for Objective 6.


Objective 6

The student will demonstrate an understanding of geometric relationships and spatial

reasoning.

G(b)(4) Geometric structure. The student uses a variety of representations to describe geometricrelationships and solve problems.

(A) The student selects an appropriate representation ([concrete,] pictorial, graphical,verbal, or symbolic) in order to solve problems.

G(c)(1) Geometric patterns. The student identifies, analyzes, and describes patterns that emergefrom two- and three-dimensional geometric figures.

(A) The student uses numeric and geometric patterns to make generalizations aboutgeometric properties, including properties of polygons, ratios in similar figures andsolids, and angle relationships in polygons and circles.

(B) The student uses the properties of transformations and their compositions to make

connections between mathematics and the real world in applications such astessellations or fractals.

(C) The student identifies and applies patterns from right triangles to solve problems,including special right triangles (45-45-90 and 30-60-90) and triangles whose sides arePythagorean triples.

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G(e)(3) Congruence and the geometry of size. The student applies the concept of congruence to justify properties of figures and solve problems.

(A) The student uses congruence transformations to make conjectures and justify properties of geometric figures.



identify and use formal geometric terms; and

use geometric concepts, properties, theorems, and definitions to solve problems.

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30

1 Charlotte designed a floor pattern for her newgame room. She used only translations of thefollowing tile to produce the pattern.

Which pattern did Charlotte produce?

A

B*

C

D

2 The cable cars of a ski lift rise 5,000 verticalfeet from the base at a constant 30° angle of inclination.

What is the approximate straight-linedistance that a cable car travels from the baseto the summit of the mountain?

A 2,500 ft

B 2,900 ft

C 8,500 ft

D* 10,000 ft

30°

5,000 ft,000 ft5,000 ft

Summit




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3 ∆WXY is graphed on the coordinate grid below.

Which set of coordinates represents the vertices of a triangle congruent to ∆WXY ?

A (2, 6), (2, 12), (7, 11)

B* (2, 6), (2, 13), (7, 12)

C (3, 8), (3, 13), (8, 12)

D (3, 8), (3, 14), (8, 11)

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Understanding two- and three-dimensional representations of geometric relationships and

shapes is important because the structure of the world is based on geometric properties. The conceptscovered in this objective are an integral part of many fields, such as molecular chemistry, aviation, pattern design, etc. These concepts build spatial-reasoning skills that help develop an understandingof distance, location, area, and space. The knowledge and skills contained in Objective 7 will allowstudents to understand how the basic concepts of geometry are related to the real world. Masteringthe knowledge and skills in Objective 7 at eleventh grade will help students master the knowledgeand skills in other TAKS objectives in eleventh grade.

Objective 7 groups together the fundamental concepts of two- and three-dimensional shapes foundwithin the TEKS. The concepts of geometry and spatial reasoning found in the lower grades formthe foundation for Objective 7.


Objective 7

The student will demonstrate an understanding of two- and three-dimensional representations

of geometric relationships and shapes.

G(d)(1) Dimensionality and the geometry of location. The student analyzes the relationship between three-dimensional objects and related two-dimensional representations and usesthese representations to solve problems.

(B) The student uses nets to represent [and construct] three-dimensional objects.

(C) The student uses top, front, side, and corner views of three-dimensional objects tocreate accurate and complete representations and solve problems.

G(d)(2) Dimensionality and the geometry of location. The student understands that coordinatesystems provide convenient and efficient ways of representing geometric figures and usesthem accordingly.

(A) The student uses one- and two-dimensional coordinate systems to represent points,

lines, line segments, and figures.

(B) The student uses slopes and equations of lines to investigate geometric relationships,including parallel lines, perpendicular lines, and [special segments of] triangles andother polygons.

(C) The student [develops and] uses formulas including distance and midpoint.

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G(e)(2) Congruence and the geometry of size. The student analyzes properties and describesrelationships in geometric figures.

(D) The student analyzes the characteristics of three-dimensional figures and their component parts.



identify and use formal geometric terms;

use geometric concepts, properties, theorems, and definitions to solve problems; and

match a two-dimensional representation of a solid with a three-dimensional representation of thesame solid or vice versa.

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1 The top, side, and front views of an object built with cubes are shown below.

How many cubes are needed to construct this object?

A 7

B* 10

C 13

D 17

Top view Side view Front view


2 Two perpendicular lines with the equations

y = x + 5 and y = mx − 3 contain consecutive

sides of a rectangle. What is the value of m in

the second linear equation?

A

B

C −

D* −73

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3 A diameter of a circle has endpoints P (−5, − 4) and Q (−1, 2). Find the

approximate length of the radius.

A 2.2 units

B* 3.6 units

C 4.5 units

D 7.2 units




Understanding the concepts and uses of measurement and similarity has many real-worldapplications and provides a basis for developing skills in geometry. These skills are important in real-world applications and in other academic disciplines. The concept of surface area is essential ineveryday tasks such as laying carpet, upholstering furniture, painting houses, etc. Businesses involvedwith packing and shipping find the effect of changes in area, perimeter, and volume critical in their work. Understanding the basic concepts included in Objective 8 will prepare students to applymeasurement skills in various situations. Mastering the knowledge and skills found in Objective 8 ateleventh grade will help students master the knowledge and skills found in other TAKS objectives ineleventh grade.

Objective 8 groups together the concepts and uses of measurement and similarity found within theTEKS. The concepts and uses of measurement found in the lower grades form the foundation for Objective 8.


Objective 8

The student will demonstrate an understanding of the concepts and uses of measurement and

similarity.

G(e)(1) Congruence and the geometry of size. The student extends measurement concepts to findarea, perimeter, and volume in problem situations.

(A) The student finds area of polygons and composite figures.

(B) The student finds areas of sectors and arc lengths of circles using proportionalreasoning.

(C) The student [develops, extends and] uses the Pythagorean Theorem.

(D) The student finds surface area and volumes of prisms, pyramids, spheres, cones, andcylinders in problem situations.

G(f)(1) Similarity and the geometry of shape. The student applies the concepts of similarity to

justify properties of figures and solve problems.

(A) The student uses similarity properties and transformations to [explore and] justifyconjectures about geometric figures.

(B) The student uses ratios to solve problems involving similar figures.

(C) In a variety of ways, the student [develops,] applies, and justifies triangle similarityrelationships, such as right triangle ratios, [trigonometric ratios,] and Pythagoreantriples.

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(D) The student describes the effect on perimeter, area, and volume when length, width, or height of a three-dimensional solid is changed and applies this idea in solving problems.



identify and use formal geometric terms;

describe, in the form of a verbal expression or mathematical solution, the effect on perimeter,area, and volume when any measurement of a three-dimensional solid is changed (for example,if the sides of a rectangle are doubled in length, then the perimeter is doubled, and the area isfour times the original area; if the edges of a cube are doubled in length, the volume is eighttimes the original volume); and

use geometric concepts, properties, theorems, formulas, and definitions to solve problems.

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1 When viewed from above, a metal spiral staircase appears to be a circle, and each step appears to be asector.

The staircase has a diameter of 5 feet 6 inches. A total of 16 steps can be used to form the circle. If thearea of the center pole is ignored, what is the approximate area of the top surface of each step?

A 177 in. 2

B 207 in. 2

C* 214 in. 2

D 272 in. 2

Top view Side view




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2 A net for a right cone is shown below.

Use the ruler on the Measurement Chart to measure the dimensions of the cone to the nearest tenth of a centimeter. Find the total surface area of the cone to the nearest square centimeter.

A 27 cm 2

B 35 cm 2

C* 45 cm 2

D 80 cm 2

This item specifically instructs students to measure the dimensions of the cone to thenearest tenth of a centimeter. Students need to use the correct ruler on the Mathematics

Chart based on the unit of measure in the problem.



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3 The radius of the larger sphere shown below was multiplied by a factor of to produce the smaller

sphere.

How does the surface area of the smaller sphere compare to the surface area of the larger sphere?

A The surface area of the smaller sphere is as large.

B The surface area of the smaller sphere is as large.

C* The surface area of the smaller sphere is as large.

D The surface area of the smaller sphere is as large.

Students should recognize that the scale factor is . Therefore, the change in area is

( )2

, or .14

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1π

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Radius = r Radius = r 1–2




Understanding percents, proportional relationships, probability, and statistics will help students become informed consumers of data and information. Percent calculations are important in retail, realestate, banking, taxation, etc. As students become more skilled in describing and predicting the resultsof a probability experiment, they should begin to recognize and account for all the possibilities of agiven situation. Students should be able to compare different graphical representations of the samedata and solve problems by analyzing the data presented. Students must be able to recognizeappropriate and accurate representations of data in everyday situations and in information related toscience and social studies (for example, in polls and election results). The knowledge and skillscontained in Objective 9 are essential for processing everyday information. Mastering the knowledgeand skills in Objective 9 at eleventh grade will help students master the knowledge and skills in other TAKS objectives in eleventh grade.

Objective 9 groups together the concepts of percents, proportional relationships, probability, and

statistics found within the TEKS. The probability and statistics found in the lower grades form the

foundation for Objective 9.


Objective 9

The student will demonstrate an understanding of percents, proportional relationships,

probability, and statistics in application problems.

(8.3) Patterns, relationships, and algebraic thinking. The student identifies proportionalrelationships in problem situations and solves problems. The student is expected to

(B) estimate and find solutions to application problems involving percents and proportional relationships such as similarity and rates.

(8.11) Probability and statistics. The student applies the concepts of theoretical and experimental probability to make predictions. The student is expected to

(A) find the probabilities of compound events (dependent and independent); and

(B) use theoretical probabilities and experimental results to make predictions anddecisions.

(8.12) Probability and statistics. The student uses statistical procedures to describe data. Thestudent is expected to

(A) select the appropriate measure of central tendency to describe a set of data for a particular purpose; and

(C) construct circle graphs, bar graphs, and histograms, with and without technology.

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(8.13) Probability and statistics. The student evaluates predictions and conclusions based onstatistical data. The student is expected to

(B) recognize misuses of graphical or numerical information and evaluate predictions andconclusions based on data analysis.



choose a proportion that can be used to solve a problem situation or solve a problem situation byusing a proportion;

understand and distinguish between theoretical probability and experimental results;

understand and distinguish between mean, median, mode, and range to determine which is mostappropriate for a particular purpose;

match a given set of data in the form of a verbal description, chart, tally, graph, etc., with itscircle graph, bar graph, or histogram or vice versa; and

interpret a set of data and match it to a statement describing a prediction or conclusion.

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42

1 Richard bought a jacket priced at $29.70. Thetotal cost of the jacket, including sales tax,was $32.15. What was the sales tax rate to thenearest hundredth of a percent?

A 2.45%

B 7.62%

C* 8.25%

D 12.12%

2 The table below shows high-temperaturereadings for a January day in various Texascities.

Which measure of the data would be leastaffected if the 53°F reading in Galveston hadbeen 50°F?

A Mean

B* Median

C Mode

D Range

City High Temperature

Austin 46°F

Dallas 34°F

El Paso 45°F

Galveston 53°F

Houston 50°F

San Antonio 49°F





Knowledge and understanding of underlying processes and mathematical tools are critical for students to be able to apply mathematics in their everyday lives. Problems that occur in the real worldoften require the use of multiple concepts and skills. Students should be able to recognizemathematics as it occurs in real-life situations, generalize from mathematical patterns and sets of examples, select an appropriate approach to solving a problem, solve the problem, and then determinewhether the answer is reasonable. Expressing these problem situations in mathematical language andsymbols is essential to finding solutions to real-life problems. These concepts allow students tocommunicate clearly and use logical reasoning to make sense of their world. Students can thenconnect the concepts they have learned in mathematics to other disciplines and to higher mathematics. Through an understanding of the basic ideas found in Objective 10, students will beable to analyze and solve real-world problems. Mastering the knowledge and skills in Objective 10 ateleventh grade will help students master the knowledge and skills in other TAKS objectives ineleventh grade.

Objective 10 groups together the underlying processes and mathematical tools within the TEKSthat are used in finding mathematical solutions to real-world problems. The underlying processes

and mathematical tools found in the lower grades form the foundation for Objective 10.


Objective 10

The student will demonstrate an understanding of the mathematical processes and tools used in

problem solving.

(8.14) Underlying processes and mathematical tools. The student applies Grade 8 mathematics tosolve problems connected to everyday experiences, investigations in other disciplines, andactivities in and outside of school. The student is expected to

(A) identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics;

(B) use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness; and

(C) select or develop an appropriate problem-solving strategy from a variety of differenttypes, including drawing a picture, looking for a pattern, systematic guessing andchecking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem.

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(8.15) Underlying processes and mathematical tools. The student communicates about Grade 8mathematics through informal and mathematical language, representations, and models. Thestudent is expected to

(A) communicate mathematical ideas using language, efficient tools, appropriate units, andgraphical, numerical, physical, or algebraic mathematical models.

(8.16) Underlying processes and mathematical tools. The student uses logical reasoning to makeconjectures and verify conclusions. The student is expected to

(A) make conjectures from patterns or sets of examples and nonexamples; and

(B) validate his/her conclusions using mathematical properties and relationships.



identify the question that is being asked or answered;

identify the information that is needed to solve a problem;

select or describe the next step or a missing step that would be most appropriate in a problem-solving situation;

choose the correct supporting information for a given conclusion;

select the description of a mathematical situation when provided a written or pictorial prompt;

match informal language to mathematical language and/or symbols; and

draw a conclusion by investigating patterns and/or sets of examples and nonexamples, which can be defined as counterexamples.

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45

1 Rectangle R represents 250 students in eleventh grade at a school. Circle P represents the 200 studentswho went to a school pep rally. Circle G represents the 180 students who went to the big game. A totalof 140 students went to both the pep rally and the big game.

Which table correctly shows the number of students who went only to the pep rally, went only to the biggame, or went to neither?

A* C

B DPep rally only

Big game only

Neither

Event Number of Students

70

50

50

Pep rally only

Big game only

Neither


50

70

50

Pep rally onlyBig game only

Neither


4060

10

Pep rally only

Big game only

Neither


60

40

10

140P G

R




2 The circle graph most accurately representswhich of the situations below?

A In the election for class president, Sarahreceived 40% of the votes, Eddie received25%, Carol received 15%, and Matthewreceived 20%.

B During a special sale at Calvert AutoMart, Edward sold 30% of the cars sold,Janet sold 5%, Edith sold 40%, and Mitchsold 25%.

C Mr. and Mrs. Johnson spent 30% of theirincome on housing, 25% on utilities, 35%on food, and 10% on miscellaneous

expenses.D* In a recent survey about favorite pets,

45% of those surveyed chose dogs, 35%chose cats, 5% chose horses, and 15%chose other animals.

III e Grade11 Taksobj

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