Sell put options graph 3x2y 6



Fill-in response items may ask students to complete an inequality that satisfies a domain or a range. Monomials may have no more than three variables. The direction of the rotation is usually expressed as clockwise or counterclockwise. An integral equation is said to be singular when either one or both. A geometric progression is a succession of terms such that each.




The copyright notice at the bottom of this page must be included in all copies. All trademarks and trade names found in this publication are the property of their respective owners and are not associated with the publishers of this publication. Questions regarding use of these copyrighted materials should be sent to the following: The Administrator Benchmarks Assessed on Algebra 1 End-of-Course Assessment and Geometry End-of-Course Assessment Individual Benchmark Specifications for Algebra 1 End-of-Course Assessment Appendix A: FCAT 2.

First, inoutside consultants ssll the Standards and suggested that the benchmark language offer greater specificity to indicate clearly what teachers should teach and what students should be able to do. Second, federal legislation through the No Child Left Behind Act of NCLB holds schools and school sel accountable for how well each child is learning, which further emphasized the need to hone expectations for all students. The NGSSS are subdivided into benchmarks that identify what a student should know and be able to sfll.

This document, Algebra 1 End-of-Course Assessment Test Item Specifications Specificationsprovides information about the benchmarks, the stimulus types, and the test items. End-of-course EOC assessments measure achievement of Florida students who have completed coursework in Algebra 1, Biology 1, Civics, Geometry, and U. The Algebra 1 EOC Assessment measures achievement of Florida students enrolled in Algebra 1, or an equivalent course, by assessing student progress on benchmarks from gralh NGSSS opfions are assigned optioons Algebra 1 course descriptions.

The Florida Department of Education and committees of experienced Florida educators developed and approved the Specifications. The Specifications is a resource document that defines the content and format of the test and test items for item writers and reviewers. Each Specifications document indicates the alignment of items with the NGSSS. It also serves to provide all stakeholders with information about the scope and function of the FCAT 2.

The Specifications for the Algebra 1 EOC Assessment provides general guidelines for the development of all test items used in the Algebra 1 EOC Assessment. Three additional Specifications documents provide the same information for FCAT 2. The Overall Considerations section in yraph Introduction provides an explanation of the mathematics elements assessed by the test.

The Pkt for Algebra 1 End-of-Course Assessment Items section addresses the quality of the stimuli and test items and selection and development of multiple-choice and fill-in response items. The Item Difficulty and Cognitive Complexity section addresses cognitive-complexity levels as well as item difficulty and universal design. The Individual Benchmark Specifications rgaph contains specific grah about each benchmark.

This section provides benchmark clarification statements, content limits, stimulus attributes, response attributes, and a sample item for each benchmark grouping. Sepl section of the Specifications describes the otpions that apply to all test items developed for the Algebra 1 EOC Assessment. Overall considerations are broad item-development issues that should be addressed during the development of test items.

Other sections relate more specifically to one aspect of the development e. Each test item should be written to measure primarily one benchmark; however, other benchmarks may also be reflected in the item content. When benchmarks slel combined for assessment, the individual specification indicates which benchmarks are combined. Test items sepl be course appropriate for students in terms of difficulty, cognitive development, and reading level.

Test items will exhibit a varied range of difficulty. Test items should not disadvantage or exhibit disrespect to anyone in regard to age, gender, race, ethnicity, language, religion, socioeconomic status, disability, or geographic region. For the Algebra 1 End-of-Course Assessment, a four-function calculator will be allowed. For the Geometry End-of-Course Assessment, a scientific calculator will be allowed. Test items may require the student to apply mathematical knowledge described in NGSSS benchmarks from lower grades; however, the benchmarks from lower grades will not be assessed in isolation.

Test items graoh provide clear and complete instructions to students. Each test item should be written clearly and unambiguously to elicit the desired response. A reference sheet containing appropriate formulas and conversions is provided to students taking the Algebra 1 EOC Assessment and the Geometry EOC Assessment during testing. Copies of the reference sheets are included in Appendix G of this document. Test items on the EOC assessments should be written so that students are expected to select or provide the most accurate answer possible.

In most cases, front-end estimation and truncation are not accurate processes for estimation. The Algebra 1 EOC Assessment includes two types of sel items: multiple-choice grsph MC and fill-in response items FR. That is, some graphics contain information married options trading hours is necessary for answering the question, while other graphics illustrate or support the context of the question.

All artwork must be high quality. Most of the individual benchmark specifications sell put options graph 3x2y 6 the Specifications indicate the extent sell put options graph 3x2y 6 which graphics should be used swll support test items developed for the benchmark. When no reference is made to the use of graphics, graphics are not required, although they grapy be used. This section presents stylistic guidelines and formatting directions that should be followed while developing test items.

Guidelines are provided separately for each item type to be developed. Items should be clear and concise, and they should use vocabulary and sentence structure appropriate for the assessed grade level. The final sentence of any Slel or FR item stem must be expressed as a question. If an item or oltions asks a question involving the word not, the word not should be emphasized by all uppercase letters e. For MC and FR items that refer to an estimate nounlowercase letters should be used.

As appropriate, boldface type o;tions be used to emphasize key words in the test item question e. Masculine pronouns should NOT be used to refer to both sexes. Plural forms should be used whenever possible to avoid gender-specific pronouns e. An equal balance of male and sell put options graph 3x2y 6 names should be used, including names 8. For clarity, operation symbols, equality signs, and ordinates should be preceded and followed by one space.

Decimal numbers between -1 and 1 including currency should have a leading Metric numbers should be expressed in a single unit when possible e. Decimal notation should be used for numbers with metric units e. The comma should be used in a number greater than or equal to 1, when the number is given in the context of the problem. Currency forex learn online trading currency exchange 21 first news a number greater than or equal to 1, is presented in an equation or an algebraic expression, no comma should be used.

Metric numbers with four digits should be presented without a comma or a space e. For metric numbers with more than four digits, a thin space should be inserted optionns place of a comma e. Units of measure should be spelled out, except in graphics where an abbreviation may be used e. Abbreviations that also spell a word must be punctuated to avoid confusion. For example, to avoid confusion with the preposition in, the abbreviation in. If an abbreviation is used in a graphic, an explanation of the meaning optoons the abbreviation should be included in the stem.

In sell put options graph 3x2y 6 for tables and charts and in labels for axes, the units of measure should be included, preferably in lowercase and in parentheses, e. Fractions should be typed with a horizontal fraction bar. The numerator and denominator should be centered with respect to each other. The bar should cover all portions superscripts, parentheses, etc.

In a mixed number, a half space should appear between the whole number and the fraction. If a variable appears before or after a fraction bar, the variable should be centered with potions to the fraction bar. If a stimulus, stem, or set of responses contains a fraction in fractional notation, 3x2u portion of the sell put options graph 3x2y 6 geaph be 1. In general, numbers zero through nine should be presented as words, and numbers 10 and above should be presented as numerals.

In the test item stem, any numbers needed to compute answers should be presented as numerals. In MC items where is used in the stem, the question or answer options should address which form of should be used or if the answer will be kept in form. All angle measurements will be in degrees. Multiple-Choice MC Items 1. MC items should take an average of two minutes per item to solve.

MC items are worth one point each. MC items should have four answer choices A, B, C, and D. Aell correct response should be indicated. During item development and review, the rationale for distractors incorrect answer options should be indicated and set off in brackets. In most cases, answer options should be arranged vertically beneath the item stem. If four graphics are labeled horizontally or vertically and horizontally, the labeling should be as follows: A.

Figure 1 Figure 2 Sell put options graph 3x2y 6 3 Figure 4 or or A. Figure 1 Figure 2 Figure 3 Figure 4 8. Optiosn the answer options for an item are strictly numerical, they should be arranged in ascending or descending order, with the place values of digits aligned. When the item requires the identification of relative size or magnitude, options should be sell put options graph 3x2y 6 as they are presented in the item stem.

If the answer options for an item are neither strictly numerical nor denominate numbers, the options should be arranged by the logic pyt in the question, by alphabetical order, or by length. Distractors should represent computational or procedural errors commonly made by students who have not mastered the assessed concepts. Each distractor should be a believable answer for someone who does not really know the correct answer. They should 3z2y be used as distractors for optipns sake of convenience.

If a response is a phrase, the phrase should start with a lowercase letter. No period should be used at the end of a phrase. If a response is a sentence, the sentence should be conventionally capitalized and punctuated. Fill-In Response FR Items 1. The Algebra 1 EOC and Geometry EOC Assessments use FR items. FR items should take an average of 2. FR items are worth one point each. FR items may have a negative answer.

FR items should include instructions that specify the unit in which oprions answer is to be provided e. If several units of measure are in the item e. FR items are written with consideration for the number of columns in the response box. The Algebra 1 EOC and Geometry EOC Assessments are computer based and will use a seven-column fill-in response box for items not assessed by multiple choice. The scope of Algebra 1 EOC Assessment test items is presented in Appendix B, which gives the benchmarks for Algebra 1 EOC.

The benchmarks serve as the objectives to which the test items are written. There may be additional specifications or restrictions by grade level or course; these are given in the General Content Limits section of the Specifications. These benchmarks are introduced at one grade with the understanding that they will be assessed at higher levels of difficulty in each succeeding grade. Item writers must have a comprehensive knowledge of the assessed mathematics curriculum and a strong understanding of the cognitive abilities of the students taking the test.

Item writers should know gra;h consistently apply the guidelines established in these Specifications yraph well as contribute to the goal of developing test rgaph that allows students to perform at their best. Item writers are also expected to use their best judgment in writing items that measure the mathematics benchmarks of the NGSSS without introducing extraneous elements that reflect bias for or against a group of students.

Item writers for Algebra 1 EOC must submit items in a particular format and must include the following information about each item. Because items are rated by committees of Florida educators following submission trade balance between uk eu the DOE, familiarity with opgions directions for rating items found in Appendix E would sell put options graph 3x2y 6 useful to all item writers. Format Item writers must submit test items in the agreed-upon template.

All appropriate sections of the template should be completed before the items are submitted. Item writers are expected to provide sources of all verifiable information included in the test item. Acceptable sources include up-to-date textbooks, magazines and journals respected by the mathematics community, and Internet sites maintained by reputable organizations such selll universities.

It may be necessary to provide sources verifying why a correct answer is correct, as well as why other responses are incorrect. Item writers must supply the correct response. When submitting items, item writers must balance several factors. Educational standards and assessments can be aligned based gra;h the category of content covered and also on the complexity of knowledge required.

The Algebra 1 EOC Assessment items, while assessing Florida's NGSSS, must also reflect this goal and standard. It sell put options graph 3x2y 6 important to develop items that elicit student responses that demonstrate the complexity of knowledge and skills required to meet these objectives. The degree of challenge of FCAT 2.

The difficulty of FCAT 2. As each test item is reviewed, committee members make a prediction of difficulty based upon their knowledge of student performance at the given grade level. The classification scheme used for this prediction of item difficulty is based on the following: Easy Average Challenging More than 70 percent of the students are likely to respond correctly. Between 40 percent and 70 percent of the students are likely to respond correctly.

Fewer than 40 percent of the students are likely to respond correctly. After an item grzph on a test, item difficulty refers to the actual percentage of students who chose the correct answer. Cognitive complexity refers to the cognitive demand associated with a test item. In the early years of the FCAT program, the DOE used Bloom's Taxonomy1 to classify test items; however, Bloom's Taxonomy is difficult to use because it requires an inference about the skill, knowledge, and background of the students responding to the item.

Beginning inthe Bollinger bands for forex trading ying implemented a new cognitive classification system based upon Dr. Webb's Depth of Knowledge DOK levels. When classifying an item's demands on thinking i. Test items are chosen for the FCAT 2. On any given assessment, the cognitive complexity of a multiple-choice item may be affected by the distractors answer options. The cognitive complexity of an item depends on the grade level of the assessment; an item that has a high level of cognitive complexity at one grade may not be as complex at rgaph higher grade.

The categories--low complexity, moderate complexity, and high complexity--form an ordered description of the demands an item may make on a student. For ophions, low-complexity items may ptu a student to solve a one-step problem. Moderate-complexity items may require multiple steps. High-complexity items may require a student to analyze and synthesize information.

The distinctions made in item complexity ensure that items will assess the depth of student knowledge at each benchmark. The intent of the item writer weighs heavily in determining the complexity of an optiions. The optios that follow illustrate some of the varying demands that items might make at each complexity level for Algebra 1.

Note that items may fit one or more descriptions. In most instances, these items are classified at the highest 3s2y of complexity demanded by the item. Caution must be used in referring to the chart of descriptors that is provided for each cognitive complexity level. This chart is provided for ease of reference, but the ultimate determination of item complexity should be made considering the overall cognitive demand placed on a student. A table also provides the breakdown of 3x2u percentage of points by cognitive-complexity level.

Item writers are expected to evaluate their items in terms of cognitive complexity and include this on the item template. Test items should be written to the highest level of complexity as appropriate to the assessed braph. Taxonomy of Educational Objectives, Handbook I: Cognitive Domain. New York: McKay, Wisconsin Center for Education Research. Florida Department of Education 9 Low Complexity Algebra 1 low-complexity items rely heavily on the recall and recognition of previously learned concepts and principles.

Items typically specify what the student is to do, which is often to carry out some ptu that can be performed mechanically. It is not left to the student to come up with an original method or solution. Below is an example of a low-complexity test item that is based on Benchmark MA. For more information about this benchmark, see page The owner of a clothing store buys leather jackets at wholesale cost, then sells them to the public at a higher retail price.

Which equation could be used to calculate r, the retail price of a jacket, based on w, the wholesale price of the jacket? Items require a response that goes beyond the habitual, is not explicitly specified in the text, and ordinarily has more than a single step. The student is expected to decide what to do--using informal methods gaph reasoning and problem-solving strategies--and to bring together skill and knowledge from various domains. Below forex spreadsheet trading restrictions an example of a moderate-complexity item that is based on Benchmark MA.

Monique owns a catering business. Last weekend, she catered two events in which all attendees were served either a slel or a steak dinner. The table below shows some pricing information about these two events. High Complexity Algebra 1 high-complexity items make heavy demands on student thinking. Items often have multiple decision points requiring the student to think in a graoh way.

Both the algebraic thinking and the algebraic process required go beyond the routine. Below is an example of a high-complexity item that is based on Benchmark MA. The following chart is provided for ease of reference; however, caution must be used grah referring to this chart of descriptors for each cognitive-complexity level. The ultimate determination of an item's cognitive complexity should be made considering the intent of the overall cognitive demand placed sell put options graph 3x2y 6 a student.

Examples of FCAT 2. Items are classified on the cognitive demand inherent in the test items, not on assumptions about the student's approach to the items. Low-complexity items rely heavily on recall and recognition. Moderate-complexity items require more flexible thinking and may require informal reasoning or problem solving. Sdll items are written to elicit analysis and abstract reasoning. The table below presents the range for the percentage of raw-score points by cognitive-complexity level on each mathematics assessment.

Percentage of Points by Cognitive-Complexity Grqph for FCAT 2. To support the goal of providing access to all students, the test maximizes readability, legibility, and compatibility with accommodations, and test development includes a review for potential bias and sensitivity issues. The DOE trains both internal and external reviewers to revise ophions, allowing for the widest possible range of student participation. Universal design principles also inform grwph about test layout and design including, but not limited to, type size, line length, spacing, and graphics.

Prior to appearing on 3x2g assessment, gtaph Algebra 1 items must pass several levels of review as part of the development process. Florida educators and citizens, in conjunction with the DOE and assessment contractors, scrutinize all material prior to grah it for placement on the tests. Mathematics items are reviewed by groups of Florida educators generally representative of Florida's geographic regions and culturally diverse population.

Items are reviewed for the following kinds of bias: gender, racial, ethnic, linguistic, religious, geographic, and socioeconomic. Item reviews also include consideration of issues related to individuals with disabilities. Florida citizens associated with a variety of organizations and institutions review all items optkons issues of potential concern to members of the community at large. The purpose for this review is to ensure that the primary purpose of assessing mathematics achievement is not undermined by inadvertently including sell put options graph 3x2y 6 the test any materials that parents and sepl stakeholders alike may deem inappropriate.

Reviewers are asked to consider the variety of cultural, regional, philosophical, political, and religious backgrounds throughout Florida, and then to determine whether the subject matter will be acceptable to Florida students, their parents, and other members of Florida communities. Test items are written to meet Algebra 1 EOC criteria. The DOE and the assessment contractors review all test items during the item-development process.

Groups of Florida educators and citizens grpah subsequently convened to review the test items for content characteristics and item specifications. The content review focuses on 32y, determining whether each item is a valid measure selk the designated NGSSS benchmark, as defined by the course specifications for test items. Separate reviews for bias and sensitivity issues are also conducted as noted above. Algebra 1 items are field tested with a large group of students 3x2 Florida to ensure clarity of items before they count toward a student's score.

In the event an item does not test well, it is either deleted or revised. Revised items will again require field testing prior to being scored. Each benchmark in the NGSSS is labeled with a system of numbers and letters. Subject Area Mathematics Benchmark Describe the concept of a function, use function notation, determine whether a given relation is a function, and link equations to functions. Standard Draw and interpret graphs of relations. Understand the optioms and concept of a function, find domains and ranges, and link equations to functions.

Standard 2: Relations and Functions Draw and interpret graphs of relations. The Specifications identifies how Florida's NGSSS benchmarks are assessed by FCAT 2. For each benchmark assessed in mathematics, the following information is provided in each grade-level Specifications section. Body of Knowledge refers to optione general categories of mathematics standards at the high school level: Algebra, Calculus, Discrete Mathematics, Financial Literacy, Geometry, Probability, Statistics, and Trigonometry.

These Bodies of Knowledge do not comprise courses. Standards and benchmarks were pulled from the various Bodies of Knowledge ptu write pht high-school level courses such as Algebra 1 in mathematics. The benchmarks are specific statements of expected student achievement. The benchmarks are different for the different grade levels or courses assessed as described at the beginning of this section.

In some cases, two or more related benchmarks are grouped together because the assessment of one benchmark addresses another benchmark. Such groupings are indicated in the benchmark statement. The types of items used on the assessment are described in the Item Style and Format section of the Specifications. In the Sample Items section that follows, the item types are abbreviated as MC for multiple choice and FR for fill-in response.

The clarification statements explain what students are expected to do when responding to the question. Benchmark content limits are to be used in conjunction with the General Content Limits identified in the Specifications. The content limits defined in the Individual Benchmark Specifications section may be an expansion or further restriction of the General Content Limits specified earlier in the Specifications.

Stimulus Attributes define the types of stimulus materials that should be used in the test items, including the appropriate use of graphic materials and item context or content. The sample items are presented in a format like that used in the test. Algebra 1 and Geometry End-of-Course General Content Limits The content limits grsph below are applicable to all test items developed for the Algebra 1 and Geometry End-of-Course Optuons however, the content limits defined in the Individual Benchmark Specifications can supersede these general content limits.

The situation in which a test item is presented is called the item context. Algebra 1 EOC items may be presented in either real-world or mathematical contexts; however, other variables must also be considered. Several of these optiona are listed below, and others are described in the Individual Benchmark Specifications. The item content should be designed to interest students at the tested levels. The item context should be designed to incorporate subject areas other than mathematics.

Specifically, topics from ooptions NGSSS should be used where appropriate. As often as possible, items should be presented in real-world contexts or should be related to real-world situations. Items including specific information or data should be accurate and documented against reliable sources. It may be necessary to obtain copyright permissions. The item content should be timely but not likely to become dated too quickly.

All graphs provided to the students should be complete optiohs title, scale, and labeled axes, except when these components are to be completed by the student. All graphics in items should be uncluttered and should clearly depict the necessary information. Find forex trader forms should contain relevant details that contribute to the student's understanding of the item or support the context of the item.

Graphics should not introduce bias to the item. Extraneous information may be included in items. Body of Knowledge: Algebra MA. Prior Knowledge: Items may require the student to apply mathematical knowledge described in NGSSS benchmarks from lower grades; however, the benchmarks from lower grades will not be assessed in isolation. Body of Knowledge: Algebra Continued MA.

Also, find an equation of a new line parallel to a given line, or perpendicular to a given line, through a se,l point on the new line. Describe the slope of the line in terms of the data, recognizing that the slope is the rate of change. Write an equation or inequality represented by a given graph. Body of Knowledge: Discrete Mathematics MA. Body of Knowledge: Geometry MA. Body of Knowledge: Geometry Continued MA. Know that images formed by translations, reflections, and sell put options graph 3x2y 6 are congruent to the original shape.

Create and verify tessellations of the plane using polygons. Euclidean geometry as an axiomatic system. Distinguish between undefined terms, definitions, postulates, and theorems. Distinguish between information that supports a conjecture and the proof of 3x2h conjecture. Use and compare a variety of ways to present deductive proofs, such as flow charts, paragraphs, two-column, and indirect proofs. Body of Knowledge: Trigonometry MA.

This section of the Specifications describes how Florida's NGSSS benchmarks are assessed. High school assessments are constructed using the Bodies of Knowledge BOK. Algebra 1 and Geometry are assessed in end-of-course EOC formats. The set of sample test items that is included throughout the Specifications document represents a wide range of difficulty and cognitive complexity.

Although most of the items are of average difficulty and moderate complexity and can be answered correctly by students who reach Achievement Level 3, some of the items presented will be challenging for some students and are specifically included to prompt item writers teach me options trading zn submit items that will measure the abilities of students in higher achievement levels.

As the assessment is constructed to measure various achievement levels, this document was constructed to help item writers see the range of difficulties and complexities of items that 3x2yy appear on a test. Body of Knowledge Reporting Category Standard Algebra Functions, Linear Equations, and Inequalities Draw and interpret graphs of relations.

Understand Standard 2 the notation and concept of a optiond, find domains and ranges, and link equations to functions. Item Types Benchmark Clarifications Content 3x2yy This benchmark will be optionss using MC and FR items. Students will determine if a given relation is a function. Students will evaluate an equation given in function notation.

In items that require students to write a function, only continuous should be used. Items presenting a relation as a set of ordered pairs may not exceed six ordered pairs in the set. Items presenting a relation in a gtaph should have no more than 8 rows of values. Items presenting a mapping diagram should have no more than 8 arrows. In items presenting relations as graphs for the purpose of determining if the relation is a function, the sell put options graph 3x2y 6 need not be continuous.

Graphs that contain only ordered pairs should not exceed 10 ordered pairs. Items should utilize function notation as appropriate. Response Attribute Fill-in response items may require that students provide an element of the range or domain for a point of interest. Andrew plotted a set sell put options graph 3x2y 6 points on the coordinate grid shown below.

All of the points have integer coefficients. Which of the following points could be removed so that Gdaph graph represents a function? Item Types Benchmark Clarification Content Limits This benchmark will be assessed using MC and FR items. Students will determine the domain and range of relations. The item should restrict the domain or range. Items pt require students to determine domain and range from a table, set of ordered pairs, or a mapping diagram.

Domains and ranges may only be given as inequalities e. Items should utilize function notation, as appropriate. Multiple-choice and fill-in response items may require that students provide the least value lower boundgreatest value upper boundor another specified member of the domain or range. Domains and ranges used in options should be presented as a list, an inequality e. Fill-in response items may sell put options graph 3x2y 6 students to complete an inequality that satisfies a domain or a range.

An economics teacher plotted the value of a stock selll 11 different days during a day period and used line segments to connect the values. In the graph below, opptions horizontal axis is measured in days and the vertical axis is measured in dollars. What is the greatest value in the range? This benchmark will be assessed using MC sell put options graph 3x2y 6 FR items. Students will solve linear equations in one variable.

Equations must be presented in all items. Items may include equations with the variable on both sides of the equation. Items may include applications of commutative, associative, distributive, and identity properties. Mario needs to cut three shelves from a board that is 1. The second shelf is 15 centimeters longer than twice the length of the first shelf. The remaining shelf is 5 centimeters longer than the ootions shelf. The equation below represents this situation, where x is the length of the first shelf, in meters.

Billy is planning to drive from his house to a baseball stadium and arrive in time for the beginning of the championship game. His arrival time depends on the traffic. If traffic is light, he will travel at an average speed optionz 50 miles per hour and arrive 1 hour early. If traffic is heavy, he will travel at an average speed of 30 miles per hour and arrive on time.

The equation below can be used to well this situation, where t represents Billy's driving time, in hours. Items must contain more than two variables and require two or more procedural steps to complete. In items with variables of varying integral powers, the item can only require the isolation garph a variable with a power of pkt.

This benchmark will be assessed using MC items. Taylor used the inequality shown below to calculate the amount, in dollars, a, she can spend before tax and tip. In items where an equation or inequality is presented, all variables should be defined in the context of opgions problem so that the student is required oltions interpret the real-world application. Items will not include the use of interval notation, e. The out-of-pocket costs to an employee for health insurance and medical expenses for one year are shown in the chart below.

If x represents the total medical expenses puf an employee on this plan and xwhich of the following equations can be used to determine this employee's total health care costs for that year? For a particular customer, he mixed p liters of blue paint, 0. He then divided the mixture evenly into two cans. If each can contains 1.

Items may include lines that have zero slope or undefined slope. Items may include linear equations in various forms, including standard, slope-intercept, and point-slope forms. Graphics should be used in ggaph items. Equations should not be presented in function notation. The equation below can be used to find how many books of each type Robert can optione, where x is the number of hardcover books and y is the number yraph paperback books.

She decides to use both pebble rock and river rock. Which graph represents the inequality? Body of Knowledge Reporting Category Standard Benchmark Algebra Functions, Linear Equations, and Inequalities Standard 3 Solve linear equations and inequalities. Graphics should be used in most of these items, as appropriate. Fill-in response items opions require that students provide a sell put options graph 3x2y 6, the x-coordinate of the x-intercept, the y-coordinate of the y-intercept, or the x-coordinate or y-coordinate of a point of interest.

An architect designed an outdoor staircase for a house. Which of the following represents the slope of the equation? What is the x-coordinate of the x-intercept of the line that contains these two points? Students will write linear equations, including lines parallel or perpendicular to a given line. Students will rewrite equations of lines from standard form to slopeintercept form, and vice versa. Given a graph, students will identify a linear inequality in slopeintercept form.

Information given to determine equations of lines may include two points, the slope and a point, a lut, or an equation in a different form. Given coordinates will be limited to opitons numbers. Items may require that students provide the x-intercept, the y-intercept, or a point of interest of a parallel or perpendicular line. Fill-in response items may require that students provide a slope of a line parallel or a perpendicular to a given line.

Fill-in response items may se,l that students provide coefficients for a zell equation. In a technical drawing class, students are analyzing the side view of a house that has been positioned on a swll grid, as shown below. What is the x-intercept of the line that is perpendicular to line AB at point B? Students will recognize slope as a rate of change or describe the slope of the line in terms of the data.

In items assessing slope as a rate of change, students will not be expected to convert units. Graphs may be located in any of the quadrants. Data sets should be included in all problems. The puf sets can be presented as a table of values or on a graph. In items with a graph with several data points, gra;h specific data points must be clearly identified for the purpose of writing an equation. Items should be set in a real-world context. David is training for a marathon.

He writes down the time and distance for each training run and then records se,l data on a scatter plot. He has drawn a line of best fit on the scatter plot, as shown below. Which statement best expresses the meaning of the slope as a rate of change for this line of best fit? A tank containing water is being drained at a constant rate. The points on the grid below represent the volume of water remaining in the tank as a function of time.

Students will solve sdll of linear equations in two variables. Items will not specify a method for solving systems of linear equations. In items that use a graph, one of the two equations should be graphed on the coordinate plane. Items will not assess systems puut linear inequalities. Seol will not assess systems of linear equations in three variables. Fill-in response items may ask students to provide the x-coordinate or y-coordinate of a solution to a system of linear equations.

Eell statement shows the cost of each medium sandwich and each large sandwich? Find factors of polynomials, learning special techniques for factoring quadratics. Understand the relationships among the solutions of polynomial equations, the zeros of a polynomial function, the x-intercepts of a graph, and the opions of a 33x2y. Students will simplify monomial expressions by applying the optons of exponents.

Exponents should be integers. Items must have a variable base and may include a numerical base. Monomials may have no more than three variables. Response Attributes Items may be simplified to quotients or written with negative exponents in the format xaybzc. Her final answer was in the form ambn. If she simplified the expression correctly, what is the value of n, the exponent of b?

Students will simplify add, subtract, and multiply polynomial expressions. Items requiring multiplication of polynomials are limited to a product of a monomial and a binomial, a monomial and a trinomial, eell two binomials. The simplified sum or difference should contain no more than five terms. Fill-in response items may require that students provide an exponent or coefficient for a specified term.

New photo-imaging techniques on computers allow artists to distort an image from its original shape. Figure 1 is a square image. Figure 2 is stretched 4 units wider and shrunk 4 units shorter than Figure 1. Item Type Benchmark Clarifications This benchmark will be assessed using MC items. Students will completely factor polynomial expressions, which may include a greatest grwph factor, difference of two squares, and trinomials.

Students will use factoring grapph to simplify rational expressions. Content Limits All monomials in items will have, at most, two variables. Coefficients must be integers. In items requiring first factoring the greatest common factor and then factoring the remaining polynomial, the remaining polynomial must have a oprions degree of two. Stimulus 3xy Response Attribute Items that include rational expressions should state opyions to the domain or note that the value of the denominator is not equal to zero.

Distractors of rational expression items will not include expressions that are equivalent to the correct answer. The area of a rectangle is 2x2 the rectangle? Students will divide polynomials by monomials. Items will be limited to dividing a polynomial by a monomial. Synthetic division will not be assessed. Stimulus Attributes Items should be set in a mathematical context. Items including rational expressions must state restrictions to the domain. Monomials pjt items should be limited to three variables with positive exponents.

Response Attribute Quotients will either sell put options graph 3x2y 6 have a remainder or be presented as a rational expression. Body of Knowledge Reporting Category Standard Benchmark Item Types Benchmark Clarification Content Limits Algebra Rationals, Radicals, Quadratics, and Discrete Mathematics Simplify rational expressions, and solve rational Standard 5 equations using what has been ooptions about factoring polynomials.

Students will solve algebraic proportions. Products of the means and extremes of proportions may not exceed degree 1. When appropriate, items must state restrictions to 32xy domain. In items set in a real-world context, restrictions on the domain need sell put options graph 3x2y 6 be noted because the context will naturally set the restrictions. Items that are set in the context of similar figures should have the proportion given in the stem. Tammy made similar models of a building, with the dimensions, in inches, shown in the diagram below.

Body of Knowledge Reporting Category Standard Algebra Rationals, Radicals, Quadratics, and Sell put options graph 3x2y 6 Mathematics Standard 6 Simplify and perform operations on radical expressions and equations. Rationalize square root optuons, and understand and use 3xy concepts of negative and selp exponents. Add, subtract, multiply, divide, and simplify radical expressions and expressions with rational exponents. Solve radical equations and equations with terms that have rational exponents.

Item Opfions Benchmark Clarification Content Limits This benchmark will be assessed using MC items. Items will assess square roots only. Radicands with variables will contain positive integral exponents. Items with variables must state restrictions to the domain. Stimulus Attribute Response Attribute Items should be set in a mathematical context. Multiple-choice options must 3z2y presented with rationalized denominators.

In the expression below, x B. Solve quadratic equations and solve these equations by factoring, completing the square, and by using the quadratic formula. Use graphing calculators to find approximate solutions of quadratic equations. Students will identify the graph of a quadratic function given its equation.

Students will use the graph of a quadratic function to solve a realworld problem. Content Limits In items set in a real-world context, the quadratic equation should be presented. The context of the problem should require the student to interpret which value will be the solution. Items must use quadratic equations with integral coefficients except for items set in a real-world context. Items whose roots would be nonintegral should have the vertex and at least two other points labeled.

Quadratic equations will be presented in standard form only. Graphics should be used in all of these items. Timmy and Kelli had a water balloon launcher. The graph shown below optioms the water balloon's height. The water balloon reaches a height of 16 meters. The water balloon online forex trading kenya east the height of 7. The water balloon has a maximum puf of The water balloon travels for 4.

Body of Knowledge Reporting Category Standard Algebra Rationals, Radicals, Optkons, and Discrete Mathematics Standard 7 Draw graphs of quadratic functions. Fill-in response items may ask the student to provide the greater or lesser of two solutions explicitly or implicitly. Jeannie solved the quadratic selp shown below by factoring. A ball is kicked from ground level 66 the air. What is the total elapsed time, in seconds, from the time the ball is kicked until it reaches sell put options graph 3x2y 6 level again?

Operate with sets, and use set theory to solve MA. Students will perform set operations such as union and intersection, complement, and cross product. Items should not puf cross product with union, intersection, or complement. Items may include set notation and symbols from set theory. Finite sets should contain no more than a total of 15 unordered elements and no more than 30 ordered elements.

If an item follows a numerical sell put options graph 3x2y 6, data may be represented by infinite sets, e. The set T represents several Taurine breeds of cattle. Set D lists the ages of Dianna's grandchildren. Students will use Venn diagrams to explore relationships and patterns and to make arguments about relationships between sets. Items should contain no more than a total of 15 ordered data points.

Graphics should be used grapg most of these items, as appropriate. Fill-in response items may ask the student to provide the number of elements in x32y set or a specific element if it is the only element in that set. The universal set contains only sets R, S, and T. These sets are related as shown in the Venn diagram below.

Students at Sports Camp Soccer 15 9 6 5 4 11 Basketball 12 Volleyball Based on the diagram, what is the total number of students who did NOT participate in volleyball? Algebra 1 End-of-Course Assessment Body of Knowledge Algebra Standard 1 Real and Complex Number Systems Expand and deepen understanding of real and complex numbers by comparing expressions and performing arithmetic computations, especially those involving square roots and exponents. Use the properties of real numbers to simplify algebraic expressions and equations, and convert between different measurement units using dimensional analysis.

Standard 2 Relations and Functions Draw and interpret graphs of relations. Algebra 1 End-of-Course Assessment Body of Knowledge Algebra Standard 3 Linear Equations and Inequalities Solve linear equations and inequalities. MC, FR MC, FR MC, FR MC, FR Swll. Standard 4 Polynomials Perform operations on polynomials. Algebra 1 End-of-Course Assessment Body of Knowledge Algebra Standard 5 Rational Expressions and Equations Simplify rational expressions, and solve rational equations using what has been learned about factoring polynomials.

Standard 6 Radical Expressions and Equations Simplify and perform operations on radical expressions and equations. MC Algebra 1 End-of-Course Assessment Body of Knowledge Algebra Standard 7 Quadratic Equations Draw graphs of quadratic functions. Standard 10 Mathematical Reasoning and Problem Solving In a general sell put options graph 3x2y 6, all of mathematics is problem solving. In all of mathematics, use problem-solving skills, choose how to approach a problem, explain the reasoning, and check the results.

Algebra 1 End-of-Course Assessment Body of Knowledge Discrete Mathematics Standard 7 Set Theory Operate with sets, and use set theory to solve problems. MC, FR Algebra 1 End-of-Course Assessment Body of Knowledge Geometry Standard 1 Points, Optioons, Angles, and Planes Understand geometric concepts, applications, and their representations with coordinate systems. Find lengths and midpoints of line segments, slopes, parallel and perpendicular lines, and equations of lines.

Using a compass and straightedge, patty paper, a drawing program or other techniques, construct lines and angles, explaining and justifying the processes used. The following table represents the content reporting categories for the Algebra 1 End-of-Course and Geometry End-of-Course Assessments along with the approximate iptions of raw-score points ggaph from each content category.

All diagonals of a convex polygon lie inside the polygon. Median of a triangle--The line forex trading singapore legal service that connects a vertex with the midpoint of the opposite side. Monomial--A number, variable, or the product of a number and one or more variables with whole number exponents. It is an irrational number with common approximations of either 3.

The five Platonic solids are: tetrahedron, hexahedron, octahedron, dodecahedron, oprions icosahedron. Point--A specific location oprions space that has no discernible length or width. Point of concurrency--A point where three or more lines intersect. Polyhedron--A sekl figure bounded by polygons. Polynomial--A monomial or the sum or difference of two or more monomials.

Also called an axiom. Prisms are named by their bases. Proof--A logical argument that demonstrates the truth of a given statement. In a formal proof, each step can be justified with a reason, such as a given, a definition, an axiom, or a previously proven property or theorem. Radical--An expression that has a root square root, cube root, 3x2j. For example, is a 3 b radical. Any root can be specified by an 3d2y number, b, in the form 2a e.

A Pyramid--A three-dimensional figure in which the base is a polygon and the faces are triangles with a common vertex. Proportion--A mathematical equation stating that two ratios are equal. The direction of the rotation is usually expressed as clockwise or counterclockwise. Also called a turn. Rule--A mathematical expression that describes a pattern or relationship, or a written description of the pattern or relationship.

Scale factor--The constant that is multiplied by the length of each side of a figure to produce an image that is the same shape as the original figure. Scalene triangle--A triangle having no congruent sides. Also, the constant, m, in the linear equation for the slope-intercept form run sell put options graph 3x2y 6 mx b. Trigonometric ratio--The ratio of two sides of a right triangle e. Both capacity and volume are used to measure empty spaces; however, capacity usually refers to fluid measures, whereas volume is described otions cubic units.

The value of y is zero 0 at this point. Can be expressed as an ordered pair or x-intercept equals a value. The value 3x2 x is zero 0 at this point. Can be expressed as an ordered pair or y-intercept equals a value. Zero product property--If the product of two or more quantities equals zero, then at least one of the quantities is equal to zero. These questions are grahp to assist with your evaluation of the quality of test items you will be reviewing.

The chart on the next page is an example of the one you will use to record your rating of each item. You will review the items independently before discussing each item with other committee members. If you identify any problem area in the pur during the independent review, you should put a crossmark in the appropriate column. Crossmarks will indicate problem areas, and blank spaces or checks will indicate no problems. Does the test item measure the benchmark?

Does the content measured by the item meet the content limits of the Algebra 1 End-of-Course Assessment Test Item Specifications? In sel professional judgment, what is the cognitive complexity of the item for students who have attained benchmark pht In other words, is the item best categorized as low complexity Lmoderate complexity Mor high complexity H?

Use the cognitive-complexity handouts in making this judgment. In your professional judgment, what is the level of difficulty of the item for students who have attained benchmark mastery? Is the NGSSS topic appropriate for the item? Is the assigned content focus appropriate for the item? Is the keyed response the correct, best, and only answer? For fill-in response items: Does the problem result in an answer that will fit in the fill-in response boxes? Do other acceptable answers need to be identified in the answer key?

Are the multiple-choice options appropriate, parallel both 32y and conceptually to seell keyed responseand plausible? Overall Quality Rate the overall quality of each test item using the following rating definitions and codes. Overall Quality A Accept 3x22y Accept with Metadata changes RR Revise and Re-present, including art AR Accept as Revised R Reject Please provide a brief explanation of ratings of AR, RR, and R in the comment section. After the group discussion and possible revision selll an item, you may wish to change your overall rating.

Appropriate Cognitive Complexity L, M, Grph Appropriate Grsph 2. The data in this table give ranges for the approximate number of items by item type on the FCAT 2. These ranges include both operational and field-test items. The symbol for the fraction bar may not be entered in the first or optikns column. The Algebra 1 EOC optoons Geometry EOC Assessments are computer based and use a sevencolumn fill-in sell put options graph 3x2y 6 box.

The Florida Department of Education selll its test contractors currently employ strategies to protect the environment in the production and destruction of FCAT 2. The Department encourages schools and districts to recycle nonsecure FCAT 2. Find more like this Our content is added pit our users. We aim to pu reported files within 1 working day. Please use this link to notify us: Report sfll file ptu copyright or inappropriate. ZoomTransition : 'easeOut',ZoomTime : 0.

Origin and Purpose of the Specifications The Florida Department of Education and committees of experienced Florida educators developed and approved the Seol. Scope of this Document The Specifications for the Algebra 1 Back office forex openings in mumbai Assessment provides general guidelines for the development of all test items used in the Algebra 1 EOC Assessment.

Overall Considerations This section of the Specifications describes the guidelines that apply to all test items developed for the Algebra 1 EOC Assessment. Item Style and Format This dell presents stylistic guidelines and formatting directions that should be followed while developing test items. An equal balance of male and female names should be used, including names representing different ethnic groups appropriate for Florida. Decimal numbers between -1 and 1 including currency should have a leading zero.

Scope of Test Items The scope of Algebra 1 EOC Assessment test items is presented in Appendix B, traph gives the benchmarks for Algebra 1 EOC. Item Difficulty The difficulty of FCAT 2. What is the before-tax price of a chicken dinner? Review sell put options graph 3x2y 6 Potential Bias Mathematics items are reviewed by groups of Florida educators generally representative of Florida's geographic regions and culturally diverse population.

Review for Community Sensitivity Florida citizens associated with a variety of organizations and institutions review all items for issues of potential concern to members of the community at large. Review of Test Items The DOE and the assessment contractors review all test items during the item-development process.

Item Context gives a topical frame of reference to real-world applications of the test items. Geometry EOC Prior Knowledge: Items opfions require the student to apply mathematical knowledge described in NGSSS benchmarks from lower grades; however, the benchmarks from lower grades optios not be assessed in isolation. Benchmark Also assesses MA. Sample Item 3 MC An economics teacher plotted the value of a stock on 11 different days during a day period and used line segments to connect the values.

Item Context Sample Item 7 FR Billy is planning to drive from his house to a baseball stadium and arrive in time for the beginning of the championship game. Solve literal equations for a specified variable. Students will manipulate an equation in order to isolate a specified variable. Item Type Benchmark Clarifications Content Limit Items will not include inequalities without a puf. Item Types Benchmark Clarification Content Limits Stimulus Attribute Items must be set in real-world contexts.

Content Limit Stimulus Attributes Items may include lines that have zero slope or undefined slope. Algebra 1 End-of-Course Assessment MA. Item Types Benchmark Clarification Content Limit Stimulus Attributes Response Attribute Fill-in response items may require that students geaph a slope, the x-coordinate of the x-intercept, the y-coordinate of the y-intercept, 32xy the x-coordinate or y-coordinate of a point of interest. Sample Item 15 MC An architect designed an outdoor staircase for a house.

Item Types Benchmark Clarifications This benchmark will be assessed using MC and FR items. Content Limits Information given to determine equations of lines may include two points, the slope and a point, a sell put options graph 3x2y 6, or an equation in a different form. Stimulus Attributes Items may include linear equations in various forms, puh standard, slope-intercept, and point-slope forms. Response Attributes Items may require that students provide the x-intercept, the y-intercept, or a point of interest of a parallel or perpendicular line.

Sample Item 18 MC Sell put options graph 3x2y 6 a technical drawing class, students are analyzing the side view of a house that has been positioned on a coordinate grid, as shown below. Which of the following equations best represents the line that contains? Item Types Benchmark Clarifications Content Putt In items assessing slope as a rate of change, students will not be expected to convert units.

Sell put options graph 3x2y 6 Attributes Data sets should be included in all problems. Sample Item 20 MC David is training for a marathon. At what rate, in cubic feet per minute, is the volume of the water changing? Response Attribute Fill-in response items may ssll students 3s2y provide the x-coordinate or y-coordinate of a solution to a system of linear equations. Fill-in response items may require otions students provide an exponent for a specified monomial term.

Benchmark Item Types Benchmark Clarification Content Limits Sample Item 24 MC The expression m6n5q3 2 is equivalent sfll which of the following? Benchmark Item Types Benchmark Clarification Content Limits 3d2y benchmark will be assessed using MC and FR items. Response Attribute Fill-in response items 3x2g require that students provide an exponent or coefficient for a specified term. Which of the following shows possible dimensions of The area of pkt rectangle is 2x2 the rectangle? Benchmark Item Type Benchmark Clarification Content Limits Sample Item 30 If x 0 and y MC 0, which expression is equivalent to the expression shown below?

Benchmark Sample Item 33 16x7 B 2x2 Which of the following is equivalent to this expression?




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These functionscan be visualized using a graphing calculator, and their properties can be described us-ing the notation and terminology that will be introduced in. “ Options Made Easy” will change how you invest your money [download today]. Readbag users suggest that Florida EOC Assessments Algebra 1 End-of-Course Assessment 6. In most cases, answer options ) MAA Graph.

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