Blueprint End-of-Course Algebra II Test

Transcription

1 Blueprint End-of-Course Algebra II Test for te 2001 Matematics Standards of Learning Revised July 2005 Tis revised blueprint will be effective wit te fall 2005 administration of te Standards of Learning Tests.

2 2005 by te Commonwealt of Virginia, Department of Education, P.O. Box 2120, Ricmond, Virginia All rigts reserved. Except as permitted by law, tis material may not be reproduced or used in any form or by any means, electronic or mecanical, including potocopying or recording, or by any information storage or retrieval system, witout written permission from te copyrigt owner. Commonwealt of Virginia public scool educators may reproduce any portion of tese Blueprints for noncommercial educational purposes witout requesting permission. All oters sould direct teir written requests to te Virginia Department of Education, Division of Assessment and Reporting at te above address or by to Virginia SOL Assessment: End-of-Course Algebra II Test Blueprint, Revised 7/05 i

3 Algebra II Blueprint Table of Contents Standards of Learning (SOL) Test Blueprint Introduction...1 Test Development Guidelines...3 Blueprint Summary Table...4 Expanded Blueprint...5 Formula Seet...8 Virginia SOL Assessment: End-of-Course Algebra II Test Blueprint, Revised 7/05 ii

4 Wat is a test blueprint? Standards of Learning (SOL) Test Blueprint Introduction A test blueprint is a guide for test construction and use. Te Standards of Learning (SOL) test blueprints serve a number of purposes. One, tey serve as a guide to test developers as tey write test questions and construct te SOL tests. Two, tey serve as a guide to educators, parents, and students in tat tey sow (a) te SOL covered by te test and wic, if any, ave been excluded; (b) wic SOL are assigned to eac reporting category; (c) te number of test items in eac reporting category and on te total test; (d) general information about ow te test questions were constructed; and (e) te materials tat students are allowed to use wile taking te test. How is te test blueprint organized? Tere is a blueprint for eac test (e.g., grade 3 Englis, grade 5 matematics, grade 8 science, U.S. History). Eac blueprint contains te following information: 1. Test Development Guidelines: guidelines used by te testing contractor and te members of te Content Review Committees in developing te SOL tests. Tis section contains tree parts: A. General Considerations lists general considerations tat are used in developing te test as well as considerations specific to a particular content area. B. Ancillary Materials lists any materials (e.g., calculators, rulers, protractors, compasses, dictionaries) tat students are allowed to use wile taking eac test. 2. Blueprint Summary Table: a summary of te blueprint wic displays te following information: reporting categories for eac test; number of test items in eac reporting category; Standards of Learning (SOL) included in eac reporting category. SOL are identified by numbers and letters tat correspond to te original SOL document (letters are assigned to te bullets in te original document); SOL wic are excluded from te SOL test; number of operational items on te test; number of field-test items on te test; and total number of items (operational and field-test items) on te test. 3. Expanded Blueprint: provides te same information as te Blueprint Summary Table except tat te full text of eac SOL is included. Virginia SOL Assessment: End-of-Course Algebra II Test Blueprint, Revised 7/05 1

5 Wat is a reporting category? Eac test assesses a number of SOL. In te test blueprint, SOL are grouped into categories tat address related content or skills. Tese categories are labeled Reporting Categories. For example, a Reporting Category for te Grade 5 Matematics test is Computation and Estimation. Eac of te SOL in tis reporting category addresses computation using addition, subtraction, multiplication, or division or requires te student to estimate te answer to a problem. Wen te results of te SOL tests are reported, te scores will be presented in terms of scores for eac Reporting Category and a total test score. Are some SOL assigned to more tan one reporting category? In Algebra II matematics, eac standard, as well as eac letter under a standard, is assigned to only one reporting category. Will all SOL listed in te blueprint be assessed eac time te SOL tests are given? Eac SOL will not be assessed on every SOL test form. To keep te lengt of a test reasonable, te test will measure a selection of te SOL witin a reporting category. However, every SOL in te blueprint is eligible for inclusion on eac form of an SOL test. Over time all SOL in a reporting category will be assessed. Virginia SOL Assessment: End-of-Course Algebra II Test Blueprint, Revised 7/05 2

6 A. General Considerations Algebra II Test Development Guidelines 1. All items included in tis test will address te knowledge and skills specified in te 2001 Virginia Standards of Learning in Algebra II. 2. Te items will be free of stereotyping or bias directed at a particular age, gender, economic status, racial, etnic or religious group, or geograpic region. 3. Te test will be untimed. 4. Tere is no penalty for guessing. Students scores will be based on te number of correct answers out of te total number of operational items on te test. 5. Were appropriate, real-life examples and situations tat te student would likely encounter will be used to present data or ask questions. 6. Items will be appropriate for adolescents in terms of difficulty, interest, and reading level. 7. Students will be permitted scratc paper at any time during te test. 8. Students will be permitted to use only graping calculators during te test. Te calculator s memory must be reset prior to test administration, clearing all memory contents not built into te calculator s system. 9. Students will be permitted to use standard (e.g., inces) and metric rulers during te test. 10. Students will be provided a formula seet and an approximation of π. A copy of te formula seet follows te expanded blueprint. B. Ancillary Materials Refer to te current examiner s manual or te Department of Education s Web site for ancillary materials tat may be used. Virginia SOL Assessment: End-of-Course Algebra II Test Blueprint, Revised 7/05 3

7 Algebra II Test Blueprint Summary Table Reporting Categories No. of Items SOL Expressions and Operations 10 AII.1 AII.2 AII.3a,b AII.5 AII.17 Relations and Functions 16 AII.8 AII.9 AII.15 AII.16 AII.19 AII.20 Equations and Inequalities 10 AII.4 AII.6 AII.7 Analytical Geometry 6 AII.10 AII.18 Systems of Equations/Inequalities 8 AII.11 AII.12 AII.13 AII.14 Total Number of Operational Items 50 Field Test Items* 10 Total Number of Items 60 *Tese field test items will not be used to compute students scores on te test. Virginia SOL Assessment: End-of-Course Algebra II Test Blueprint, Revised 7/05 4

8 Expanded Blueprint Reporting Category: Expressions and Operations Number of Items: 10 Algebra II SOL in Tis Reporting Category: AII.1 AII.2 AII.3 AII.5 AII.17 Te student will identify field properties, axioms of equality and inequality, and properties of order tat are valid for te set of real numbers and its subsets, complex numbers, and matrices. Te student will add, subtract, multiply, divide, and simplify rational expressions, including complex fractions. Te student will a) add, subtract, multiply, divide, and simplify radical expressions containing positive rational numbers and variables and expressions containing rational exponents; and b) write radical expressions as expressions containing rational exponents and vice versa. Te student will identify and factor completely polynomials representing te difference of squares, perfect square trinomials, te sum and difference of cubes, and general trinomials. Te student will perform operations on complex numbers and express te results in simplest form. Simplifying results will involve using patterns of te powers of i. Reporting Category: Relations and Functions Number of Items: 16 Algebra II SOL in Tis Reporting Category: AII.8 AII.9 Te student will recognize multiple representations of functions (linear, quadratic, absolute value, step, and exponential functions) and convert between a grap, a table, and symbolic form. A transformational approac to graping will be employed troug te use of graping calculators. Te student will find te domain, range, zeros and inverse of a function; te value of a function for a given element in its domain; and te composition of multiple functions. Functions will include exponential, logaritmic, and tose tat ave domains and ranges tat are limited and/or discontinuous. Te graping calculator will be used as a tool to assist in investigation of functions. Virginia SOL Assessment: End-of-Course Algebra II Test Blueprint, Revised 7/05 5

9 Reporting Category: Relations and Functions (continued) Number of Items: 16 Algebra II SOL in Tis Reporting Category (continued): AII.15 AII.16 AII.19 AII.20 Te student will recognize te general sape of polynomial, exponential, and logaritmic functions. Te graping calculator will be used as a tool to investigate te sape and beavior of tese functions. Te student will investigate and apply te properties of aritmetic and geometric sequences and series to solve practical problems, including writing te first n terms, finding te nt term, and evaluating summation formulas. Notation will include Σ and a n. Te student will collect and analyze data to make predictions and solve practical problems. Graping calculators will be used to investigate scatterplots and to determine te equation for a curve of best fit. Models will include linear, quadratic, exponential, and logaritmic functions. Te student will identify, create, and solve practical problems involving inverse variation and a combination of direct and inverse variations. Reporting Category: Equations and Inequalities Number of Items: 10 Algebra II SOL in Tis Reporting Category: AII.4 AII.6 AII.7 Te student will solve absolute value equations and inequalities grapically and algebraically. Graping calculators will be used as a primary metod of solution and to verify algebraic solutions. Te student will select, justify, and apply a tecnique to solve a quadratic equation over te set of complex numbers. Graping calculators will be used for solving and for confirming te algebraic solutions. Te student will solve equations containing rational expressions and equations containing radical expressions algebraically and grapically. Graping calculators will be used for solving and for confirming te algebraic solutions. Virginia SOL Assessment: End-of-Course Algebra II Test Blueprint, Revised 7/05 6

10 Reporting Category: Analytical Geometry Number of Items: 6 Algebra II SOL in Tis Reporting Category: AII.10 AII.18 Te student will investigate and describe troug te use of graps te relationsips between te solution of an equation, zero of a function, x-intercept of a grap, and factors of a polynomial expression. Te student will identify conic sections (circle, ellipse, parabola, and yperbola) from is/er equations. Given te equations in (, k) form, student will sketc graps of conic sections, using transformations. Reporting Category: Systems of Equations/Inequalities Number of Items: 8 Algebra II SOL in Tis Reporting Category: AII.11 AII.12 AII.13 AII.14 Te student will use matrix multiplication to solve practical problems. Graping calculators or computer programs wit matrix capabilities will be used to find te product. Te student will represent problem situations wit a system of linear equations and solve te system, using te inverse matrix metod. Graping calculators or computer programs wit matrix capability will be used to perform computations. Te student will solve practical problems, using systems of linear inequalities and linear programming, and describe te results bot orally and in writing. A graping calculator will be used to facilitate solutions to linear programming problems. Te student will solve nonlinear systems of equations, including linear-quadratic and quadratic-quadratic, algebraically and grapically. Te graping calculator will be used as a tool to visualize graps and predict te number of solutions. Virginia SOL Assessment: End-of-Course Algebra II Test Blueprint, Revised 7/05 7

11 Algebra II Formula Seet Geometric Formulas b r l b 1 2 A = b s p = 4s A = s 2 s b A = b b 1 b 2 1 A = 2 (b 1 + b 2 ) l w V = lw S.A.= 2(lw + l + w) V = r 2 S.A.= 2 r( + r) r 1 V = 3 r 2 S.A.= r(l + r) l B V = B S.A.= lp + B w r a c l p = 2(l + w) A = lw C = 2 r A = r 2 b c 2 = a 2 + b 2 milligram mg gram g kilogram kg milliliter ml liter L kiloliter kl millimeter mm centimeter cm meter m kilometer km square centimeter cm 2 cubic centimeter cm 3 Abbreviations ounce pound quart gallon inc foot yard mile square inc square foot cubic inc cubic foot oz lb qt gal. in. ft yd mi. sq in. sq ft cu in. cu ft Pi Quadratic Formula x = b ± b2 4ac 2a volume total surface area area of base V S.A. B year mont our minute second yr mon r min sec 2003 by te Commonwealt of Virginia Department of Education, James Monroe Building, 101 N. 14t Street, Ricmond, Virginia, All rigts reserved. Except as permitted by law, tis material may not be reproduced or used in any form or by any means, electronic or mecanical, including potocopying or recording, or by any information storage or retrieval system witout written permission from te copyrigt owner. Please contact te Commonwealt of Virginia Department of Education at (804) , Division of Assessment and Reporting, to request written permission