Arithmetic Properties w. A = lw Additive Inverse: a + (ˉa) = 0 l 1 Multiplicative Inverse: a = 1 a

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1 KEYSTONE REFERENCE ALGEBRA I FORMULA SHEET Formulas that you may need to solve questions on this exam are found below. You may use calculator π or the number Arithmetic Properties w A = lw Additive Inverse: a + (ˉa) = 0 l 1 Multiplicative Inverse: a = 1 a h V = lwh Commutative Property: a + b = b + a a b = b a l w Associative Property: (a + b) + c = a + (b + c) (a b) c = a (b c) Linear Equations Identity Property: a + 0 = a a 1 = a y 2 Slope: m = y 1 x 2 x 1 Point-Slope Formula: (y y 1 ) = m(x x 1 ) Distributive Property: a (b + c) = a b + a c Multiplicative Property of Zero: a 0 = 0 Slope-Intercept Formula: y = mx + b Additive Property of Equality: If a = b, then a + c = b + c Standard Equation of a Line: Ax + By = C Multiplicative Property of Equality: If a = b, then a c = b c Copyright 2011 by the Pennsylvania Department of Education. The materials contained in this publication may be duplicated by Pennsylvania educators for local classroom use. This permission does not extend to the duplication of materials for commercial use.

2 CONSTRUCTED-RESPONSE ITEM 13. Go to the next page to finish question 13. Pennsylvania Keystone Algebra I Item and Scoring Sampler

3 13. Continued. Please refer to the previous page for task explanation. Pennsylvania Keystone Algebra I Item and Scoring Sampler

4 SCORING GUIDE #13 ITEM INFORMATION Alignment A1.1.2 Depth of Knowledge 3 Mean Score 1.60 ITEM-SPECIFIC SCORING GUIDELINE Score Nonscorables Description Demonstrates a thorough understanding of how to write and solve a system of linear equations (including problem situations) using substitution or elimination and interpret solutions to problems in the context of the problem situation by correctly solving problems and clearly explaining procedures. Demonstrates a general understanding of how to write and solve a system of linear equations (including problem situations) using substitution or elimination and interpret solutions to problems in the context of the problem situation by correctly solving problems and clearly explaining procedures with only minor errors or omissions. Demonstrates a partial understanding of how to write and solve a system of linear equations (including problem situations) using substitution or elimination and interpret solutions to problems in the context of the problem situation by correctly performing a significant portion of the required task. Demonstrates minimal understanding of how to write and solve a system of linear equations (including problem situations) using substitution or elimination and interpret solutions to problems in the context of the problem situation. The response has no correct answer and insufficient evidence to demonstrate any understanding of the mathematical concepts and procedures as required by the task. Response may show only information copied from the question. B Blank, entirely erased, or written refusal to respond F Foreign Language K Off-task U Unreadable Pennsylvania Keystone Algebra I Item and Scoring Sampler

5 Top Scoring Response: t + s = 20 AND 6t + 4s = 94 Part A Answer What? OR equivalent OR equivalent Why? (2 score points) 1 point for each correct equation What? Part B Answer Why? 7 (packages of towels) [Note: carry over any errors from part A] (1 score point) 1 point for correct answer What? Part C Answer Why? Since John is buying soap in packages of 10 bars, the number of bars of soap he buys must be a multiple of 10. Since 16 is not a multiple of 10, it would not be possible for John to buy exactly 16 bars of soap. OR equivalent (1 score point) 1 point for correct answer Pennsylvania Keystone Algebra I Item and Scoring Sampler

6 STUDENT RESPONSE RESPONSE SCORE: 4 POINTS 13. Student has given two correct equations, t + s = 20 and $6t + $4s = $94. Student has given a correct answer, 7. Go to the next page to finish question 13. Pennsylvania Keystone Algebra I Item and Scoring Sampler

7 13. Continued. Please refer to the previous page for task explanation. Student has given a complete explanation. Pennsylvania Keystone Algebra I Item and Scoring Sampler

8 STUDENT RESPONSE RESPONSE SCORE: 3 POINTS Question 13 Student has given two correct equations, 6t + 4s = 94 and t + s = 20. Student has given an incorrect answer, 10. Pennsylvania Keystone Algebra I Item and Scoring Sampler

9 Question 13 Student has given a complete explanation. Pennsylvania Keystone Algebra I Item and Scoring Sampler

10 STUDENT RESPONSE RESPONSE SCORE: 2 POINTS 13. Student has given one correct equation, t 6 + s 4 = 94. Student has given an incorrect answer, 8. Go to the next page to finish question 13. Pennsylvania Keystone Algebra I Item and Scoring Sampler

11 13. Continued. Please refer to the previous page for task explanation. Student has given a complete explanation. Pennsylvania Keystone Algebra I Item and Scoring Sampler

12 STUDENT RESPONSE RESPONSE SCORE: 1 POINT Question 13 Student has given one correct equation, $6t + $4s = $94, and one incorrect equation, 8t + 10s = 20. Student has given an incorrect answer, 2. Pennsylvania Keystone Algebra I Item and Scoring Sampler

13 Question 13 Student has given an incorrect explanation. Pennsylvania Keystone Algebra I Item and Scoring Sampler

14 STUDENT RESPONSE RESPONSE SCORE: 0 POINTS 13. Student has given two incorrect equations, 20 = sx and 20 = tx. Student has given an incorrect answer, 10. Go to the next page to finish question 13. Pennsylvania Keystone Algebra I Item and Scoring Sampler

15 13. Continued. Please refer to the previous page for task explanation. Student has given an incorrect explanation. Pennsylvania Keystone Algebra I Item and Scoring Sampler

Pennsylvania Keystone Exams

Pennsylvania Keystone Exams Algebra I Item and Scoring Sampler 2015 Keystone Algebra I Sampler Table of Contents INFORMATION ABOUT ALGEBRA I Introduction...1 About the Keystone Exams...1 Item and Scoring