2005 NAEP Mathematics Sample Questions at Grade 12

The sample questions below give a brief introduction to the materials used to assess the mathematical ability of twelfth-grade students. All questions are based on the NAEP mathematics framework, which defines the test design and content. The framework was developed through an extensive national consensus process and adopted by the National Assessment Governing Board. Visit the Governing Board's website to browse the full text of the mathematics framework. In addition to the overall percentage of students who answered the question correctly, the percentage of students at each achievement level who answered correctly is presented. To learn more about achievement levels, read specific descriptions of the *Basic*, *Proficient*, and *Advanced* achievement levels in mathematics.

Several other tools are available to help students, parents, and teachers look more closely at NAEP questions. View the item maps that provide concrete examples of what students at various achievement levels likely know and can do. Visit the NAEP Questions Tool to see over 1,800 released items in all NAEP subject areas.

The following multiple-choice question comes from the measurement and geometry content area. The question required students to determine an angle formed by a cross street between two parallel streets.

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View this question, at score 142, on a map of NAEP mathematics items.

The following is a short constructed-response question from the algebra content area. The question asked students to determine the composition *f* ° *g* of a quadratic function *f* and a linear function *g*. Responses were rated as “Correct,” “Partial,” or “Incorrect.” The sample student response below was rated "Correct."

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View this question, at score 195, on a map of NAEP mathematics items.