Appendices — Office of Academic Compliance

Appendix A: Quantitative Reasoning Assessment Instrument and Item Analysis

Test questions are available internally and upon request. Please contact assess@virginia.edu with questions.

Appendix B: Student Sample

Institutional Research and Analytics collaborated with programs across seven undergraduate schools to recruit a representative sample of 369 fourth-year students who consented to participate in the assessment.

**Table B1.** Quantitative Reasoning Assessment Participation by School for Fourth-Year Students in Spring 2024
School	Number of Participants	Participant Percentage	Total Population	Total Population Percentage
Architecture	11	3%	123	3%
Arts and Sciences	172	47%	2386	58%
Commerce	45	12%	393	10%
Continuing and Professional Studies	0	0%	137	3%
Education and Human Development	33	9%	156	4%
Engineering	74	20%	702	17%
Leadership and Public Policy	17	5%	100	2%
Nursing	17	5%	128	3%

Quantitative Reasoning Assessment Participation by School Totals:

Number of Participants: 369
Total Population 4125

Appendix C: Question Topic Matrix

The test questions were designed to address three major topics in quantitative reasoning:

general mathematics/mathematical reasoning (including arithmetic, geometry, and algebra) (14 questions);
statistics/statistical reasoning (6 questions);

calculus/trigonometry (5 questions).

**Table C1. Question Matrix by Three Major Topics in Quantitative Reasoning**
Question	Question Difficulty	Category
1. What is the prob. that person lives in City?	Easy	General Math/Math Reasoning
2. What is the prob. that person alone is not 65+?	Moderate	General Math/Math Reasoning
3. A store marks up the wholesale price…	Easy	General Math/Math Reasoning
4. A business meeting includes 6 vice presidents..	Easy	General Math/Math Reasoning
5. If the average of three numbers x, y, and z…	Easy	General Math/Math Reasoning
6. The number of websites on the Internet…	Easy	General Math/Math Reasoning
7. If the population was 100,000…what does the model suggest…	Moderate	General Math/Math Reasoning
8. In 1992 the consumer price index…	Easy	General Math/Math Reasoning
9. All three sides of a certain triangle are two inches long…	Moderate	General Math/Math Reasoning
10. The Ace Corporation believes that the retail price of its widgets…	Hard	General Math/Math Reasoning
11. A box contains fuses…prob. that a total of 2 fuses are selected…	Moderate	General Math/Math Reasoning
12. During a recent trip to the grocery store…	Moderate	General Math/Math Reasoning
13. If the correlation between body weight…	Easy	Stats/Stats Reasoning
14. …research relies on results from a sample…	Moderate	Stats/Stats Reasoning
15. For 1 month, 500 elementary students…	Moderate	Stats/Stats Reasoning
16. A study was conducted…for treating AIDS patients…	Hard	Stats/Stats Reasoning
17. A new medication is being tested…	Easy	Stats/Stats Reasoning
18. A recent survey by a large American magazine..	Moderate	Stats/Stats Reasoning
19. Suppose x and y are positive numbers…	Easy	General Math/Math Reasoning
20. Joe has a rectangular garden…	Moderate	General Math/Math Reasoning
21. Consider two functions, f and g…	Easy	Calculus/Trig
22. If the domain of the function y=…	Moderate	Calculus/Trig
23. What could be the graph of…	Hard	Calculus/Trig
24. The radius of a circle is given as 10 cm…use the concept of differentials…	Hard	Calculus/Trig
25. …where f is the function whose graph is shown…	Hard	Calculus/Trig

Appendix D: Test Blueprint and Accomplished Learning Outcomes Matrix (Accomplished Learning Outcomes)

The test questions were designed to address three major topics in quantitative reasoning and each question was mapped back to the defined learning outcomes.

Proposed replacement for matrix table above:

Questions	Learning Outcomes (1-10) See Legend Below
1. What is the prob. that person lives in City?	1
2. What is the prob. that person alone is not 65+?	1
3. A store marks up the wholesale price…	3, 5
4. A business meeting includes 6 vice presidents...	3, 5
5. If the average of three numbers x, y, and z…	3, 6
6. The number of websites on the Internet…	3, 6
7. If the population was 100,000…what does the model suggest…	1, 3
8. In 1992 the consumer price index…	3
9. All three sides of a certain triangle are two inches long…	3
10. The Ace Corporation believes that the retail price of its widgets…	1, 3, 4, 6
11. A box contains fuses…prob. that a total of 2 fuses are selected…	3
12. During a recent trip to the grocery store…	3, 5, 8
13. If the correlation between body weight…	7
14. …research relies on results from a sample…	10
15. For 1 month, 500 elementary students…	7, 9, 10
16. A study was conducted…for treating AIDS patients…	7, 9
17. A new medication is being tested…	9
18. A recent survey by a large American magazine...	10
19. Suppose x and y are positive numbers…	1, 3
20. Joe has a rectangular garden…	3, 4, 5, 8
21. Consider two functions, f and g…	3
22. If the domain of the function y=…	3
23. What could be the graph of…	3
24. The radius of a circle is given as 10 cm…use the concept of differentials…	4
25. …where f is the function whose graph is shown…	3, 4

Learning Outcomes Legend

A graduating fourth-year undergraduate student at the University of Virginia will be able to:

Interpret mathematical models such as formulas, graphs, tables, and schematics, and draw inferences from them.
Communicate mathematical information symbolically, visually, numerically, and verbally.
Use arithmetical, algebraic, geometric, and analytic methods to solve problems.
Estimate and check answers to mathematical problems to determine reasonableness.
Solve word problems using quantitative techniques and interpret the results.
Apply mathematical/statistical techniques and logical reasoning to produce predictions, identify optima, and make inferences based on a given set of data or quantitative information.
Judge the soundness and accuracy of conclusions derived from quantitative information, recognizing that mathematical and statistical methods have limits and discriminating between association and causation.
Solve multi-step problems.
Apply statistics to evaluate claims and current literature.
Demonstrate an understanding of the fundamental issues of statistical inference, including measurement and sampling.

Appendix E: Disaggregated Data

Disaggregated data are available internally and upon request. Please contact assess@virginia.edu with questions.