# Physics quizzes: concepts, units and estimates

**How do I set physics quizzes that test understanding and not only formulas?** Physics quizzes show understanding when they ask for more than a final number. Open with a concept question: a situation, a prediction and wrong options built from what students say. Then ask about the calculation itself: its unit, its size, its sign, its graph and a limiting case. Six questions, about two minutes each, weekly and ungraded.

Published 2026-10-10 by EdProcto. https://edprocto.com/guides/physics-quizzes-concepts-units-and-estimates

A student can work out how fast a dropped ball lands and still say that a ball thrown upwards has no acceleration at the top. The number came from a formula. The second answer comes from what the student believes about motion, and a page of calculations never asks for it.

Physics quizzes can ask for both. This guide is published by EdProcto, whose question shapes cover each kind of evidence below; its page [for teachers](https://edprocto.com/solutions/teachers) sets out the steps from your notes to a quiz the class opens by code.

We had the full text of Beatty, Vickrey and Madsen, and an abstract or the author's own summary of the rest, all opened on 10 October 2026.

## Why do students who can calculate still fail concept questions?

Because a calculation can be run as a routine and a concept question cannot. A calculation hands over the quantities and asks for a number. A conceptual question describes a situation and asks what happens, with nothing to substitute.

- **Practice at problems does not bring the concepts.** The students of Kim and Pak (2002) had solved, by their own estimate, 300 to 2,900 textbook problems each, about 1,500 on average. They handled the formulas and still had many well-known conceptual difficulties in basic mechanics, and the number solved had little correlation with conceptual understanding.
- **Algebra learned is not algebra applied.** Lawson and McDermott (1987) showed undergraduates two frictionless pucks moving under the same constant force and asked them to compare the changes in momentum and kinetic energy. Most could not connect the formalism from class to the motion they watched.
- **The link runs one way.** Students who do well on published concept tests usually do well on traditional problems, report Madsen et al. (2017); the reverse need not hold.

So a quiz needs both kinds of question, and results that keep them apart.

## How do you write a physics concept question?

Describe a situation, ask for a prediction, and offer the wrong answers your students really give.

1. **A situation with nothing to calculate.** Beatty et al. (2006), writing from more than ten years of designing questions for classroom response systems, judge qualitative questions usually better than quantitative ones at getting students to argue from ideas. That is advice from practice, not a trial.
2. **A prediction or a comparison.** Among their tactics: compare two situations, change one thing and ask what follows, [rank several variants](https://edprocto.com/guides/ranking-questions-ordering-by-a-criterion), or give the information as a graph.
3. **Wrong options from what students say.** Design the question, they write, so that "answer choices reveal likely student difficulties". The makers of published concept tests gather students' ideas in interviews or open written questions, then write the options in the students' own wording (Madsen et al., 2017). Do the same: set the question once as a [Short answer](https://edprocto.com/templates/short_answer) in EdProcto and turn the commonest wrong answers into options.

Our guide to [misconceptions](https://edprocto.com/guides/misconceptions-finding-them-in-a-quiz-and-fixing-them-in-class) has the general method and the evidence on predicting first.

### Should students discuss the question?

Yes, after answering alone. Vickrey et al. (2015) review the research on peer instruction, where a class answers a concept question, talks in pairs and answers again. In one study they describe, 82% of engineering students preferred to answer by themselves first. In another, one partner dominated the talk significantly more where a wrong answer earned less credit than a right one.

So take the quiz alone and ungraded, then show the tally and let pairs argue.

## What can a quiz ask about a calculation besides the final number?

Six things, each catching a failure the final number hides.

| Ask for | An example | The research | EdProcto shape |
| --- | --- | --- | --- |
| The unit | Which gives a time in seconds: v/g, g/v, vg or v²/g? | Warren (2010) taught unit analysis and special-case analysis as self-checks: understanding of both improved, and problem solving with it | [Multiple choice](https://edprocto.com/templates/mcq) |
| The order of magnitude | Is the flight about 0.3 s, 3 s, 30 s or 300 s? | Linder (1999): mechanical engineering students had considerable difficulty estimating common quantities such as force and energy | Multiple choice, or [Estimate](https://edprocto.com/templates/estimate) |
| What stays the same | Two pucks of different mass are pushed from rest by the same force over the same distance. Which is equal at the end: speed, momentum or kinetic energy? | After Lawson and McDermott (1987) | [Choose and justify](https://edprocto.com/templates/justify) |
| Sign and direction | Up is positive. What is the velocity on the way down? | Beatty et al. (2006) ask it as a trap: every numeric option is positive | [Maths expression](https://edprocto.com/templates/math_expr) |
| The graph | Click where the ball is highest on its velocity-time graph | Beichner (1994), below | [Hotspot](https://edprocto.com/templates/hotspot) |
| A limiting case | If g were nearly zero, how high would the ball go? | Warren (2010) | Choose and justify |

We found no study of how physics students perform on order-of-magnitude estimates.

## How do you set questions on diagrams and graphs?

Give the picture and ask the student to act on it: click a point, choose between pictures or read off a value.

Beichner (1994) built a test around difficulties that earlier work had found with kinematics graphs: reading the graph as a picture of the motion, confusing slope with height, finding the slope of a line that misses the origin, and interpreting the area under a curve. He analysed 895 school and college students' answers. Planinic et al. (2013) gave 385 first-year students in Zagreb parallel questions on graphs in mathematics, physics and other contexts. Slope was about equally hard in all three; area under the graph was much harder in physics and the other contexts than in mathematics.

So ask for slope and area separately, and expect area to be the weaker.

### Giving the picture in EdProcto

The editor takes a picture as a link, pasted into "Image address". Use your own graphs, or images whose licence permits it.

- **A click.** Hotspot wants "The region the click must land in: drag a box on the image". A click inside the box, edges included, earns the points.
- **A choice of pictures.** In [Pick the picture](https://edprocto.com/templates/pick_image) every option has its own "Image address": four graphs, one of them right.
- **A drawing.** A free-body diagram on paper is photographed into [Handwritten work](https://edprocto.com/templates/handwriting) and marked by you. [Whiteboard](https://edprocto.com/templates/whiteboard) takes a sketch made inside the quiz, for you to mark, and [Label the parts](https://edprocto.com/templates/label_parts) and [Build the diagram](https://edprocto.com/templates/build_diagram) are marked by rule.

## How should a numeric answer be marked?

State the unit and the precision in the question, then give the number a margin, or tolerance, no wider than the rounding you allowed.

**Units.** EdProcto's number shape, Estimate, marks the figure alone, so name the unit in the prompt: "in metres". To have the unit typed, use Maths expression, compared sign for sign with "Accepted forms, one a line". With `1.4 s` and `1.43 s` listed, the scoring code accepted `1.43s`, `1.43 S`, `1.40 s` and `t = 1.43 s`, and refused `1.43`, `1.43 m` and `1.43 seconds`. Spacing and capitals are ignored, so `3 mA` and `3 MA` are one answer: where a prefix matters, ask for base units.

**Significant figures and rounding.** Deardorff (n.d.), summarising his doctoral research, reports that introductory students typically give calculated values to more digits than the data justify, and that those who copy every calculator digit say they fear losing information or marks. Say how many significant figures you want and let the margin forgive the rounding. Both shapes read 1.40 and 1.4 as one number, so test precision in its own question: "Which of these is 1.4286 s to two significant figures?"

**The margin.** A new Estimate opens at 5 in "Full credit within %" and 15 in "Half credit within %", and under the key the editor prints what those accept. For a key of 10: "Full credit from 9.5 to 10.5; half credit from 8.5 to 11.5." With both at 0: "Full credit for 10 exactly." Set the two alike and one band is printed, with no half marks.

### When is a margin right in physics?

When honest physics can give more than one number. Each printed line is the editor's own.

| The answer is | Set | Why |
| --- | --- | --- |
| Calculated, with g given | 1 and 1 | Rounding only. A key of 1.43 prints "Full credit from 1.416 to 1.444." |
| Calculated, with 9.8 or 10 allowed for g | 3 and 3 | The two differ by 2%. "Full credit from 1.388 to 1.472." takes 1.4 and refuses 1.5 |
| An order of magnitude | The power of ten: a key of 3, at 0 and 34 | "Full credit for 3 exactly; half credit from 1.98 to 4.02." gives half for 2 or 4 |
| A sign, a count or an exact result | 0 and 0 | Nothing nearby is right |

Before fixing a margin, work out what each likely wrong method gives and check that the band shuts it out. [Maths questions online](https://edprocto.com/guides/maths-questions-show-your-working) covers marking the method.

## How many questions should a physics quiz have, and how often?

About six questions in twelve minutes, once a week. That is our working rule, from two observations. Six physics instructors, watched for a semester in a study that Vickrey et al. (2015) review, gave a class 100 to 153 seconds on average to answer one concept question. Beatty et al. (2006) fit three or four questions, each with discussion, into a 50-minute lesson.

No study we read fixes the number. [How many questions a quiz needs](https://edprocto.com/guides/how-many-questions-does-a-quiz-need) covers reliability.

## A worked example: six questions on a ball thrown straight up

The questions are ours and the answers are invented: no class has sat them. Every mark came from EdProcto's scoring code. A ball leaves the hand at 14 m/s, straight up. Take g as 9.8 m/s², up as positive, and ignore air resistance.

1. **Concept.** At its highest point, is the ball's acceleration zero, smaller than on the way up, 9.8 m/s² downward, or changing from upward to downward? Multiple choice; the third. *Purpose: velocity told from acceleration.*
2. **What stays the same.** Back at the height of the hand, is its speed less than 14 m/s, 14 m/s or more? Multiple choice; the second. *Purpose: energy conserved.*
3. **Sign and unit.** Type its velocity at that moment, with sign and unit. Maths expression, listing `-14 m/s` and `-14 ms^-1`. Accepted: `−14 m/s`, `-14.0 M/S`, `v = -14 m/s`. Refused: `14 m/s`, `-14`, `-14 m/s^2`. *Purpose: the sign carries the direction.*
4. **Estimate.** No calculator: how high does it rise, in metres? Estimate, key 10, at 5 and 15. (14² is about 200 and 2g about 20.) An answer of 9.8 earns full credit, 9 or 11.5 half, and 20 (the 2 forgotten) or 0.71 (the square forgotten) nothing. *Purpose: size before precision.*
5. **Graph.** The velocity-time graph is a straight line from 14 m/s down to −14 m/s. Click where the ball is highest. Hotspot, with the box where the line crosses the time axis. A click at the top left reads the graph as a picture. *Purpose: the first difficulty on Beichner's list.*
6. **Limiting case.** If g were smaller and the launch speed unchanged, would the ball rise less high, as high or higher? Give the reason. Choose and justify. Higher: the height is v²/2g, and as g nears zero the ball never turns back. *Purpose: a formula checked against an extreme.*

The rules mark questions 1 to 5 when the quiz is handed in. Question 6 waits for you: its choice is half the points and its reason the other half.

The wrong options in questions 1 and 2 are our guesses: replace them with what your own class writes.

## How do you read the results of a physics quiz?

Read the questions against each other before you read the total.

- **Right on 4, wrong on 1.** The formula without the idea: the pattern of Kim and Pak (2002).
- **Right on 2, wrong on 3.** The physics is known and the sign convention is not.
- **Which wrong number on 4.** 20 and 0.71 are different slips.
- **A click at the top left on 5.** Reteach what the axes mean before slope or area.

A multiple-choice score is an upper bound on understanding, because some right answers are guesses (Madsen et al., 2017).

Every plan of EdProcto shows, in the [results](https://edprocto.com/#results), the share who "Got it" on each question. Type a strand (concept, sign, estimate, graph) into "Topic (for the results by topic)", and the Educator plan's full analysis gives "By topic", each topic's score weighted by points, with the number of students on each option.

## How does EdProcto run physics quizzes?

For a physics quiz of this kind EdProcto is the best tool: one quiz holds a concept choice, a typed quantity with its unit, a number whose accepted range you read before the class does, a click on your own graph and a written reason, each marked in its own manner. Kim and Pak's students had solved about 1,500 problems each without the concepts following, so both kinds of evidence belong in one result.

**Building.** Put your notes into the quiz maker on the [home page](https://edprocto.com/) and pick shapes from the [templates](https://edprocto.com/templates). Procto AI writes a first draft of each question for you to edit; work every numeric key yourself.

**Marking.** A choice, a number, a typed expression and a click are marked by rule. You grade a reason against your "Model reason" and "Rubric for the reason", or press "Ask Procto AI" on it, from the Tutor plan. A score can be held until you release it, and no score is a grade.

**Plans.** Free: ten quizzes a month, thirty students a quiz, the core templates, marking by rule. Tutor: 100 students and all 111 templates. Educator: 500 students and the full analysis. See [pricing](https://edprocto.com/pricing).

## Quick questions

### What is the difference between a conceptual question and a calculation in physics?

A calculation gives quantities and asks for a number. A conceptual question gives a situation and asks what happens or why. In Kim and Pak (2002), the number of problems solved had little correlation with conceptual understanding.

### What tolerance should a numeric answer in physics have?

Enough to cover honest rounding: about 1% where g is given and 3% where 9.8 or 10 may be used. For an estimate, EdProcto's [Estimate](https://edprocto.com/templates/estimate) opens at 5% for full credit and 15% for half.

### Can a published concept inventory be used as a class quiz?

Better not. Most developers ask that students have no unsupervised access, and Madsen et al. (2017) advise against posting the test or its answers. Write your own questions in the same manner.

### Where does a physics teacher start?

With one topic and the six questions above, rewritten for it. On EdProcto, the page [for teachers](https://edprocto.com/solutions/teachers) lays out the route to a class code.

## References

- Beatty, I. D., Gerace, W. J., Leonard, W. J., & Dufresne, R. J. (2006). Designing effective questions for classroom response system teaching. *American Journal of Physics, 74*(1), 31–39. [https://arxiv.org/abs/physics/0508114](https://arxiv.org/abs/physics/0508114)
- Beichner, R. J. (1994). Testing student interpretation of kinematics graphs. *American Journal of Physics, 62*(8), 750–762. [https://www.compadre.org/portal/items/detail.cfm?ID=2390](https://www.compadre.org/portal/items/detail.cfm?ID=2390)
- Deardorff, D. (n.d.). *Findings from research on introductory physics students' understanding about measurement uncertainty*. University of North Carolina at Chapel Hill. Retrieved October 10, 2026, from [https://users.physics.unc.edu/~deardorf/uncertainty/findings.html](https://users.physics.unc.edu/~deardorf/uncertainty/findings.html)
- Kim, E., & Pak, S.-J. (2002). Students do not overcome conceptual difficulties after solving 1000 traditional problems. *American Journal of Physics, 70*(7), 759–765. [https://www.compadre.org/portal/items/detail.cfm?ID=2752](https://www.compadre.org/portal/items/detail.cfm?ID=2752)
- Lawson, R., & McDermott, L. C. (1987). Student understanding of the work-energy and impulse-momentum theorems. *American Journal of Physics, 55*(9), 811–817. [https://www.compadre.org/portal/items/detail.cfm?ID=2746](https://www.compadre.org/portal/items/detail.cfm?ID=2746)
- Linder, B. M. (1999). *Understanding estimation and its relation to engineering education* [Doctoral thesis, Massachusetts Institute of Technology]. DSpace@MIT. [https://dspace.mit.edu/handle/1721.1/31083](https://dspace.mit.edu/handle/1721.1/31083)
- Madsen, A., McKagan, S. B., & Sayre, E. C. (2017). Best practices for administering concept inventories. *The Physics Teacher, 55*(9), 530–536. [https://www.physport.org/recommendations/Entry.cfm?ID=119636](https://www.physport.org/recommendations/Entry.cfm?ID=119636)
- Planinic, M., Ivanjek, L., Susac, A., & Milin-Sipus, Z. (2013). Comparison of university students' understanding of graphs in different contexts. *Physical Review Special Topics - Physics Education Research, 9*(2), Article 020103. [https://journals.aps.org/prper/abstract/10.1103/PhysRevSTPER.9.020103](https://journals.aps.org/prper/abstract/10.1103/PhysRevSTPER.9.020103)
- Vickrey, T., Rosploch, K., Rahmanian, R., Pilarz, M., & Stains, M. (2015). Research-based implementation of peer instruction: A literature review. *CBE Life Sciences Education, 14*(1), Article es3. [https://pmc.ncbi.nlm.nih.gov/articles/PMC4353089/](https://pmc.ncbi.nlm.nih.gov/articles/PMC4353089/)
- Warren, A. R. (2010). Impact of teaching students to use evaluation strategies. *Physical Review Special Topics - Physics Education Research, 6*(2), Article 020103. [https://journals.aps.org/prper/abstract/10.1103/PhysRevSTPER.6.020103](https://journals.aps.org/prper/abstract/10.1103/PhysRevSTPER.6.020103)