Experimental Design FRQ AP Physics 1 — How to Write It (2026)
The experimental design FRQ is one of the five free response questions on AP Physics 1 and is worth 12 points. It is one of the most distinctive — and most failed — question types on the exam. This guide covers exactly what AP readers look for and how to earn full marks.
What Is the Experimental Design FRQ?
The experimental design FRQ asks you to design a controlled experiment to test a specific physics relationship. Unlike other FRQs that ask you to analyze given data, this question requires you to create the experimental setup from scratch.
You will be given:
- A physics relationship to investigate (e.g., "how does the mass of a cart affect its acceleration?")
- A list of available equipment
- Specific tasks: describe the procedure, identify variables, explain data analysis, and address sources of error
This question appears in Part B (no calculator) of the AP Physics 1 FRQ section.
Experimental Design FRQ: 12-Point Breakdown
| Task | Points | What to Write |
|---|---|---|
| Identify the independent variable | 1 | The variable you change |
| Identify the dependent variable | 1 | The variable you measure |
| Describe procedure clearly enough to replicate | 3 | Step-by-step, specific, complete |
| Identify controlled variables | 1 | What you hold constant and why |
| Describe data collection and analysis | 3 | What you graph, expected shape, how to find the quantity |
| Address sources of error or uncertainty | 2 | Specific, not generic ("human error" is not accepted) |
| Connect analysis to physics principle | 1 | Why this experiment tests the relationship |
Step-by-Step: How to Write the Experimental Design FRQ
Step 1: Identify and state your variables clearly
Independent variable (IV): What you deliberately change between trials. Dependent variable (DV): What you measure as a result. Controlled variables: Everything else you keep constant.
Example prompt: "Design an experiment to determine how the length of a pendulum affects its period."
- IV: Length of the pendulum (L)
- DV: Period of oscillation (T)
- Controlled: Mass of the bob, release angle (keep it small, <15°), location (same g)
Always write these out explicitly. AP readers award the variable identification points separately from the procedure.
Step 2: Write a replicable procedure
Your procedure must be specific enough that another student could follow it and get the same result. Vague language loses points.
❌ Too vague:
"Change the length and measure the period."
✅ Specific and replicable:
"1. Set up a pendulum by attaching a 50 g bob to a string fixed to a rigid support. 2. Measure the length L from the pivot to the center of the bob using a meter stick. 3. Displace the bob 10° from vertical and release from rest. 4. Use a stopwatch to measure the time for 10 complete oscillations. Divide by 10 to find the period T. 5. Repeat steps 2–4 for at least 5 different string lengths ranging from 0.20 m to 1.00 m. 6. Record L and T for each trial."
Procedure checklist:
- Specific equipment named (not just "measuring device")
- Specific values given where relevant (angles, distances, repetitions)
- Multiple trials mentioned (at least 5 data points)
- How the DV is measured is clear
- How IV is varied is clear
Step 3: Describe your data analysis
AP readers want to know:
- What you graph (DV vs IV or a linearized version)
- What the expected shape is
- How you extract the physics quantity from the graph
Example (pendulum):
"Plot T (y-axis) vs √L (x-axis). For a simple pendulum, $T = 2\pi\sqrt{L/g}$, so plotting T vs √L should give a straight line through the origin with slope $2\pi/\sqrt{g}$. Use the slope of the best-fit line to calculate g: $g = (2\pi/\text{slope})^2$."
Why linearize? If you plot T vs L directly, you get a curve. Curves are hard to analyze. Linearizing the relationship (plotting T vs √L) gives a straight line whose slope contains the physics.
Common linearization transformations:
| Relationship | Plot | Slope Equals |
|---|---|---|
| $y = kx$ | y vs x | k |
| $y = kx^2$ | y vs x² | k |
| $y = k/x$ | y vs 1/x | k |
| $y = k\sqrt{x}$ | y vs √x | k |
Step 4: Identify controlled variables with justification
Do not just list controlled variables — explain why each must be controlled.
❌ "Keep mass constant."
✅ "Keep the mass of the bob constant because for a simple pendulum the period is independent of mass, but varying mass could introduce air resistance differences that would confound the results."
Step 5: Address sources of error specifically
"Human error" and "measurement error" are not accepted by AP readers. You must name a specific source and explain its effect.
Accepted error sources:
- "The release angle may vary between trials if released by hand. A larger angle violates the small-angle approximation, making the period longer than the model predicts."
- "Air resistance acts on the pendulum, slightly lengthening the measured period compared to the ideal frictionless model."
- "The string may stretch slightly as the bob swings, effectively increasing L and artificially increasing T."
Structure for full credit:
"[Specific source] causes [specific effect on the measurement], which would [overestimate/underestimate] [the DV/slope/result]."
Common Mistakes on the Experimental Design FRQ
Describing the relationship instead of the experiment. "The period increases as the length increases" describes the physics but does not describe what you would actually do. Write the procedure, not the prediction.
Forgetting to address multiple trials. One data point is not an experiment. AP readers expect at least 5 data points across a range of the IV. State this explicitly.
Vague error analysis. "There could be errors in measurement" earns zero points. Name the source, name the effect.
Not linearizing the graph. If the expected relationship is not linear, plotting the raw variables gives a curve that is hard to use for analysis. Always linearize and explain the slope.
Mixing up IV and DV. The IV is what you control. The DV is what you observe. If you say "measure the mass to find the period," you've implied mass is the DV — wrong.
Example: Full-Credit Experimental Design Response
Prompt: Design an experiment to determine the relationship between the net force on a cart and its acceleration.
Variables:
- IV: Net force applied to the cart (F), varied by hanging different masses over a pulley
- DV: Acceleration of the cart (a), measured using a motion detector
- Controlled: Total mass of the cart system, track surface (frictionless or consistent friction), string length
Procedure:
- Set up a low-friction track with a cart of mass M. Connect a string over a pulley at the end of the track to a hanging mass m.
- Use a motion detector at the end of the track to record the cart's position vs. time.
- Release the cart from rest. Use the motion detector software to find acceleration a from the slope of the velocity-time graph.
- Repeat with at least 6 different hanging masses (e.g., 20 g, 40 g, 60 g, 80 g, 100 g, 120 g). Record F = mg (weight of hanging mass) and a for each trial.
- Keep M constant by not changing the cart or adding masses to it.
Data Analysis: Plot a (y-axis) vs F (x-axis). By Newton's second law, $a = F/M$, so the graph should be linear through the origin with slope 1/M. Use the slope of the best-fit line to calculate M and compare to the directly measured mass of the cart.
Source of error: Friction in the pulley and between the cart and track reduces the net force on the cart. This means the actual acceleration is less than F/M predicts, causing the slope to be slightly less than 1/M and overestimating M.