FRQ 3 – Experimental Design

Overview

AP Physics 1 FRQ 3 is the Experimental Design and Analysis question (often called the LAB question), worth 10 points with a suggested time of 25-30 minutes. It's the third of four free-response questions in Section II, which gives you 95 minutes total and counts for 50% of your AP Physics 1 score. The question has two halves: first you design an experiment to answer a scientific question, then you analyze real data from a similar (but not identical) experiment, usually by plotting points, drawing a best-fit line, and extracting a physical quantity from the slope.

This is the only AP Physics 1 FRQ where you're in charge of the setup. You decide what to measure, what to vary, what to hold constant, and how to turn messy data into a clean answer. The skills tested are creating quantitative graphs, calculating unknown quantities, predicting how variables depend on each other, and designing experimental procedures.

How AP Physics 1 FRQ 3 Is Scored

FRQ 3 is worth 10 of the 40 free-response points, and those points split roughly evenly between the Design half and the Analysis half. The exact distribution shifts from year to year, but released scoring guidelines follow a consistent pattern. Here's what typically earns credit:

Two scoring realities are worth internalizing. First, graders reward procedures that could actually be performed in a typical high school lab with realistically obtainable equipment. A laser interferometer loses you points; a meter stick and a motion sensor earn them. Second, your procedure must vary a single parameter and measure how that change affects a single characteristic. Changing two things at once breaks the experiment.

Heads up: starting with the May 2027 exam, the free-response section shrinks slightly from 100 to 95 minutes (and the multiple-choice section grows to 42 questions in 85 minutes). There are still 4 FRQs, so plan on the same 25-30 minutes for this question.

How to Answer FRQ 3, Step by Step

The winning move is to plan your analysis before you write your procedure. If you know you'll plot pressure vs. depth and pull density from the slope, your procedure writes itself: measure pressure at several depths. Here's a timeline that fits the 25-30 minute window.

Minutes 0-3: Read both halves first

Read the entire question before writing anything. The Design half and the Analysis half investigate related physics, so the data table in the second half often hints at what kind of procedure the first half wants. Note what relationship you're investigating and what equipment you're given. The equipment list is a constraint, not a suggestion. If the problem says "no scale," your procedure can't weigh anything.

Minutes 3-9: Write the procedure

A scoring procedure answers four questions, and you can write it as short numbered steps:

• What will you vary? (the independent variable)
• What will you measure, and with what tool? (the dependent variable)
• What stays constant? (everything else)
• How will you reduce uncertainty? (multiple trials at each value, then average)

Specificity is the difference between credit and no credit. "Measure the force" is vague. "Use a spring scale to measure the force needed to pull the block at constant velocity" shows you understand how the measurement actually happens. Plan for at least 5 data points across a wide range so a trend is visible. You don't need lab-manual length. Four or five tight, numbered steps earn full credit faster than two paragraphs.

Minutes 9-13: Describe the analysis plan

State exactly what goes on each axis and what feature of the graph answers the question. This is where linearization comes in. Physics relationships are often non-linear, but a straight line is the only graph whose slope means one consistent thing. So you transform a variable until the relationship looks like $y = mx + b$.

Example: for a pendulum, $T = 2\pi\sqrt{L/g}$, so plotting $T$ vs. $L$ gives a curve. Square both sides: $T^2 = \frac{4\pi^2}{g}L$. Now $T^2$ vs. $L$ is a line with slope $\frac{4\pi^2}{g}$, and $g = \frac{4\pi^2}{\text{slope}}$. Writing that one algebra step in your answer shows the grader exactly why your graph works.

"Graph the data" earns nothing. "Plot $T^2$ on the vertical axis and $L$ on the horizontal axis; the slope equals $4\pi^2/g$, so $g = 4\pi^2/\text{slope}$" earns everything.

Minutes 13-21: Build the graph

This is precision work, and it's often around 30% of the question's points. Take the time to:

• Choose scales in easy multiples (1, 2, 5, 10) that spread the data across most of the grid
• Label both axes with the quantity and its units
• Plot points carefully and visibly
• Draw a best-fit line with a ruler that balances points above and below it

Your best-fit line should NOT connect the dots, and it should NOT be forced through the origin unless the physics says the intercept is zero. If you transformed a quantity (like calculating $v^2$ from measured $v$), fill in the blank table column with your calculated values before plotting.

Minutes 21-28: Calculate and interpret

Compute the slope using two points on your best-fit line, not two data points. Pick points far apart on the line for accuracy, show $m = \frac{y_2 - y_1}{x_2 - x_1}$ with numbers and units, then connect the slope back to the physics. If the slope equals $2g$, write that explicitly and divide by 2 to report your experimental value of $g$, with units.

Minutes 28-30: Check

Verify every axis has units, your procedure actually isolates one variable, and your final answer responds to the question asked. Then move on. FRQ 4 is waiting.

Worked Example: The Liquid Density Question

A released AP Physics 1 FRQ 3 gives students a cylindrical container half filled with a liquid of unknown density $\rho$, plus extra liquid, meter sticks, and a pressure sensor. No scale. The task: design an experiment and a graph to determine $\rho$.

The design logic. The relevant physics is $P = P_0 + \rho g h$, where $h$ is depth below the surface. The pressure sensor measures $P$; the meter stick measures $h$. So a scoring procedure looks like this (example response, written the way a grader wants to see it):

1. Place the pressure sensor at a measured depth $h$ below the liquid's surface, using the meter stick to measure $h$.
2. Record the pressure $P$ at that depth.
3. Repeat for at least 5 different depths spanning the container.
4. Take multiple pressure readings at each depth and average them to reduce uncertainty.

The analysis plan. Plot $P$ on the vertical axis and $h$ on the horizontal axis. The equation $P = P_0 + \rho g h$ is already linear in $h$, with slope $\rho g$. So $\rho = \text{slope}/g$. No linearization needed here, just the recognition that the slope, not any single point, gives the density.

The data half. The same question then hands students data from a different experiment: water exits a small hole in a cylinder, and the table lists hole depth $h$ vs. exit speed $v$, governed by $v = \sqrt{2gh}$. Plotting $v$ vs. $h$ gives a curve, so you linearize: $v^2 = 2gh$. Plot $v^2$ (calculated in the blank table column) against $h$, draw a best-fit line, and the slope equals $2g$. Compute the slope from the line, divide by 2, and you have an experimental value for $g$. That full chain (transform, plot, fit, slope, interpret) is exactly the sequence FRQ 3 rewards every year.

Linearization Patterns Worth Memorizing

Most FRQ 3 analysis sections come down to recognizing one of a few transformations. If the relationship is $y = kx^2$, plot $y$ vs. $x^2$. If it's $y = k\sqrt{x}$, plot $y^2$ vs. $x$ (or $y$ vs. $\sqrt{x}$). If it's $y = k/x$, plot $y$ vs. $1/x$. In every case, the goal is the same: get the equation into $y = mx + b$ form, then identify what physical combination of constants the slope $m$ represents before you ever touch the graph paper.

Common setups that show up because they're feasible in a school lab: carts and objects on inclines (vary angle, measure acceleration), spring and pendulum oscillations (vary mass or length, measure period), fluid pressure vs. depth, and collisions analyzed with photogates or video analysis. For each one, ask yourself what single variable you'd change and what straight-line graph you'd build. That habit is the best FRQ 3 prep there is.

Common Mistakes

• Vague procedures. "Measure the velocity" doesn't tell a grader how. Fix: name the tool and the measurement ("use a motion sensor to record position vs. time, then find velocity from the slope").
• Forgetting controls. Varying one quantity while accidentally changing another invalidates the experiment. Fix: always include an explicit statement of what stays constant.
• Skipping uncertainty reduction. This is often a dedicated point. Fix: write "repeat each trial 3 times and average the measurements" somewhere in your procedure, every time.
• Connecting the dots instead of drawing a best-fit line. Real data has scatter, and a dot-to-dot zigzag has no meaningful slope. Fix: draw one straight ruler line that balances points above and below it, and don't force it through the origin unless the physics demands a zero intercept.
• Computing slope from data points. The slope point comes from your best-fit line. Fix: pick two widely separated points on the line itself, even if no data point sits there.
• Stopping at the slope. A number without interpretation leaves points behind. Fix: explicitly state what the slope represents (for example, slope $= 2g$) and solve for the quantity requested, with units.

Practice and Next Steps

The fastest way to improve at FRQ 3 is repetition with feedback: write a full procedure-graph-slope response, then compare it line by line against a scoring guide. Work through real released questions in the AP Physics 1 past exams collection, and use FRQ practice with instant scoring to see exactly which rubric points you're earning and which you're leaving behind. The FRQ question bank has more LAB-style prompts to drill the linearization step until it's automatic.

Since FRQ 3 sits inside a 100-minute section, practice it alongside the other question types so your pacing holds up. The companion guides on FRQ 1, Mathematical Routines and FRQ 4, Qualitative/Quantitative Translation cover the rest of the section. When you're ready to simulate the full exam, take a full-length AP Physics 1 practice exam under timed conditions and see where your score lands.