5 Last-Minute Physics Formulas Every ACT Student Must Memorize

The ACT Science section throws graphs, data tables, and experimental scenarios at you at lightning speed. While it’s not a pure physics test, about 40% of the questions involve interpreting scientific data that assumes you know basic physics relationships. When you’re staring at a velocity-time graph or a force diagram with 45 seconds left on the clock, having these formulas locked in your memory can mean the difference between guessing and scoring.

Why Physics Formulas Matter on the ACT

The ACT doesn’t hand you a formula sheet.

You need these relationships stored in your brain, ready to deploy when a passage describes motion, density, or force. The test writers assume you’ve seen basic physics concepts in your science classes. They build questions around interpreting graphs and tables that represent these relationships.

Understanding formulas helps you spot patterns in data faster. When you see a linear relationship on a graph, recognizing it as distance versus time lets you calculate speed without second-guessing yourself. When a table shows mass and volume, density calculations become automatic.

The Science section moves at a brutal pace. You have about 52 seconds per question across 40 questions. Spending 15 seconds trying to remember whether force equals mass times acceleration or acceleration times mass costs you precious time.

The Five ACT Physics Formulas to Memorize

These five formulas appear repeatedly in ACT Science passages. Master them, and you’ll handle the majority of physics-related questions the test throws at you.

1. Density Formula

d = m / V

Density equals mass divided by volume.

This formula shows up constantly in chemistry and physics passages. The ACT loves giving you a table with mass and volume measurements, then asking which substance is densest or how density changes with temperature.

Example: A passage shows three metal cubes. Cube A has mass 80g and volume 10 cm³. Cube B has mass 120g and volume 20 cm³. Which is denser?

Cube A: 80g / 10 cm³ = 8 g/cm³
Cube B: 120g / 20 cm³ = 6 g/cm³

Cube A wins. The calculation takes 10 seconds if you know the formula cold.

Common ACT twist: They’ll ask about floating or sinking. Remember that objects float in fluids less dense than themselves. If water has density 1 g/cm³, anything above that sinks.

2. Speed and Velocity

v = d / t

Velocity (or speed) equals distance divided by time.

Motion graphs dominate ACT Science. You’ll see distance-time graphs, velocity-time graphs, and acceleration-time graphs. Knowing this relationship helps you interpret slopes and calculate values from data points.

Example: A car travels 150 miles in 3 hours. What’s its average speed?

v = 150 miles / 3 hours = 50 mph

The ACT often flips this formula around. They might give you speed and time, asking for distance. Rearrange: d = v × t. If a runner moves at 5 m/s for 20 seconds, they cover 100 meters.

Watch your units. The test loves mixing meters per second with kilometers per hour. If units don’t match, your answer will be wrong even if your math is perfect. Converting units correctly matters as much as knowing the formula, and mental math tricks that will transform your calculation speed can help you handle these conversions under time pressure.

3. Newton’s Second Law

F = ma

Force equals mass times acceleration.

This formula connects three fundamental concepts: how hard you push something (force), how much stuff you’re pushing (mass), and how fast it speeds up (acceleration).

Example: A 10 kg box accelerates at 2 m/s². What force is applied?

F = 10 kg × 2 m/s² = 20 Newtons

The ACT uses this in scenarios about rockets, cars, friction, and falling objects. They might describe an experiment where different forces are applied to objects of varying masses, then ask you to predict acceleration.

Understanding why objects fall at the same rate regardless of mass helps clarify how this formula works in gravitational scenarios. On Earth, gravity provides constant acceleration (about 10 m/s²), so heavier objects need proportionally more force to achieve that same acceleration.

Common mistake: Confusing mass with weight. Mass is measured in kilograms. Weight is a force (mass times gravitational acceleration), measured in Newtons. The ACT will test whether you know the difference.

4. Slope Formula

m = (y₂ – y₁) / (x₂ – x₁)

Slope equals the change in y divided by the change in x.

Technically this is math, not physics, but it’s absolutely critical for ACT Science. Nearly every passage includes graphs. Reading slope tells you rates of change, relationships between variables, and trends in data.

Example: A temperature graph shows a substance at 20°C at time 0 and 80°C at time 10 minutes. What’s the rate of temperature increase?

m = (80 – 20) / (10 – 0) = 60 / 10 = 6°C per minute

Positive slopes mean both variables increase together. Negative slopes mean one increases while the other decreases. Zero slope means no change. Undefined slope (vertical line) means one variable changes while the other stays constant.

The ACT asks about slope interpretation constantly. “Which graph shows the fastest rate of cooling?” means “Which has the steepest negative slope?” Knowing the formula helps you calculate exact values when eyeballing isn’t enough.

5. Work and Energy

W = Fd

Work equals force times distance.

This formula connects energy transfer to physical motion. When you push a box across a floor, you’re doing work. The amount depends on how hard you push (force) and how far the box moves (distance).

Example: You push a cart with 50 Newtons of force for 10 meters. How much work did you do?

W = 50 N × 10 m = 500 Joules

The ACT uses this in energy passages. They’ll describe machines, ramps, or lifting scenarios, then ask about energy efficiency or work output.

Related concept: Power equals work divided by time (P = W/t). If you do 500 Joules of work in 10 seconds, you’re generating 50 Watts of power. The test sometimes combines these formulas in multi-step questions.

Understanding what happens to energy during elastic and inelastic collisions extends this concept to scenarios where energy transforms between different types rather than being created or destroyed.

How to Apply These Formulas on Test Day

Knowing formulas isn’t enough. You need a system for recognizing when to use them.

Step 1: Identify the Variables in the Question

Read the question and passage carefully. What measurements are given? What’s being asked?

If you see mass and volume, think density. If you see distance and time, think speed. If you see force and mass, think acceleration.

The ACT rarely uses physics terminology directly. Instead of saying “calculate the density,” they might ask “which substance has the greatest mass per unit volume?” Same concept, different words.

Step 2: Match the Scenario to Your Formula List

Once you know what’s given and what’s needed, match it to your memorized formulas.

Create a mental checklist:
– Density: Do I have mass and volume?
– Speed: Do I have distance and time?
– Force: Do I have mass and acceleration?
– Slope: Am I looking at a graph?
– Work: Do I have force and distance?

This matching process should take 5 seconds max. If it’s taking longer, you probably need more practice with the formulas.

Step 3: Plug In and Solve

Insert the numbers, do the math, check your units.

The ACT loves answer choices that differ by powers of 10. If you get 0.5 but the closest answer is 5.0, you probably made a unit conversion error or forgot to move a decimal point.

Double-check that your answer makes physical sense. If you calculate a car’s speed as 5,000 mph, something went wrong. If a density comes out negative, you made a sign error somewhere.

“The students who score highest on ACT Science aren’t necessarily the ones who know the most physics. They’re the ones who recognize patterns in data fastest and apply basic formulas accurately under time pressure. Speed comes from confidence, and confidence comes from practice.”

Common Mistakes and How to Avoid Them

Even students who know these formulas make predictable errors under test pressure. Recognizing these traps helps you avoid them.

Mistake	Why It Happens	How to Fix It
Mixing up numerator and denominator	Density vs. volume per mass	Write d = m/V on scratch paper at test start
Forgetting to square or cube units	Volume is cm³, not cm	Always write units in your calculation
Using wrong slope points	Reading graph coordinates incorrectly	Mark your points clearly before calculating
Confusing speed and velocity	Treating them as different formulas	For ACT purposes, they’re the same
Multiplying when you should divide	Panicking and guessing the operation	Rearrange formula algebraically before plugging numbers

Understanding common algebra mistakes and how to avoid them helps prevent calculation errors that plague many students during timed tests.

The unit trap catches more students than any other mistake. If a question gives you kilometers and hours but asks for meters per second, you must convert before calculating. Missing this step guarantees a wrong answer.

Memory Tricks That Actually Work

Memorizing five formulas sounds easy until test anxiety hits and your mind goes blank. These techniques help lock the formulas in long-term memory.

Create acronyms: “Dumb Monkeys Vote” for d = m/V (density). “Violent Dogs Turn” for v = d/t (velocity). Make them weird and memorable.

Use physical gestures: When you think “force equals mass times acceleration,” make a pushing motion. Physical memory reinforces mental memory.

Practice with real scenarios: Don’t just memorize symbols. Calculate your own walking speed from home to school. Estimate your backpack’s density. Use the formulas in contexts you actually experience.

Write them out 20 times: Old-school, but effective. Writing engages different brain pathways than reading. Do this three days before the test, then again the night before.

Test yourself randomly: Set phone reminders throughout the day. When they go off, recite all five formulas from memory. If you can do this while distracted, you’ll definitely remember during the test.

The goal isn’t just memorization. You want these formulas to become automatic, like knowing your phone number. When you see mass and volume, “d = m/V” should pop into your head instantly.

Practice Problems to Test Your Knowledge

Try these ACT-style scenarios. They mirror the format and difficulty you’ll see on test day.

Problem 1: A student measures three rock samples. Sample A: 45g, 15 cm³. Sample B: 60g, 12 cm³. Sample C: 75g, 25 cm³. Which has the highest density?

Calculate each:
– A: 45/15 = 3 g/cm³
– B: 60/12 = 5 g/cm³
– C: 75/25 = 3 g/cm³

Answer: Sample B.

Problem 2: A graph shows distance (meters) on the y-axis and time (seconds) on the x-axis. At t=0, d=0. At t=10, d=50. What’s the object’s speed?

Slope = (50-0)/(10-0) = 5 m/s

Answer: 5 m/s.

Problem 3: A 5 kg object accelerates from rest at 4 m/s². What force is applied?

F = ma = 5 × 4 = 20 N

Answer: 20 Newtons.

Problem 4: A worker pushes a crate with 100 N of force for 8 meters. How much work is done?

W = Fd = 100 × 8 = 800 J

Answer: 800 Joules.

If you solved all four correctly in under two minutes, you’re ready. If not, review the formulas and try again tomorrow.

What the ACT Actually Tests

The ACT Science section doesn’t ask you to derive formulas or explain theoretical physics. It tests data interpretation skills using scientific contexts.

You’ll see passages describing experiments, then questions asking you to:
– Read values from graphs and tables
– Identify trends and patterns
– Make predictions based on data
– Compare experimental results
– Calculate simple values using given information

Physics formulas support these tasks. When a graph shows a linear relationship between force and acceleration, recognizing F = ma helps you understand what the graph represents and predict what happens if mass changes.

The test also includes chemistry and biology passages, but the same principle applies. Basic formulas and concepts help you interpret data faster. Knowing that density determines whether objects float helps you answer questions about experimental setups involving liquids and solids.

About 15 of the 40 questions directly involve calculations or formula applications. The rest test reading comprehension, graph interpretation, and logical reasoning. But having formulas memorized gives you confidence and speed, which helps on every question type.

Building Speed Through Repetition

Knowing formulas helps. Knowing them instantly wins.

The difference between a 25 and a 30 on ACT Science often comes down to speed. Students who finish with time to review their answers score higher than equally knowledgeable students who barely finish.

Formula fluency builds speed. When you don’t need to pause and remember whether density is mass over volume or volume over mass, you save 5 seconds per question. Across 15 calculation questions, that’s 75 seconds, enough time to review 5-6 answers.

Practice timed drills:
– Set a timer for 30 seconds
– Solve a density problem
– Check your answer
– Repeat with different numbers

Do 10 problems in a row. Track your time for each. Your goal is consistent 20-second solutions. When you hit that mark, you’re ready for test conditions.

Mix formula types randomly. In real passages, you won’t know which formula you need until you read the question. Practicing mixed problems builds the pattern-recognition skills that make test day easier.

Beyond Formulas: Understanding Relationships

Formulas are tools, not magic spells. Understanding the relationships they represent makes you a better problem solver.

Density isn’t just m/V. It’s the concept that materials pack atoms together differently. Lead atoms pack tightly. Styrofoam atoms spread out. That’s why lead sinks and styrofoam floats, even though both are solid matter.

Speed isn’t just d/t. It’s how position changes over time. A steep slope on a distance-time graph means fast motion. A flat slope means standing still. The formula quantifies what the graph shows visually.

Force isn’t just ma. It’s the relationship between how hard you push, how much stuff you’re pushing, and how fast it speeds up. Doubling the force doubles the acceleration. Doubling the mass halves the acceleration. The formula captures these proportional relationships.

When you understand these concepts, you can handle weird ACT questions that twist formulas in unexpected ways. “If mass triples and acceleration doubles, what happens to force?” You know force must increase by a factor of six (3 × 2) because you understand the relationship, not just the symbols.

This deeper understanding also helps with common misconceptions about Newton’s third law of motion, which frequently appears in force-related passages.

The Night Before the Test

Your study strategy changes in the final 24 hours.

Don’t try to learn new formulas or concepts. Focus on reinforcing what you already know.

Review your five formulas one last time:
– d = m/V
– v = d/t
– F = ma
– m = (y₂ – y₁)/(x₂ – x₁)
– W = Fd

Write them on a notecard. Read them before bed. Read them again in the morning. Read them in the car on the way to the test center.

Visualization helps. Picture yourself seeing a data table with mass and volume. Imagine writing d = m/V on your scratch paper. See yourself calculating the answer and bubbling it in confidently.

Get good sleep. A tired brain makes calculation errors even when you know the formulas perfectly. Eight hours of sleep helps more than two extra hours of cramming.

Eat breakfast. Your brain runs on glucose. Low blood sugar during the test means slower processing and more mistakes.

Bring a watch. Time management matters. If you’re spending two minutes on a single question, move on and come back if time permits.

Making These Formulas Stick Permanently

Test day will come and go, but these formulas have value beyond the ACT.

They show up in:
– AP Physics and Chemistry courses
– College science requirements
– Engineering programs
– Medical school prerequisites
– Everyday problem-solving

Investing time to truly master them now pays dividends for years. The student who memorizes formulas the night before forgets them by next week. The student who understands them and practices regularly builds permanent knowledge.

Use spaced repetition. Review the formulas today, tomorrow, three days from now, a week from now, and a month from now. Each review session strengthens the memory pathways.

Teach someone else. Explaining density to a friend or family member forces you to understand it deeply enough to make it clear to others. Teaching reveals gaps in your knowledge that passive review misses.

Apply them outside of practice problems. Calculate your car’s fuel efficiency (distance per gallon). Estimate the density of objects around your house. Figure out how much force your legs generate when you jump. Real-world application makes abstract formulas concrete and memorable.

Your Formula Checklist for Test Day Success

Walking into the test center with these five formulas memorized gives you a massive advantage. You’ll move through science passages faster, answer calculation questions accurately, and have more time for the harder interpretation questions.

But memorization alone isn’t enough. You need recognition speed. When you see a passage about planetary motion with distance and time data, “v = d/t” should flash in your mind immediately. When a chemistry experiment reports mass and volume measurements, “d = m/V” should be your instant thought.

That speed comes from practice. Do 50 problems using each formula. Mix them randomly. Time yourself. Push for faster recognition and calculation each session.

The ACT Science section rewards preparation. Unlike the reading section where passages are unpredictable, science passages follow patterns. Physics concepts repeat. These five formulas handle the majority of calculation questions you’ll encounter.

Master them, practice applying them, and walk into the test with confidence. You’ve got this.