How to Prepare for College Math and Physics as an Incoming Freshman

Short answer: To prepare for college math, make your algebra, functions and trigonometry automatic, review precalculus the summer before, and take your placement test seriously. Then get used to working independently: college courses move faster, assign harder problem sets and expect you to find help on your own. Start six to eight weeks before classes.

Most students who struggle in first-year calculus or physics do not struggle with the new ideas. They struggle because old skills, like factoring or trig identities, are not fast enough to keep up. A focused summer fixes that.

Key points

• Algebra is everything: Weak algebra causes more calculus mistakes than calculus itself.
• Precalc is the bridge: Functions, trig and limits carry straight into Calculus I.
• Placement matters: Your placement score decides your first course, so prepare for it.
• Faster and deeper: College covers more per week and asks for explanations, not just answers.
• Physics needs calculus: Most STEM majors take calculus-based physics alongside calculus.
• Independence counts: Office hours, study groups and planning replace daily teacher check-ins.

How is college math different from high school math?

The topics may sound familiar, but the experience changes in three ways.

College problem sets often ask you to explain why a method works or to combine two ideas you learned separately. Students who learned math as a list of steps feel this shift most.

Our math tutor Jake sees the same pattern in many students:

“About a third of my students miss details or don’t really understand the steps they’re using. They also struggle to take what they learned in algebra or geometry and apply it to something new. It’s almost as if they forget it exists.”

Jake Gerhardt, Alexander Tutoring math tutor

Are incoming students ready for college math?

Many are not, and professors have noticed. UC Berkeley math professor Zvezdelina Stankova reports that 71% of incoming students tested from 2018 to 2020 were ready or nearly ready for calculus, compared with 44% of those tested from 2021 to 2023. The two years used different diagnostic tests, which she acknowledges, but the drop is large (The San Francisco Standard, August 2026).

In May 2026, more than 600 University of California faculty signed a letter warning of preparation gaps so severe that instructors must reteach middle school math (EdSource).

• 71% of UC Berkeley test-takers calculus-ready or nearly ready, 2018-2020
• 44% ready or nearly ready, 2021-2023
• 600+ UC faculty who signed the 2026 letter on math preparation

The good news: the gaps are usually in specific, fixable skills. Our SAT tutors also see that students with strong SAT math tend to be ready for early college courses such as precalculus, because the test rewards the same algebra fluency.

What math should you review before college?

Focus on the skills Calculus I uses every day. If any of these feel slow, start there.

• Algebra: factoring, simplifying fractions with variables, solving equations and inequalities, working with exponents and radicals.
• Functions: domain and range, composition, inverses, and graphs of linear, quadratic, polynomial, exponential and logarithmic functions.
• Trigonometry: the unit circle, radian measure, graphs of sine and cosine, and core identities.
• Limits: if your precalculus course covered them, review limits and continuity, since they are the starting point of calculus.

Tutor tip: Our curriculum notes flag trig identities as a huge sticking point and limits as the biggest topic carried from precalculus into calculus. If you only have a few weeks, spend them there.

See our guide to 12th grade math for how precalculus sets up calculus, and trigonometry basics for a refresher.

Quick readiness check

Try these without a calculator. If any take more than a minute, that skill needs practice.

1. Simplify (x² − 9) ÷ (x − 3). Factor the top as (x − 3)(x + 3), then cancel to get x + 3 (for x ≠ 3). This exact move appears in your first week of limits.
2. Solve 2ˣ = 32. Since 32 = 2⁵, x = 5.
3. Find sin(π/6) and cos(π/3). Both equal 1/2, straight from the unit circle.
4. If f(x) = x² and g(x) = x + 1, find f(g(2)). First g(2) = 3, then f(3) = 9.

How do you prepare for college physics?

College physics comes in two main versions. Algebra-based physics is common for many life science and pre-health students. Calculus-based physics is usually required for physics, engineering and most physical science majors, and is often taken alongside or right after Calculus I.

• Math you need: algebra, trigonometry (for vectors and components) and, for calculus-based physics, derivatives and integrals.
• Vectors: breaking forces and velocities into x and y components with sine and cosine comes up from week one.
• Problem-solving: draw a diagram, list knowns and unknowns, and solve symbolically before plugging in numbers.
• Labs: expect more independent work and longer reports that explain the physics behind your results.

For more, read how to get better at physics.

What should you do the summer before college?

A simple plan beats a vague goal. Here is a sample timeline for a student starting in late August:

Leave room for rest. A steady half hour a day for eight weeks is more effective than a week of cramming, and spaced practice is one of the best-supported study techniques in learning research (Dunlosky et al., 2013).

How do you succeed once classes start?

1. Do problems the day they are assigned. Start problem sets early so you have time to get stuck and get help.
2. Go to office hours in the first two weeks. Before you need help, so it feels normal when you do.
3. Join or form a study group. Explaining a solution to someone else shows whether you really understand it.
4. Analyze every mistake. On quizzes and problem sets, figure out exactly where and why you went wrong.
5. Take short, organized notes. Focus on definitions, theorems and worked examples, then review them the same day.

Tutor tip: Error analysis is where growth happens. When you miss a problem, do not just read the correct solution. Find the exact line where your work went wrong and name the reason.

AI chatbots can help explain a concept, but they can also hide gaps. As our math tutor puts it:

“AI is a powerful tool, but it’s misunderstood and overused. Students are relying on it too heavily. It can be a scaffold for learning, but not a replacement for it.”

Jake Gerhardt, Alexander Tutoring math tutor

For more habits that work, see how to study for math. Students coming from AP classes can also read how to succeed in AP math.

Frequently asked questions