How to Prepare for College Math and Physics as an Incoming Freshman
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So, you’ve registered for your first college math or physics class. What should you expect? The depth, pace, and focus of the material are often different from what you encountered in your high school classes. With a bit of preparation, though, you can adapt to the change of pace in college math and start your freshman year with confidence.
College math takes a deeper dive into abstract theories and mathematical proofs, and many instructors expect students to take a more independent approach to their work. Whether you’re a long-term math whiz or have always had to put in a little extra work, preparing for college math in the weeks and months leading up to your first course makes it easier to navigate these changes.
High School vs. College Math: What Changes and Why It Matters
Adjusting your expectations is important when making the transition to college math. Although math placements and course structure vary by institution, you can expect to see some significant shifts between your high school and college math courses, no matter which school you attend.
Procedural to Conceptual Understanding
One of the biggest differences in college math vs. high school math is the introduction of more abstract concepts. Rather than focusing on computation and memorization, college math courses require you to think analytically about problems and develop proofs to demonstrate your understanding of core concepts.
This change is clear when looking at some of the courses you take during high school compared to those in college. For example, you might have already taken single-variable calculus in high school, but you usually don’t study multivariable calculus until college. Similarly, some high school math courses introduce differential calculus, but you’ll study it in much more depth in Calculus I and Calculus II.
Increased Pace, Workload, and Independence
College math courses typically move more quickly than those in high school, with a general expectation that you will be more independent and proactive in your learning, both inside and outside the classroom. Compared to college instructors, high school teachers tend to provide more guidance and explicit instructions on how to complete problems and apply mathematical concepts.
This is true of many college courses, from social studies to computer science, but the shift in math is especially dramatic. For instance, high school math homework reinforces concepts from class by having you complete worksheets or textbook problems.
Homework in college courses, on the other hand, may require you to complete problem sets. These are groups of mathematical problems you have to prove using analysis and, in many cases, multiple concepts from the course. To complete these problem sets, you often have to work together with your classmates, carefully review the class material, and perform a deep analysis of what you’ve learned.
Understanding the High School Physics Curriculum vs. College Expectations
Like math courses, physics differs significantly from high school to college, particularly in terms of the mathematical concepts you need to know. While high school courses address basic aspects of physics, college courses require a more nuanced look at energy, matter, and the universe.
Algebra-Based Physics vs. Calculus-Based Physics
Many physics courses are either algebra- or calculus-based, and which one you take depends on the school and your major. Algebra-based classes teach you how to describe the foundational principles of physics using algebraic equations. Aside from some AP courses, most high school physics classes are algebra-based.
Calculus-based courses are more challenging to many students because they look at the underlying principles of physics but dig deeper, require more precision, and involve greater mathematical knowledge. Many colleges offer both algebra- and calculus-based physics, but they usually require students in STEM majors to take calculus-based courses to complete their degrees.
Rigorous Labs and Real-World Problem-Solving
Physics labs are a central part of the learning experience in high school and college, but the experience becomes more demanding from one level to the next. In high school, these sessions are more teacher-guided, and you usually write relatively short lab reports describing the results of your lab work.
College physics labs address advanced topics and real-life issues, and your work on experiments and analysis is more independent. Lab reports are also lengthier and more comprehensive, requiring you to detail the concepts you’re using and how they apply to different scenarios.
Math Skills Required for Mastering College Physics
Mathematical principles are critical to understanding physics. When building your class schedule for college, you’ll need to determine whether you’ve met the math prerequisites and have the necessary skills to take your first physics course.
These are some areas of math you need to understand to succeed in your college physics courses:
- Algebra: You’ll study algebraic equations and mathematical thinking skills, which are essential when exploring physics. Linear algebra is particularly important to succeeding in physics.
- Geometry and trigonometry: Learning how to determine the properties of objects will help you make sound deductions in physics. Some students also take analytical geometry, which combines concepts from algebra and geometry.
- Calculus: Single-variable and multivariable calculus are essential to solving physics equations. College calculus courses also cover differential equations, which are crucial during all levels of physics courses.
- Probability and statistics: Probability and statistics aren’t usually necessary when taking introductory physics classes. However, you’ll need to understand probabilistic formulas before taking advanced classes and studying quantum mechanics.
- Classical mechanics: Classical mechanics is typically a college-level subject drawing on calculus, algebra, and differential equations. It is the mathematical language of physics and describes how things move, including motion, forces, and vectors.
You don’t need to study all these subjects before applying for college admission and registering for classes. Although you’ll gain some of the knowledge you need for physics during high school, you’ll also need to take college-level courses to broaden and deepen your skills.
The Hidden Skill Gap: What Schools Don’t Always Teach
When you finish high school, you can make a list of the math and physics concepts you haven’t studied yet — but those might not be the only things you still need to learn. Your high school may not provide the training you need in specific mathematical and scientific principles and other areas, such as:
- Building mathematical intuition: You might not associate math with gut feelings, but college courses encourage you to go beyond formulas and rely on your intuition. During high school, you may not have learned to internalize the concepts you need to understand instinctively how to tackle complex math problems.
- Managing time and problem-solving under pressure: Most math courses at the high school level include more in-class time than college courses, allowing you to be more lax in your time management. This can leave you ill-prepared to cope with the intense pace of college courses, which teach and test concepts more quickly.
- Studying conceptual subjects without memorization: High school math courses involve extensive memorization of formulas and how to plug in information to solve them. They sometimes neglect to teach you how to consider the foundations of these principles and how to apply them, which is central to math and physics classes in college.
- Self-directed learning: Learning tends to be teacher-led in high school, which can discourage you from taking ownership over your experience. Having to navigate challenges without regular one-on-one support from a teacher during college is a jarring switch if you haven’t already worked independently in high school.
If your high school hasn’t given you the opportunity to establish these skills, you can develop them on your own. For example, you can practice completing more advanced math problems within a certain time limit to prepare for stricter and shorter deadlines in college.
Plan Your Transition: Academic and Personal Goal Setting
The shift from high school to college math can feel overwhelming, but there are plenty of ways to prepare. Creating a schedule can help you stay on track so you cover all the material you want to review before the upcoming academic year.
Consider making a month-by-month prep timeline with milestones you want to meet. For example, you might set a target of mastering pre-calculus by July and finishing your physics review by August. These smaller goals will help make your preparation feel more manageable and organized.
When developing your calendar, remember to factor in time for other needs. Leave enough hours for sleep and fun activities as part of your stress management routine, whether that means going for a walk or spending time with family and friends. In addition, keep your mental health in mind by thinking about what other obligations you need to meet. Don’t overload your schedule, or you’ll find it more difficult to stick with it and meet your goals.
Study Strategies for Academic Independence
If you want to succeed in math, physics, and your other college courses, you need to learn to study effectively. Developing certain study skills early in your college journey will make your learning experience easier and more enjoyable.
Take Notes
Taking good notes in STEM courses is one of the first and most important steps you can take. Your course notes will help you review the course material, understand your labs, and study for exams.
When you take notes in your physics and math classes, use abbreviations, headings, subheadings, and bullet points to structure them for easy reading and skimming. Don’t try to write down everything the instructor says. Instead, focus on definitions, core concepts, and connections between ideas. Once the class is over, review your notes to fill in any gaps and clarify points you find confusing.
Build Strong Habits
As soon as a course begins, you should implement solid study habits. When deciding how to study, consider doing daily reviews of the material from your most recent class. This will reinforce the points you learned and help you pinpoint questions you want to bring up the next time you see your instructor.
Some students also use spaced repetition when studying. With this strategy, you’ll review material at gradually increasing intervals to improve your knowledge retention. Studies show spacing out your learning sessions strengthens your memory, especially when compared to cramming the material all at once.
Another helpful step is to complete additional review tasks beyond what your instructor assigns. For example, you can do extra problem sets to put the concepts you’re learning into practice and identify areas where you need more guidance.
Get Support
The shift into college math and physics courses is easier if you get help from others, and you can start by turning to your classmates. Find or create a study group with other students taking the same course. Going over the material and explaining concepts to one another is a good way to check your comprehension and answer questions.
Math and physics tutoring is another valuable resource leading up to and during college. A tutor will work with you one-on-one, helping you with problem sets, homework, and exam preparation. This kind of support can help you place higher on tests and feel more confident in your STEM trajectory.
Develop a Proactive Mindset
If you know you’ll be taking math or physics during your freshman year, you can start preparing before the semester begins. Get a step ahead by reviewing foundational concepts from the courses you’ve already taken. You can also preview future subjects based on your course descriptions and syllabi. Use online resources and tutors to get an overview of the material you’ll be covering.
Math concepts build on each other, and a proactive approach helps ensure you grasp the basics before moving on to more advanced topics. It can also help reduce anxiety when your courses begin.
How Alexander Tutoring Helps Students Get Ahead
Math and physics are intimidating for many students, especially during the transition from high school to college. If you’re entering a new school year and want to feel confident in math or physics, now is the time to start preparing for college math.
Alexander Tutoring supports students in high school and college subjects, including calculus, physics, and PSAT tutoring. Get ready for your upcoming classes and keep going strong throughout the school year with support from an expert tutor.
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