Mathematics is undoubtedly the hatest subject across different grade levels, whether you are a university or high school student. Once you reach middle school, you will learn higher-level math such as Precalculus, trigonometry, etc. How hard is Precalculus in high school?
Any subject in high school may seem a little bit challenging—be it a top student or not—if you do not find the interest and drive to apprehend theories and concepts. You will find yourself investing more time expounding mathematical foundations that you already learned in your lower years, like functions, basic geometry, and algebra. Precalculus is not as difficult as you think it is.
Keep reading this article and be equipped with the proper knowledge to pass this subject without sweat. You will know a comprehensive guide to prepare you before attending precalculus classes holistically. It also unveils helpful tips from professionals and students around the world.
What is Pre-Calculus in High School?
Precalculus is simply an extension and combination of your acquired knowledge from lower years that bolsters your conceptual ability in mathematical reasoning and problem-solving. You are expected to absorb geometry, algebra, and trigonometry subjects in a bid to prepare you for the actual calculus course in universities, should you wish to pursue science and mathematics programs.
High school students start with performing geometric and algebraic operations as an entry course before expounding on these topics in Algebra 2, which extends from trigonometry to mathematical analysis. You will branch out by investigating sequence and series, limits and graphs of rational functions, etc.
In simple terms, you usually work with many diagrams—their behaviors and equations. You might have already touched on some of these topics in your basic geometry, which is straightforward if you have a strong foundation in the unit circle. Get a closer look at your high school precalculus curriculum below.
- Linear and Quadratic Functions (Lines and Points, Slopes, Quadratic Functions, Quadratic Models, etc.)
- Polynomial Functions (Remainder Factor Theorem, Maximum and Minimum, Theorems of Polynomials, etc.)
- Inequalities (Linear and Polynomial Inequalities, Absolute Value, etc.)
- Functions (Operations on Functions, Graphing Problems, Inverse Functions, Functions of Two Variables, etc.)
- Exponents and Logarithms (Exponential and Logarithmic Functions, Integral and Rational Exponent, Base Formula, etc.)
- Analytic Geometry (Equations of Circles, Hyperbolas, Parabolas, Second-degree Equations, etc.)
- Trigonometric Functions (Measurement of Angles, Sine and Cosine Functions, Inverse Trigonometric Functions, etc.)
- Trigonometric Equations (Inclination and Slope, Sine and Cosine Curves, Proving Identities, etc.)
- Triangle Trigonometry (Area of a Triangle, Laws of Sine, Navigation and Surveying, etc.)
- Trigonometry Formulas (Formulas for Cos and Tan, Solving Trig Equations, etc.)
- Polar Coordinates (Geometric and Trigonometric Representation Of Complex Numbers, Powers, and Roots of Complex Numbers, etc.)
- Sequence and Series (Sigma Notation, Mathematical Induction, Arithmetic & Geometric Sequences, and Series)
- Limits and Graphs of Rational Functions (Limits of Functions, Quotient theorem, Continuous vs. Discontinuous, etc.)
- Introduction to Calculus (Average & Exact Rate of Change, Derivatives in Curve Sketching, etc.)
- Basic Calculus (Derivatives of Products, The Chain Rule, Exponential and Log Derivatives, etc.)
It appears intimidating now that you have not yet begun the course. Nonetheless, you are assured of firm mathematical prowess once you pour your heart out, digging deeper into the basics of calculus.
Keep your cool because learning this in an instant is not mandatory. You have your whole high school years to master these preparatory topics before jumpstarting actual calculus.
Is Pre-Calculus Hard?
Someone who has never learned Precalculus would expectedly say it is complicated. It depends on layers of factors like mathematic ability and teacher influence. The good news is that most problem-solving is technically the application of concepts in Algebra II that goes just a little step further.
There is a reason why it is called pseudo-Algebra 2. Most students who went through it would consider it Algebra II redux due to topic rehash. Not to discredit their opinion but the tricky thing about Precalculus is that they establish many new concepts for you that you may or may have never encountered before.
As you go along the course, you will find that it only revolves repeatedly around the exact algebra, geometry, and trigonometry concepts. You may slack in the genesis stage but progressively becomes manageable once you get a hold of the new mathematical ideas.
It is not impossible to turn the tides in the case of students who are not gifted with mathematical abilities. Do outside work to ensure you fully grasp the concepts; there is always room for improvement. One thing that will certainly save your life is learning the unit circle as early as now.
In addition, it also depends on the teacher who handles the subject. You would see gifted students struggling with the seat works just because the teacher fails to break down the central concept into digestible pieces.
Teacher-factor is a real issue. There is no question about their intelligence, but some find it hard to elaborate on bigger pictures in an easy-to-follow manner. Some teachers are excellent at simplifying, which is an edge.
Even so, do not get embarrassed to reach out to your teacher and peers and have review courses once the waves are getting rough. Overall, it is not difficult if you have a genuine love for the subject plus the school’s syllabus. You will do great!
Why is Pre-Calculus Hard for Some Students?
The difficulty is subjective. Some students may outperform other learners in specific subjects but cannot keep up with the class on different topics. Mathematics, specifically Precalculus, encompasses several branches of knowledge. It goes exceedingly complex when the issues mix up together.
A strong background in basic mathematics is necessary to excel in this field since it is a practical combination of concepts with a twist. Students, who lack fundamental knowledge in geometry and algebra, might find the subject overwhelming.
Imagine joining a competition without proper training; you will feel burdened and get intimidated despite how good you are as an athlete. In like manner, you need to undergo a basic mathematical process until reaching an advanced standing.
The bottom line is not because Precalculus is intrinsically a complex subject to study. It is the foundation that ensures a high command in this subject, and it is the lack of preparatory comprehension that weakens your affinity to the topic.
What is the Hardest Part of Precalculus in High School?
Questions like “Is precalculus harder than trigonometry?” and “Is precalculus harder than statistics” would arise whenever someone brought up this topic. The answer is it depends on your academic affinity.
Admittedly, the transition of knowledge from primary to advanced makes it challenging to cope with the new concepts and formulas. Having to learn new ideas is the hardest part of all. It is common among beginners since you are trying to close the learning gaps from previous subjects alongside mastering higher levels of math such as exponents and logarithms, limits, and graphs, among others.
Again, there is no consensus on the difficulty. You might find some topics along the way subjectively simple than others. You sometimes lose motivation to pursue the field and suddenly go through a spike in your will.
The hardest part is to become consistent in your progress and quick-witted to follow the momentum. Remember, you are no longer dealing with a lax course, so you must expedite the whole learning process.
It is your constant battle to apply what you learned to new positions and combine two or more rules in a single case. The moment you grasp them all, rest assured that you will be fine!
Can You Take Calculus Without Precalculus?
You might be wondering now: is Precalculus required? Parkouring to calculus without introductory loads is a case-to-case basis depending on your goal and path. Generally, yes, you can take it without systemic blockage.
If you aim to secure a spot in the field of specialization, it is a wise decision to have Precalculus. High school is the best avenue to enhance your competence because it has initial subjects that consider those not blessed with mathematical abilities, unlike in college, where everyone in the specialization is expected to have mastered the above-average aptitude.
Although preloads are not required, some universities rank students based on their mathematics remarks in high school should you enroll in STEM programs. You will be shortlisted but with the least priority if you do not have a background.
Universities create equal opportunities for everyone to take a degree program, but they screen applicants based on multilateral factors, including precalculus grades and preparedness. In short, it is not required but necessary. Still, the decision lies within your hands at the end of the day.
Is Precalculus Harder than Calculus?
Precalculus and calculus are almost similar by nature. Both can be extremely difficult or remarkably easy, depending on your circumstance. As long as you have taken Precalculus in high school, you will expectedly become more advantageous than those who lack the luxury of experience.
Similar to the time-demanding transition of algebra to Precalculus, the shift from pre to proper calculus follows suit. You will likely spend time countless times reviewing old concepts that you forgot and updating your status when you study calculus in college. It is a matter of transition, application, and learning.
Generally, calculus could be dealing with advanced to proficient loads. On the brighter side, it is simply the extension of Precalculus. You are expected to apply all the theories and concepts, from basic to average, to the pre-established contexts. You need not worry when you are confident or eager to learn.
In the case of a student who lacks background, you may find it difficult if your passion is not in line with the field. It will be a constant battle to continue thriving in the program.
Sooner or later, you will discover that the concepts are just repetitions. You will apply new contexts to different problems and make alterations. Although calculus is somehow more complex, you are assured to make it once you are settled.
Wrapping Things Up: How Hard is Pre-Calculus in High School?
Dealing with a subject that you do not like is the worst part of being a student. It is natural for you, students, to ask whether or not you can pass the subject. When it comes to calculus, it could be subjective based on your experience. Again, how hard is Precalculus in high school?
It is not hard as it seems. It concerns your background, academic affinity, and other external factors. Precalculus is just a continuation of algebra and geometry in lower years but requires progressive analytical prowess. The real challenge is to bridge the two different stages and fuse them.
There are no other solutions to pass Precalculus other than taking the fundamentals seriously. Start scanning your books and learn the unit circle now, as almost everything revolves around it. Plant now and reap what you sow in the future!