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Understand functions, trigonometry, and analytic geometry

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Precalculus Topics

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Functions
Function notation
Identifying functions
Adding functions
Subtracting functions
Multiplying functions
Dividing functions
Composite functions
Reflection across the y-axis: y = f(-x)
Reflection across the x-axis: y = -f(x)
Transformations of functions: Horizontal translations
Transformations of functions: Vertical translations
Transformations of functions: Horizontal stretches
Transformations of functions: Vertical stretches
Introduction to linear equations
Even and odd functions
One to one functions
Difference quotient: applications of functions
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Polynomials
Polynomial long division
Polynomial synthetic division
Determining the equation of a polynomial function
Factor theorem
Rational zero theorem
Characteristics of polynomial graphs
Multiplicities of polynomials
Imaginary zeros of polynomials
Pascal's triangle
Binomial theorem
What is a polynomial function?
Applications of polynomial functions
Solving polynomial inequalities
Descartes' rule of signs
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Rational Functions
What is a rational function?
Point of discontinuity
Vertical asymptote
Horizontal asymptote
Slant asymptote
Graphs of rational functions
Solving rational inequalities
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Piecewise Functions
Evaluating piecewise functions
Graphing piecewise linear functions
Graphing piecewise non-linear functions
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Radical
Basic radical functions
Transformations of radical functions
Square root of a function
Solving radical equations
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Exponential and Logarithmic functions
Converting from logarithmic form to exponential form
Evaluating logarithms without calculator
Common logarithms
Evaluating logarithms using change-of-base formula
Converting from exponential form to logarithmic form
Product rule of logarithms
Quotient rule of logarithms
Combining product rule and quotient rule in logarithms
Solving logarithmic equations
Evaluating logarithms using logarithm rules
Continuous growth and decay
Finance: Compound interest
Exponents: Product rule (a^x)(a^y) = a^(x+y)
Exponents: Division rule (a^x / a^y) = a^(x-y)
Exponents: Power rule (a^x)^y = a^(x * y)
Exponents: Negative exponents
Exponents: Zero exponent: a^0 = 1
Exponents: Rational exponents
Graphing exponential functions
Graphing transformations of exponential functions
Finding an exponential function given its graph
Logarithmic scale: Richter scale (earthquake)
Logarithmic scale: pH scale
Logarithmic scale: dB scale
Finance: Future value and present value
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Roots and Rational Exponents
Square and square roots
Converting radicals to mixed radicals
Converting radicals to entire radicals
Evaluating and simplifying radicals
Rational exponents
Power of a power rule
Combining the exponent rules
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Systems of Equations
Determining number of solutions to linear equations
Solving linear systems by graphing
Using substitution method to solve systems of equations
Using elimination method to solve systems of equations
Solving 3 variable systems of equations by substitution
Solving 3 variable systems of equations by elimination
Solving 3 variable systems of equations with no or infinite solutions
Word problems relating 3 variable systems of equations
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System of Inequalities
Shortcut: The vertex formula
Solving absolute value inequalities
Graphing linear inequalities in two variables
Graphing quadratic inequalities in two variables
What is linear programming?
Linear programming word problems
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Trigonometry
Converting between degrees and radians
Radian measure and arc length
Angle in standard position
Coterminal angles
Reference angle
Find the exact value of trigonometric ratios
ASTC rule in trigonometry (All Students Take Calculus)
Unit circle
Trigonometric ratios for angles in radians
Solving first degree trigonometric equations
Determining non-permissible values for trig expressions
Use sine ratio to calculate angles and side (Sin = oh \frac{o}{h}ho​ )
Use cosine ratio to calculate angles and side (Cos = ah \frac{a}{h}ha​ )
Use tangent ratio to calculate angles and side (Tan = oa \frac{o}{a}ao​ )
Combination of SohCahToa questions
Law of sines
Law of cosines
Sine graph: y = sin x
Cosine graph: y = cos x
Tangent graph: y = tan x
Cotangent graph: y = cot x
Secant graph: y = sec x
Cosecant graph: y = csc x
Graphing transformations of trigonometric functions
Determining trigonometric functions given their graphs
Quotient identities and reciprocal identities
Pythagorean identities
Sum and difference identities
Double-angle identities
Word problems relating ladder in trigonometry
Word problems relating guy wire in trigonometry
Other word problems relating angles in trigonometry
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Bearings
Introduction to bearings
Bearings and direction word problems
Angle of elevation and depression
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Inverse Trigonometric Functions
Finding inverse trigonometric function from its graph
Evaluating inverse trigonometric functions
Finding inverse reciprocal trigonometric function from its graph
Finding exact value of inverse reciprocal trig functions
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Sequences and Series
Arithmetic sequences
Geometric sequences
Arithmetic series
Geometric Series
Infinite geometric series
Sigma notation
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Statistics
Influencing factors in data collection
Median and mode
Mean
Range and outliers
Application of averages
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Complex Numbers and Complex Plane
Introduction to imaginary numbers
Complex numbers and complex planes
Adding and subtracting complex numbers
Complex conjugates
Multiplying and dividing complex numbers
Distance and midpoint of complex numbers
Angle and absolute value of complex numbers
Polar form of complex numbers
Operations on complex numbers in polar form
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Vectors
Introduction to vectors
Magnitude of a vector
Direction angle of a vector
Scalar multiplication
Equivalent vectors
Adding and subtracting vectors in component form
Operations on vectors in magnitude and direction form
Unit Vector
Word problems on vectors
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Probability
Determining probabilities using tree diagrams and tables
Solve for the probability of an event
Path counting problems
Permutation vs. Combination
Combinations
Permutations
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Quadratic functions
Characteristics of quadratic functions
Graphing parabolas for given quadratic functions
Finding the quadratic functions for given parabolas
Solving quadratic equations by factoring
Solving quadratic equations by completing the square
Using quadratic formula to solve quadratic equations
Nature of roots of quadratic equations: the discriminant
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Conic Sections
Conics - Circle
Conics - Ellipse
Conics - Parabola
Conics - Hyperbola
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Introduction to Matrices
Notation of matrices
Adding and subtracting matrices
Scalar multiplication
Matrix multiplication
The three types of matrix row operations
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Properties of Matrices
Zero Matrix
Identity Matrix
Properties of matrix addition
Properties of scalar multiplication
Properties of matrix multiplication
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Determinants and Inverses of Matrices
The determinant of a 2 x 2 matrix
The determinant of a 3 x 3 matrix (General & Shortcut Method)
The inverse of a 2 x 2 matrix
The inverse of 3 x 3 matrices with matrix row operations
The inverse of 3 x 3 matrix with determinants and adjugate
2 x 2 invertible matrix
Solving linear systems using Cramer's Rule
Solving linear systems using 2 x 2 inverse matrices
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Transformations with Matrices
Transforming vectors with matrices
Transforming shapes with matrices
Finding the transformation matrix

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What is Precalculus?

Precalculus is a course that covers the more complex elements of both algebra and trigonometry, elements that were not necessarily explored in depth in your previous trig or algebra courses. For example, you'll dive deeper into topics like polynomial synthetic divisions, the transformation of functions, determinants and inverses of matrices, and much more.

Prerequisites for the course would be either Algebra 2 course or Geometry course. Upon completing the course, students would be better prepared to undertake lessons in Calculus.

For the most part, courses will cover standard content like functions and function composition, as well as inverse functions in relation to sets and real numbers. Outside of these topics, the course content may vary depending on the nature of the course. For example, some courses may have an emphasis on preparing students for careers within the business world, meaning that the course content has more of a focus on topics like power functions and matrices.

Regardless of your individual course content, our vast collection of precalculus help lessons will cover everything you need. We've worked to ensure that our videos cover all the topics you'd expect to find in the classroom and within modern textbooks. In addition, our videos offer step-by-step examples that, unlike the classroom, can be paused, rewound, or fast-forwarded, allowing you to learn at your own pace.

Is Precalculus Hard?

As mentioned above, precalculus explores areas of trigonometry and algebra in greater depth than in your previous courses. With that in mind, it's essential that you have a solid foundation of knowledge in trigonometry and algebra to build upon. Failing to do so will make precalculus a much tougher challenge than it needs to be.

If you feel like you need to broaden your understanding of trig and algebra before attempting precalculus, or if you are already in classes and find that it's becoming a bit of a struggle, you're not alone. We have many students like you who are using our platform to get pre cal help to tackle tricky precalculus problems and prepare for their upcoming exams.

You can start with our algebra 2 tutorials and trigonometry tutorials to further build your basic knowledge or jump straight into our online precalc help. As a subscriber, you'll have access to every video on our site, providing you with math guides whenever you need them. Regardless of the topic you need help with, our videos will break down the information into bite sized chunks, making them easier to digest and retain. We cover all the aspects of precalculus that are bound to come up in your exams, so whatever area you need help mastering, we've got the content that can help you succeed!

How to Pass Precalculus?

If you want to successfully pass your precalculus test, you should revise, revise, revise! That cannot be stressed enough, the best way to learn is with repetition. Review what you've been taught in the classroom and build effective study sessions to retain that information. Give yourself some time to assess your work and use our easy practice materials to help you highlight any areas of weakness that you may have.

Getting yourself into a good study habit of completing practice papers and sitting mock exams will help to build your confidence ahead of sitting your actual precalculus paper. Work within the time constraints of each paper and have someone else mark your tests for you. Reviewing your performance and tracking your improvement within your weaker areas, will show you that revision actually works and will encourage you to stick with it!

We at StudyPug, understand that getting yourself into the study mood can be difficult at times. We also know that many students find it boring to work from a textbook. That's why we offer an extensive collection of fun and easy to follow precalculus video tutorials that manage to deliver the same precalculus textbook answers, but in a much more conversational way that's easier to understand.

Put simply, to improve your chances of passing precalculus, you'll need to spend a good amount of time revising and you should utilize StudyPug's vast collection of content to get the most out of your revision time. We'll not only get you prepared for your exams, but we can also help you perform better in class. If there's something in your lesson that you couldn't make sense of, jump online and browse our content. We'll have video tutorials on the subject that can help clear up any confusion you have. Think of us as your online precalculus tutor, available whenever you need us, and at the fraction of the cost of a personal tutor.

PreCalculus Vs. Algebra

Elements of algebra make up certain sections of precalculus, which is why a prerequisite for most courses is a qualification in algebra 1 and algebra 2. These courses complement the content of precalculus courses and are used as the building blocks from which you will develop your understanding of the more complex elements of precalculus. To that end, precalculus is slightly more complicated and trickier than basic algebra. Learn that first and precalculus becomes easier to understand.

Teach Me Precalculus!

If you're looking for precalculus tutorial videos, you're in the right place! We offer free math tutor online 24/7 help and have 1000s of lessons across a variety of mathematical topics, including trig, algebra, and content for precalculus homework help. If you're struggling with unit circles, vectors, conic sections, polynomials, or anything else, we can help!

We're well aware that the way you learn may not be the same as everybody else and that's why we have built a platform with a "precalculus for beginners" approach that starts from the ground up, assumes no prior knowledge, and acts as a fantastic intro to calculus. Each section of our content has also been designed to flow naturally from one topic to the next, ensuring that you can build off what you've just learned, introducing more complex elements when you're ready.

To get you started with your precalculus exam prep, we're offering a collection of free math tutor precalculus lessons across the following subject areas:

  • Composite Functions
  • Reflection Across the Y-axis
  • Polynomial Long Division
  • Converting from Logarithmic Form to Exponential Form
  • Exponents: Power Rule
  • Shortcut Vertex Formula
  • And Many More!

Browse them all today and see how we can make precalculus much easier to understand.

It's worth noting that having a firm grip on precalculus can greatly impact your career success. There's a great amount of high paying jobs for people that are good at math. So get studying!

Compatible Precalculus Textbooks

We know that students who want to succeed may need revision guides to help them. We also know that not everyone can afford the expensive textbooks. To that end, our precalculus content has been thoughtfully created by expert math teachers to ensure that our content covers all the topics you'd expect to find in the following textbooks.

  • Slader - Precalculus
  • Precalculus with Limits
  • Larson precalculus with Limits
  • Precalculus for Dummies
  • Larson - Precalculus with Limits
  • Glencoe - Precalculus
  • Precalculus – Michael Sullivan
  • Precalculus with limits a graphing approach pdf
  • Precalculus Mathematics for Calculus 7th Edition
  • Blitzer - Precalculus (textbook)
  • Precalculus: Graphical, Numerical, Algebraic

Essentially, we've taken the same information found within each of these books and combined them into one subscription, granting you unlimited access to a vast range of video content. When it comes to precalculus lessons and revision guides, StudyPug is all you need.

We find that a lot of our students prefer the video format as the content is delivered in a conversational way that's easier to follow than traditional textbooks. Read our precalculus reviews from our loyal base of customers who also needed help with precalculus and see how we've managed to help students just like you succeed in their precalculus exams

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