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Gavin Walton
- August 17, 2024
You are preparing to plunge into study.com’s Math 103: Precalculus course, aren’t you? Good choice! This class is a great starting point because it leaves you with all the setup you need for the higher-level mathematics courses that you may need to undertake. If your wishes extend to engineering or technology or you just need to master the next math homework this course will suit you.
Here you will explore all about functions, trigonometric functions, and all the basic concepts that you will come across. The best part? It is also packed with juicy bits of curiosity to motivate you through the lessons even if you lack the math skills. What the author has again brought out in this book are clear explanations on the topic discussed, loaded with practical examples and sufficient problem-solving exercises that make it possible for you to master concepts that you never imagined you could. At the end of the course not only you can pass the final proctored exam, but also you will be prepared for future mathematical activities. Ready to get started? Let’s do this!
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What’s in Store for You in Math 103📖
Okay, the following are the areas that you will be covering in the study.com Math 103: Precalculus course. The final proctored exam is on its way and this channel will prepare you for a mathematical ride that will guarantee you mastery of everything required!
Functions and Transformations
The first topic revolves around functions in the world. This is where you’ll get to know common, piece-wise, rational, exponential, logarithmic, reciprocal functions, and so on, including how to operate on them and how to plot them on coordinate axes. You will learn about function notation and also about how to change, stretch, and even flip graphs such as shift, reflection, and dilation. I assure you that these basics are important because, throughout precalculus, functions are the cornerstone.
Exponential and Logarithmic Functions
The subsequent section will focus on exponential and logarithmic functions. All those concepts are absolutely fundamental and they are everywhere, they appear at the very core of such various subjects as natural science or finance. Here you also discover how these functions are shown on the coordinate plane, and how to solve equations that involve logarithms and basic logarithmic properties. This is something that will actually have a lot of questions dedicated to it in the exam, so do not miss this out!
Trigonometry and Geometry
So trigonometry may sound somewhat complex but trust me, it is very beneficial and is not as terrible as it appears. You will comprehensively make an understanding of the unit circle along with sine, cosine, and tangent ratios. Furthermore, this will demonstrate how the understood trigonometric concepts are used in practice. Geometry is also not left behind and plays a role in depicting shapes and volumes when solving problems.
Polynomial and Rational Functions
The next topics to be discussed are polynomials and rational functions. It is necessary to specify that you will find how to perform addition, subtraction, multiplication, and division of these functions as well as learn how to plot a function. Adding, subtracting, and multiplying quadratic terms will become part of your fingertips while factoring and solving quadratic equations will become easier for you. These topics are quite basic, so you should solve a lot of problems concerning them.
Every time in the course, you will find a lot of exercises and quizzes that are similar to what you may meet on the final exam. The only thing that should be kept in mind is that one should remain consistent with the studies and should take each topic as a step forward. Are you set for the strategies you need for studying this course? On to the next shall we?
Strategic Study Plan for Math 103📝
Below are the guidelines you can use to organize your schedule and get the most of your time to study: If you stick to this schedule, you will be fully prepared for the coming Study.com Math 103: Precalculus final proctored exam at the end of the study plan; Math 104 Basic Mathematics homework.
Week 1: Functions and Transformations
- Topics to Cover: Functions, function notation, vertical line test, transformations (shifts, reflections, dilations).
- Study Tips: Focus on understanding how to identify and graph different functions. Practice transformations by shifting and reflecting simple functions.
- Resources:
Week 2: Domain and Range, Function Operations
- Topics to Cover: Domain and range, adding, subtracting, multiplying, and dividing functions, composing functions.
- Study Tips: Work through examples to understand how to find the domain and range from graphs and equations. Practice combining functions and composing them.
- Resources:
- Paul’s Online Math Notes – Domain and Range
- Purplemath – Function Operations
Week 3: Exponential and Logarithmic Functions
- Topics to Cover: Exponential functions, exponential growth and decay, logarithms, properties of logarithms, solving exponential and logarithmic equations.
- Study Tips: Get comfortable with converting between exponential and logarithmic forms. Practice solving equations using logarithms.
- Resources:
Week 4: Inequalities and Systems of Equations
- Topics to Cover: Graphing inequalities, solving systems of equations, absolute value inequalities.
- Study Tips: Practice graphing one-variable and two-variable inequalities. Work on solving systems of equations using substitution and elimination methods.
- Resources:
Week 5: Polynomial and Rational Functions
- Topics to Cover: Polynomial functions, factoring quadratics, graphing rational functions, solving rational equations.
- Study Tips: Focus on mastering the factoring techniques for different types of polynomials. Practice graphing and solving rational functions.
- Resources:
- Purplemath – Factoring Polynomials
- Khan Academy – Rational Functions
Week 6: Trigonometry and the Unit Circle
- Topics to Cover: Unit circle, sine, cosine, and tangent functions, graphing trig functions, and trigonometric identities.
- Study Tips: Memorize the unit circle and the values of sine, cosine, and tangent at key angles. Practice using trigonometric identities to simplify expressions.
- Resources:
Week 7: Inverse Trigonometric Functions and Solving Equations
- Topics to Cover: Inverse trig functions, solving trigonometric equations, double and half-angle formulas.
- Study Tips: Practice finding angles using inverse trig functions. Solve equations using trig identities and double/half-angle formulas.
- Resources:
- Khan Academy – Inverse Trigonometric Functions
- Paul’s Online Math Notes – Solving Trig Equations
Week 8: Review and Practice Tests
- Activities: Take practice tests, review all topics, and identify and focus on weak areas.
- Study Tips: Use practice tests to simulate exam conditions. Review any topics that are still challenging and practice additional problems in those areas.
- Resources:
- Study.com – Precalculus Practice Test
- Quizlet – Precalculus Flashcards
Following this study plan will keep you organized and prepared as you work through the course. Now, let’s look at some external resources to help you study even more effectively!
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Find Free Study Materials for Math 103📂
It helps to have a bit of extra resources in your pocket especially if you are nearing the final exam and get stuck on a difficult topic. Below are some links that will assist you in clearing any concept that you find tricky and excel in your Study.com Math 103: Precalculus exam:
YouTube Channels and Playlists
Khan Academy
- Why it’s great: Khan Academy offers comprehensive and easy-to-follow videos on almost every precalculus topic. Their explanations are clear, and they often include practice problems.
- Khan Academy Precalculus Playlist
PatrickJMT (Patrick Just Math Tutorials)
- Why it’s great: This account, PatrickJMT , provides math problems and solutions in a simple manner divided into smaller subparts. The videos provided by him are appropriate for such people who grasp concepts easily through the graphics or need some help with particular difficulties.
- PatrickJMT YouTube Channel
Professor Leonard
- Why it’s great: If a student prefers more comprehensive explanations in his/her lectures accompanied by numerous examples, Professor Leonard is good to go. He explains all that you would wish to know about precalculus.
- Professor Leonard YouTube Channel
Flashcards and Study Tools
Quizlet
- Why it’s great: Quizlet contains other students’ and teachers’ flashcards and study sets in the public domain. It is rather helpful to revise and refresh your knowledge when you’ve solved some questions on your own.
- Quizlet Precalculus Flashcards
Cram.com
- Why it’s great: Similar to Quizlet, Cram.com offers flashcards that will enable the users to revise and practice the main precalculus terms and formulas.
- Cram.com Precalculus Flashcards
Interactive Websites
Desmos
- Why it’s great: Desmos is an online graphing calculator that could be useful when graphing functions, transformations, and many others. As a result, it is rather helpful if you need to study a highly complicated graph as well as solve the equation.
- Desmos Graphing Calculator
Wolfram Alpha
- Why it’s great: Wolfram Alpha is like a super-powered search engine for math problems. You can enter almost any equation or function, and it will provide detailed solutions and explanations.
- Wolfram Alpha
Using these external resources alongside your Study.com materials will give you a well-rounded understanding of the precalculus concepts and help you tackle any tricky problems with confidence. Now, let’s move on to the key topics to focus on for your exam!
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Important Study Topics in Math 103🔑
To make sure you’re well-prepared for the Study.com Math 103: Precalculus final proctored exam, let’s break down some of the key concepts. We’ll use tables and comparisons to help make these topics clear and easy to understand.
- Functions and Their Transformations
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Concept
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Description
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Example
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|---|---|---|
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Function Notation
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Writing functions as f(x) instead of y
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f(x) = 2x + 3
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Vertical Line Test
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A way to determine if a graph is a function
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If a vertical line crosses the graph more than once, it's not a function.
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Transformations
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Shifting, reflecting, and dilating functions on the graph
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f(x) = (x-2)2 (shift right), g(x) = -f(x) (reflect)
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- Exponential and Logarithmic Functions
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Concept
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Description
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Example
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|---|---|---|
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Exponential Functions
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Functions in the form y = ab^x, where the growth rate is constant
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y = 2x
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Logarithms
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The inverse of exponential functions, answering "To what power?"
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log2(8) = 3 because 23 = 8
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Properties of Logs
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Rules that simplify logarithmic expressions
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log_b(xy) = log_b(x) + log_b(y)
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3. Trigonometry and the Unit Circle
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Concept
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Description
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Example
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|---|---|---|
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Unit Circle
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A circle with radius 1, used to define trigonometric functions
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(cos θ, sin θ) coordinates on the unit circle
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Trig Functions
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Sine, cosine, and tangent functions
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sin(θ) = opposite/hypotenuse
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Graphs of Trig Functions
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Sine and cosine functions create wave patterns
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y = sin(x), y = cos(x)
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4. Polynomial and Rational Functions
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Concept
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Description
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Example
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|---|---|---|
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Polynomial Functions
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Functions involving terms with variables raised to whole number powers
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f(x) = 2x3 - 3x2 + x - 5
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Factoring
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Breaking down polynomials into simpler components
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x2 - 5x + 6 = (x-2)(x-3)
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Rational Functions
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Ratios of polynomial functions
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f(x) = (x2 - 1)/(x + 1)
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Real-World Examples
Exponential Growth and Decay
- Example: Population growth or radioactive decay.
- Description: Exponential functions model situations where growth or decay happens at a constant rate.
- Equation: N(t) = N_0 e(rt), where N_0 is the initial quantity, r is the growth/decay rate, and t is time.
Trigonometry in Real Life
- Example: Architecture and engineering.
- Description: Trigonometry is used to calculate heights, distances, and angles in various construction projects.
- Application: Using sine and cosine functions to determine the slope of a roof or the height of a building.
Comparing Linear and Quadratic Functions
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Feature
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Linear Functions
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Quadratic Functions
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|---|---|---|
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Equation
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y = mx + b
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y = ax2 + bx + c
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Graph
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Straight line
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Parabola (U-shaped curve)
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Key Point
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Constant rate of change (slope)
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Vertex represents the maximum or minimum point
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By focusing on these key topics and understanding their applications, you’ll have a solid foundation to tackle the final exam. Now, let’s move on to some frequently asked questions that you might have about this course!
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Math 103: FAQs❓
Q: What is the format of the final proctored exam?
A: The proctored exam is similar to the previous quizzes but all the questions are multiple choices and they test all the content in the course. Courses that students will be required to take will include functions and limits, exponential and logarithmic equations, trigonometry, and others.
Q: How can I best prepare for the exam?
A: A good start toward following such a studied week-by-week plan is choosing I, II, III, and IV as a curriculum for the week. It is important to go through all of the practice problems, characterize critical items in notes, or use additional resources, such as Khan Academy and Quizlet.
Q: Which areas of this course might be the most difficult?
A: The two most common subjects that learners consider difficult are Trigonometry and Logarithms. It suggests that the areas that should be reviewed in detail are the unit circle, trigonometric functions, and properties of logarithms. Do not skimp on the extra materials to support these concepts; they play an important role in your lessons.
Q: How many hours a week should I spend studying?
A: It is possible to plan no less than 5-7 hours per week to study. This will provide you with enough time to go over each topic carefully, solve practice exercises, and go over the material that was difficult to grasp at first.
Q: Is there any prior knowledge required for this course?
A: It is best to approach this course with a small background in algebra and maths knowledge. If you feel like you need a refresher on algebra, it could be wise to go through some of the basics of algebra before you start learning precalculus.
Q: Am I allowed to use a calculator in the exam?
A: According to the rules stated in the exam regulations of this university, yes, a student is allowed to use an approved scientific calculator during the examination. It is recommended that one should go through its application in functions, trigonometric functions, and equations.
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Summarizing Math 103📄
Congratulations! I can now say that you are well prepared with a good strategy to go through the Study.com Math 103: Precalculus course and pass the final proctored exam with flying colors. Remember, consistency is key. Following the week-by-week study plan, using the listed outside sources, and focusing on the key topics will help you be prepared and calm when the examination finally comes.
At first, you may think taking Pre Calculus as a course is going to be a tough nut to crack but believe me, you will find the course to be quite doable and even fun sometimes. Use Study where there are many quizzes, videos, and practice problems to refresh your knowledge. com and other platforms. And do not forget that with each solved problem, you are moving closer to conquering the subject they call math.
Good luck, and happy studying! You’ve got this!
