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College Algebra Topics

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video
Surface Area and Volume
Introduction to surface area of 3-dimensional shapes
Nets of 3-dimensional shapes
Surface area of 3-dimensional shapes
Surface area of prisms
Surface area of cylinders
video
Rational Numbers
Comparing and ordering rational numbers
Solving problems with rational numbers in decimal form
Solving problems with rational numbers in fraction form
Determine square roots of rational numbers
video
Powers and Exponents
Using exponents to describe numbers
Exponent rules
Order of operations with exponents
Using exponents to solve problems
video
Number System and Radicals
Understanding the number systems
Prime factorisation
Greatest Common Factors (GCF)
Least Common Multiple (LCM)
Rational vs. Irrational numbers
Converting repeating decimals to fractions
video
Radicals
Square and square roots
Cubic and cube roots
Evaluating and simplifying radicals
Converting radicals to mixed radicals
Converting radicals to entire radicals
Adding and subtracting radicals
Multiplying and dividing radicals
Rationalize the denominator
Operations with radicals
Conversion between entire radicals and mixed radicals
Adding and subtracting radicals
Multiplying radicals (advanced)
Solving radical equations (advanced)
video
Exponents
Product rule of exponents
Quotient rule of exponents
Power of a product rule
Power of a quotient rule
Power of a power rule
Negative exponent rule
Combining the exponent rules
Scientific notation
Rational exponents
Solving for exponents
video
Operations of Polynomials
What is a polynomial?
Polynomial components
Multiplying monomial by monomial
Multiplying monomial by binomial
Multiplying binomial by binomial
Multiplying polynomial by polynomial
Applications of polynomials
video
Factorising Polynomial Expressions
Common factors of polynomials
Factorising polynomials by grouping
Solving polynomials with unknown coefficients
Solving polynomials with unknown constant terms
Factorising polynomials: x^2 + bx + c
Applications of polynomials: x^2 + bx + c
Solving polynomials with the unknown "b" from ax2+bx+cax^2 + bx + cax2+bx+c
Factorising polynomials: ax2+bx+cax^2 + bx + cax2+bx+c
Factorising perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2
Find the difference of squares: (a - b)(a + b) = (a^2 - b^2)
Evaluating polynomials
Using algebra tiles to factorise polynomials
Solving polynomial equations
Word problems of polynomials
video
Introduction to Relations and Functions
Relationship between two variables
Understand relations between x- and y-intercepts
Domain and range of a function
Identifying functions
Function notation
video
Linear Functions
Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}d=(x2​−x1​)2+(y2​−y1​)2​
Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)M=(2x1​+x2​​,2y1​+y2​​)
Gradient equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}m=x2​−x1​y2​−y1​​
Gradient intercept form: y = mx + b
General form: Ax + By + C = 0
Gradient-point form: y−y1=m(x−x1)y - y_1 = m (x - x_1)y−y1​=m(x−x1​)
Rate of change
Graphing linear functions using table of values
Graphing linear functions using x- and y-intercepts
Graphing from slope-intercept form y=mx+b
Graphing linear functions using a single point and gradient
Word problems of graphing linear functions
Parallel and perpendicular lines in linear functions
Applications of linear relations
video
Absolute Value Functions
Absolute value functions
Solving absolute value equations
Solving absolute value inequalities
video
Linear Equations
Introduction to linear equations
Introduction to nonlinear equations
Special case of linear equations: Horizontal lines
Special case of linear equations: Vertical lines
Parallel line equation
Perpendicular line equation
Combination of both parallel and perpendicular line equations
Applications of linear equations
video
Solving Linear Systems
Determining number of solutions to linear equations
Solving systems of linear equations by graphing
Using elimination method to solve systems of equations
Using substitution method to solve systems of equations
Money related questions in linear equations
Unknown number related questions in linear equations
Distance and time related questions in linear equations
Rectangular shape related questions in linear equations
Solving 3 variable systems of equations by substitution
Solving 3 variable systems of equations by elimination
Solving 3 variable systems of equations (no solution, infinite solutions)
Word problems relating 3 variable systems of equations
video
Linear Inequalities
Express linear inequalities graphically and algebraically
Solving one-step linear inequalities
Solving multi-step linear inequalities
Compound inequalities
video
Inequalities in Two Variables
Graphing linear inequalities in two variables
Graphing simultaneous linear inequalities
Graphing quadratic inequalities in two variables
Graphing simultaneous quadratic inequalities
Applications of inequalities
What is linear programming?
Linear programming word problems
video
Factorising Quadratic Equations
Factorise by taking out the greatest common factor
Factorise by grouping
Factorising difference of squares: x^2 - y^2
Factorising trinomials
Factoring difference of cubes
Factoring sum of cubes
video
Quadratic Functions
Characteristics of quadratic functions
Transformations of quadratic functions
Quadratic function in general form: y = ax2+bx+cax^2 + bx+cax2+bx+c
Quadratic function in vertex form: y = a(x-p)^2 + q
Completing the square
Converting from general to vertex form by completing the square
Shortcut: Vertex formula
Graphing parabolas for given quadratic functions
Finding the quadratic functions for given parabolas
Applications of quadratic functions
video
Quadratic Equations and Inequalities
Solving quadratic equations by factorising
Solving quadratic equations by completing the square
Using quadratic formula to solve quadratic equations
Nature of roots of quadratic equations: The discriminant
Applications of quadratic equations
Solving quadratic inequalities
video
Graphing Rational Functions
Graphing reciprocals of linear functions
Graphing reciprocals of quadratic functions
Graphs of rational functions
video
Functions
Function notation
Operations with functions
Adding functions
Subtracting functions
Multiplying functions
Dividing functions
Composite functions
Inequalities of combined functions
Inverse functions
One to one functions
Difference quotient: applications of functions
video
Direct and Inverse Variation
Direct variation
Inverse variation
Joint and combined variation
video
Piecewise Functions
Evaluating piecewise functions
Graphing piecewise linear functions
Graphing piecewise non-linear functions
video
Transformations of Functions
Transformations of functions: Horizontal translations
Transformations of functions: Vertical translations
Reflection across the y-axis: y = f(-x)
Reflection across the x-axis: y = -f(x)
Transformations of functions: Horizontal stretches
Transformations of functions: Vertical stretches
Combining transformations of functions
Even and odd functions
video
Exponential Functions
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
Solving exponential equations using exponent rules
Graphing exponential functions
Graphing transformations of exponential functions
Finding an exponential function given its graph
video
Logarithmic Functions
What is a logarithm?
Converting from logarithmic form to exponential form
Evaluating logarithms without a calculator
Common logarithms
Natural log: ln
Evaluating logarithms using change-of-base formula
Converting from exponential form to logarithmic form
Solving exponential equations with logarithms
Product rule of logarithms
Quotient rule of logarithms
Combining product rule and quotient rule in logarithms
Evaluating logarithms using logarithm rules
Solving logarithmic equations
Graphing logarithmic functions
Finding a logarithmic function given its graph
video
Applications of Exponential and Logarithmic Functions
Exponential growth and decay by a factor
Exponential decay: Half-life
Exponential growth and decay by percentage
Finance: Compound interest
Continuous growth and decay
Logarithmic scale: Richter scale (earthquake)
Logarithmic scale: pH scale
Logarithmic scale: dB scale
Finance: Future value and present value
video
Sequences and Series
Arithmetic sequences
Arithmetic series
Geometric sequences
Geometric series
Infinite geometric series
Sigma notation
video
Permutations and Combinations
Fundamental counting principle
Factorial notation
Path counting problems
Permutation vs. Combination
Permutations
Combinations
Problems involving both permutations and combinations
Pascal's triangle
Binomial theorem

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What is College Algebra?

What is Algebra and why do we need it? Algebra can be defined as the branch of math that uses symbols and letters in lieu of numbers to study a variety of phenomena. Often times these symbols represent a simplification of known or unknown variables and factors involved in a complex algebraic equations or formulas. Algebraic equations and formulas are often used to describe a relationship between these variables. The study of Algebra also involves the rules that dictate how these symbols and letters operate.

Understandably, many of you may have thought you escaped Algebra after graduating high school. Kissing polynomials and inequalities goodbye must have left you overjoyed! The reality for many of you however is that Algebra will continue to be fundamental as you begin your college education - In fact, much of Algebra forms the basis of all math you have learnt up to now! The utility of Algebra is particularly prominent in fields of science, technology, engineering and math (STEM). Moving forward and beyond academia, Algebra will continue to be your friend in a process you may know as "growing up". Use StudyPug and gain more than just great grades in this intro to College Algebra! Learn life skills to improve your financial planning and budgeting, assess risks in your business or investment ventures, and make good decisions regarding healthcare insurance.

Already feeling unprepared for College Algebra and all those College Algebra formulas that will ensue? Wish you didn't burn all your Algebra 1 and Algebra 2 notes after graduating highschool? StudyPug takes learning College Algebra online, catered for all levels, beginning at College Algebra for dummies! Otherwise browse our other online math courses and get the Algebra help you need! We cover Algebra 1 problems and offer comprehensive Algebra 1 review so let us help you cut to the chase and get you up to speed with whatever you may need right away!

Is College Algebra hard?

College Algebra will definitely be harder than the likes of Algebra 1 or Algebra 2. But if you have completed these courses, you should be well prepared to tackle College Algebra. College Algebra math will build on elementary Algebra concepts you learnt in Algebra 1 and Algebra 2, so not everything will come as a surprise. Furthermore, some of the skills learnt in Algebra 1 and Algebra 2 will be accessed and advanced in College Algebra. Our College Algebra tutors are always available, 24/7 to provide you help with College Algebra. Whether you are just beginning Algebra, or feel like you need to learn Algebra alongside Algebra for dummies, find yourself solving increasingly difficult Algebra problems in no time with the help of our expert, knowledgeable tutors.

At StudyPug we want to help you learn Algebra topics at your own pace and master all things Algebra! So do not fret if you feel like some topics such as linear equations or permutations and combinations, are more challenging than others, this is normal! My Algebra skills are not the same as yours, and you can certainly expect an increase in the level of difficulty jumping from Algebra 1 or Algebra 2 into College Algebra. Rest assured, we will leave no student behind or question unanswered, so be prepared for a wealth of learning!

How to learn College Algebra?

While there is no one formula per se that you could use to learn College Algebra, we would still like to suggest the following on how to do Algebra, or how to learn algebra using StudyPug:

At StudyPug we have over 1000's of lessons, each containing several step-by-step examples to provide you with the best College Algebra study guide money can buy! With immediate access to the entire course, learn College Algebra by supplementing your learning of topics already covered in class, learn ahead to gain new skills and practice with more challenging topics, or swing back to refresh your memory and obtain complete coverage of previous topics.

Remember that some of these lessons will build on Algebra content you have previously learnt. A strong grasp of these more basic, core concepts is critical to being successful in College Algebra. Take advantage of your unlimited access to all of StudyPug and do not skip out the essentials! Do not be ashamed if you have forgotten how to solve quadratic equations, how to wrangle radicals, or operate functions. This is a place to learn and we all start somewhere!

With 24/7 help, our online College Algebra course is a great way to learn College Algebra with the confidence that no time is wasted. We want you to get the most out of your learning by practicing as many College Algebra problems as possible. Practicing is essential because it confirms that you have successful learnt, comprehended, and achieved the learning objective(s) of that lesson. Supplement your College Algebra textbook or College Algebra worksheets with our inventory of unique questions! The greater exposure you have with a variety of questions, the more learning will ensue as you encounter different styles of questions and different ways to solve problems.

Last but not least, what would learning be without any help?! Our StudyPug tutors will always be there for you, ready for all the College Algebra help you may need! Bring your questions, homework, quiz, textbook, syllabus, revision exercises to us, and lets conquer College Algebra together!

How to pass College Algebra?

Going through and successfully passing College Algebra is a big step in making sure you are well oiled for courses like Calculus and Statistics. Perhaps some of you are keeners preparing for your big CLEP exam - Passing your CLEP College Algebra exam means a lot for you as you are hoping to just jump straight into the deep waters of Calculus and Statistics as soon as you start College. Fear not as such is no secret to our team here at StudyPug. We get that exams are stressful and a lot can hang in the balance in getting the grades and meeting the academic goals you desire.

Here at StudyPug we set you up for success right from the get go: Our College Algebra lessons are geared for test takers and exam reviewers looking for a way to get more out of College Algebra practice problems. Our quick and concise College Algebra tutorials focus heavily on walking through example questions to help with your College Algebra exam prep. By explaining the thought process, looking at alternative methods to solve problems, highlighting common mistakes and identifying pro tips and strategies, we offer you the best help when exercising college algebra practice.

By providing you with a thorough yet rapid College Algebra review experience, we are able to cover more topics and questions in a shorter amount of time! Worry no more about cramming or convoluted questions and let us help you ease into the habit of making College Algebra practice easy practice! With our vast repertoire of College Algebra questions, we seek to provide you a way to sample a College Algebra practice test without the hassle of having to finding accompanying answers. Each question has been uniquely designed to offer you easy practice with College Algebra test and exam style questions. Feeling stuck? Simply swing back into the lesson and review the methods and steps required to solve similar kinds of questions.

We truly believe that practicing math problems is the best way to learn, apply and prepare yourself for any upcoming College Algebra assessment. So what are you waiting for? Dive into our collection of up to 1420 College Algebra practice questions and resurface ready and confident to pass any College Algebra assessment!

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