Ace College Algebra

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Step-by-Step Solutions

Master advanced functions, calculus, and applications

Perfect Curriculum Match

Aligned with Leaving Certificate requirements

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Most students improve one letter grade in 4-6 weeks

College Algebra Topics

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

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

Powers and Exponents

Using exponents to describe numbers

Exponent rules

Order of operations with exponents

Using exponents to solve problems

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

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)

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

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

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 $ax^2 + bx + c$

Factorising polynomials: $ax^2 + bx + c$

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

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

Linear Functions

Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Midpoint formula: $M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)$

Gradient equation: $m = \frac{y_2-y_1}{x_2- x_1}$

Gradient intercept form: y = mx + b

General form: Ax + By + C = 0

Gradient-point form: $y - y_1 = m (x - x_1)$

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

Absolute Value Functions

Absolute value functions

Solving absolute value equations

Solving absolute value inequalities

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

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

Linear Inequalities

Express linear inequalities graphically and algebraically

Solving one-step linear inequalities

Solving multi-step linear inequalities

Compound inequalities

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

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

Quadratic Functions

Characteristics of quadratic functions

Transformations of quadratic functions

Quadratic function in general form: y = $ax^2 + bx+c$

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

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

Graphing Rational Functions

Graphing reciprocals of linear functions

Graphing reciprocals of quadratic functions

Graphs of rational functions

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

Direct and Inverse Variation

Direct variation

Inverse variation

Joint and combined variation

Piecewise Functions

Evaluating piecewise functions

Graphing piecewise linear functions

Graphing piecewise non-linear functions

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

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

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

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

Sequences and Series

Arithmetic sequences

Arithmetic series

Geometric sequences

Geometric series

Infinite geometric series

Sigma notation

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.

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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.

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