# College Algebra Help & Practice

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##### 1Surface Area and Volume

##### 2Rational Numbers

##### 3Powers and Exponents

##### 4Number System and Radicals

##### 5Radicals

- 5.1Square and square roots
- 5.2Cubic and cube roots
- 5.3Evaluating and simplifying radicals
- 5.4Converting radicals to mixed radicals
- 5.5Converting radicals to entire radicals
- 5.6Adding and subtracting radicals
- 5.7Multiplying and dividing radicals
- 5.8Rationalize the denominator
- 5.9Operations with radicals
- 5.10Conversion between entire radicals and mixed radicals
- 5.11Adding and subtracting radicals
- 5.12Multiplying radicals (advanced)
- 5.13Solving radical equations (advanced)

- 5.1Square and square roots
##### 6Exponents

##### 7Operations of Polynomials

##### 8Factorising Polynomial Expressions

- 8.1Common factors of polynomials
- 8.2Factorising polynomials by grouping
- 8.3Solving polynomials with unknown coefficients
- 8.4Solving polynomials with unknown constant terms
- 8.5Factorising polynomials:
*x^2 + bx + c* - 8.6Applications of polynomials:
*x^2 + bx + c* - 8.7Solving polynomials with the unknown "b" from $ax^2 + bx + c$
- 8.8Factorising polynomials: $ax^2 + bx + c$
- 8.9Factorising perfect square trinomials:
*(a + b)^2 = a^2 + 2ab + b^2*or*(a - b)^2 = a^2 - 2ab + b^2* - 8.10Find the difference of squares:
*(a - b)(a + b) = (a^2 - b^2)* - 8.11Evaluating polynomials
- 8.12Using algebra tiles to factorise polynomials
- 8.13Solving polynomial equations
- 8.14Word problems of polynomials

- 8.1Common factors of polynomials
##### 9Introduction to Relations and Functions

##### 10Linear Functions

- 10.1Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
- 10.2Midpoint formula: $M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)$
- 10.3Gradient equation: $m = \frac{y_2-y_1}{x_2- x_1}$
- 10.4Gradient intercept form: y = mx + b
- 10.5General form: Ax + By + C = 0
- 10.6Gradient-point form: $y - y_1 = m (x - x_1)$
- 10.7Rate of change
- 10.8 Graphing linear functions using table of values
- 10.9Graphing linear functions using x- and y-intercepts
- 10.10Graphing from slope-intercept form y=mx+b
- 10.11Graphing linear functions using a single point and gradient
- 10.12Word problems of graphing linear functions
- 10.13Parallel and perpendicular lines in linear functions
- 10.14Applications of linear relations

- 10.1Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
##### 11Absolute Value Functions

##### 12Linear Equations

- 12.1Introduction to linear equations
- 12.2Introduction to nonlinear equations
- 12.3Special case of linear equations: Horizontal lines
- 12.4Special case of linear equations: Vertical lines
- 12.5Parallel line equation
- 12.6Perpendicular line equation
- 12.7Combination of both parallel and perpendicular line equations
- 12.8Applications of linear equations

- 12.1Introduction to linear equations
##### 13Solving Linear Systems

- 13.1Determining number of solutions to linear equations
- 13.2Solving systems of linear equations by graphing
- 13.3Using elimination method to solve systems of equations
- 13.4Using substitution method to solve systems of equations
- 13.5Money related questions in linear equations
- 13.6Unknown number related questions in linear equations
- 13.7Distance and time related questions in linear equations
- 13.8Rectangular shape related questions in linear equations
- 13.9Solving 3 variable systems of equations by substitution
- 13.10Solving 3 variable systems of equations by elimination
- 13.11Solving 3 variable systems of equations (no solution, infinite solutions)
- 13.12Word problems relating 3 variable systems of equations

- 13.1Determining number of solutions to linear equations
##### 14Linear Inequalities

##### 15Inequalities in Two Variables

##### 16Factorising Quadratic Equations

##### 17Quadratic Functions

- 17.1Characteristics of quadratic functions
- 17.2Transformations of quadratic functions
- 17.3Quadratic function in general form: y = $ax^2 + bx+c$
- 17.4Quadratic function in vertex form:
*y = a(x-p)^2 + q* - 17.5Completing the square
- 17.6Converting from general to vertex form by completing the square
- 17.7Shortcut: Vertex formula
- 17.8Graphing parabolas for given quadratic functions
- 17.9Finding the quadratic functions for given parabolas
- 17.10Applications of quadratic functions

- 17.1Characteristics of quadratic functions
##### 18Quadratic Equations and Inequalities

##### 19Graphing Rational Functions

##### 20Functions

- 20.1Function notation
- 20.2Operations with functions
- 20.3Adding functions
- 20.4Subtracting functions
- 20.5Multiplying functions
- 20.6Dividing functions
- 20.7Composite functions
- 20.8Inequalities of combined functions
- 20.9Inverse functions
- 20.10One to one functions
- 20.11Difference quotient: applications of functions

- 20.1Function notation
##### 21Direct and Inverse Variation

##### 22Piecewise Functions

##### 23Transformations of Functions

- 23.1Transformations of functions: Horizontal translations
- 23.2Transformations of functions: Vertical translations
- 23.3Reflection across the y-axis:
*y = f(-x)* - 23.4Reflection across the x-axis:
*y = -f(x)* - 23.5Transformations of functions: Horizontal stretches
- 23.6Transformations of functions: Vertical stretches
- 23.7Combining transformations of functions
- 23.8Even and odd functions

- 23.1Transformations of functions: Horizontal translations
##### 24Exponential Functions

- 24.1Exponents: Product rule
*(a^x)(a^y) = a^(x+y)* - 24.2Exponents: Division rule (a^x / a^y) = a^(x-y)
- 24.3Exponents: Power rule
*(a^x)^y = a^(x * y)* - 24.4Exponents: Negative exponents
- 24.5Exponents: Zero exponent:
*a^0 = 1* - 24.6Exponents: Rational exponents
- 24.7Solving exponential equations using exponent rules
- 24.8Graphing exponential functions
- 24.9Graphing transformations of exponential functions
- 24.10Finding an exponential function given its graph

- 24.1Exponents: Product rule
##### 25Logarithmic Functions

- 25.1What is a logarithm?
- 25.2Converting from logarithmic form to exponential form
- 25.3Evaluating logarithms without a calculator
- 25.4Common logarithms
- 25.5Natural log: ln
- 25.6Evaluating logarithms using change-of-base formula
- 25.7Converting from exponential form to logarithmic form
- 25.8Solving exponential equations with logarithms
- 25.9Product rule of logarithms
- 25.10Quotient rule of logarithms
- 25.11Combining product rule and quotient rule in logarithms
- 25.12Evaluating logarithms using logarithm rules
- 25.13Solving logarithmic equations
- 25.14Graphing logarithmic functions
- 25.15Finding a logarithmic function given its graph

- 25.1What is a logarithm?
##### 26Applications of Exponential and Logarithmic Functions

- 26.1Exponential growth and decay by a factor
- 26.2Exponential decay: Half-life
- 26.3Exponential growth and decay by percentage
- 26.4Finance: Compound interest
- 26.5Continuous growth and decay
- 26.6Logarithmic scale: Richter scale (earthquake)
- 26.7Logarithmic scale: pH scale
- 26.8Logarithmic scale: dB scale
- 26.9Finance: Future value and present value

- 26.1Exponential growth and decay by a factor
##### 27Sequences and Series

##### 28Permutations and Combinations