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Intermediate Algebra Topics

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1Adding and Subtracting Integers

1.1Introduction to integer addition
1.2Adding integers
1.3Introduction to integer subtraction
1.4Subtracting integers
1.5Application of integer operations

2Multiplying and Dividing Integers

2.1Understanding integer multiplication
2.2Multiplying integers
2.3Understanding integer division
2.4Dividing integers
2.5Applications of integer operations

3Operations with Decimals

3.1Adding and subtracting decimals
3.2Multiplying decimals
3.3Dividing decimals
3.4Order of operations (BEDMAS)

4Adding and Subtracting Fractions

4.1Using models to add and subtract fractions
4.2Adding fractions with like denominators
4.3Subtracting fractions with like denominators
4.4Adding and subtracting fractions with unlike denominators
4.5Adding and subtracting mixed numbers

5Multiplying and Dividing Fractions

5.1Multiplying fractions and whole numbers (free lessons)
5.2Dividing fractions with whole numbers
5.3Multiplying proper fractions
5.4Multiplying improper fractions and mixed numbers
5.5Dividing fractions and mixed numbers
5.6Applications of fraction operations

6Introduction to Variables and Expressions

6.1Evaluating algebraic expressions

7Coordinates, Quadrants, and Transformations

7.1Cartesian plane
7.2Draw on coordinate planes
7.3Introduction to transformations
7.4Horizontal and vertical distances

8Number System

8.1Understanding the number systems (free lessons)
8.2Prime factorization
8.3Greatest Common Factors (GCF)
8.4Least Common Multiple (LCM) (free lessons)
8.5Rational vs. Irrational numbers
8.6Converting repeating decimals to fractions

9Set Theory

9.1Set notation
9.2Set builder notation

10Solving Linear Equations

10.1Solving linear equations using multiplication and division (free lessons)
10.2Solving two-step linear equations: ax+b=cax + b = c, xa+b=c{x \over a} + b = c
10.3Solving linear equations using distributive property: a(x+b)=ca(x + b) = c (free lessons)
10.4Solving linear equations with variables on both sides
10.5Solving literal equations

11Introduction to Relations and Functions

11.1Relationship between two variables (free lessons)
11.2Understand relations between x- and y-intercepts
11.3Domain and range of a function (free lessons)
11.4Identifying functions
11.5Function notation (free lessons)

12Linear Functions

12.1Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} (free lessons)
12.2Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2) (free lessons)
12.3Slope equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}
12.4Slope intercept form: y = mx + b (free lessons)
12.5General form: Ax + By + C = 0 (free lessons)
12.6Point-slope form: y−y1=m(x−x1)y - y_1 = m (x - x_1) (free lessons)
12.7Rate of change
12.8Graphing linear functions using table of values
12.9Graphing linear functions using x- and y-intercepts (free lessons)
12.10Graphing from slope-intercept form y=mx+b
12.11Graphing linear functions using a single point and slope
12.12Word problems of graphing linear functions
12.13Parallel and perpendicular lines in linear functions (free lessons)
12.14Applications of linear relations

13Linear Equations

13.1Introduction to linear equations (free lessons)
13.2Introduction to nonlinear equations
13.3Special case of linear equations: Horizontal lines
13.4Special case of linear equations: Vertical lines
13.5Parallel line equation (free lessons)
13.6Perpendicular line equation
13.7Combination of both parallel and perpendicular line equations
13.8Applications of linear equations

14Absolute Value

14.1Absolute value functions (free lessons)
14.2Solving absolute value equations
14.3Solving absolute value inequalities

15Systems of Linear Equations

15.1Solving systems of linear equations by graphing
15.2Using elimination method to solve systems of equations
15.3Using substitution method to solve systems of equations
15.4Solving 3 variable systems of equations by substitution
15.5Solving 3 variable systems of equations by elimination
15.6Solving 3 variable systems of equations with no or infinite solutions
15.7Word problems relating 3 variable systems of equations
15.8Solving linear systems using Cramer's Rule
15.9Solving linear systems using 2 x 2 inverse matrices

16Inequalities in One Variable

16.1Express linear inequalities graphically and algebraically (free lessons)
16.2Solving one-step linear inequalities (free lessons)
16.3Solving multi-step linear inequalities (free lessons)
16.4Solving quadratic inequalities

17Inequalities in Two Variables

17.1Graphing linear inequalities in two variables (free lessons)
17.2Graphing systems of linear inequalities (free lessons)
17.3What is linear programming?
17.4Linear programming word problems

18Functions

18.1Function notation (free lessons)
18.2Composite functions (free lessons)
18.3Inverse functions (free lessons)

19Exponents

19.1Exponents: Product rule (ax)(ay)=a(x+y) (a^x)(a^y)=a^{(x+y)} (free lessons)
19.2Exponents: Division rule axay=a(x−y){a^x \over a^y}=a^{(x-y)}
19.3Exponents: Power rule (ax)y=a(x⋅y) (a^x)^y = a^{(x\cdot y)} (free lessons)
19.4Exponents: Negative exponents
19.5Exponents: Zero exponent: a0=1 a^0 = 1
19.6Exponents: Rational exponents
19.7Solving exponential equations using exponent rules
19.8Scientific notation

20Operations with Polynomials

20.1Adding and subtracting polynomials
20.2Multiplying monomial by monomial
20.3Multiplying monomial by binomial
20.4Multiplying binomial by binomial (free lessons)
20.5Multiplying polynomial by polynomial
20.6Polynomial long division (free lessons)
20.7Polynomial synthetic division

21Factoring

21.1Factor by taking out the greatest common factor (free lessons)
21.2Factor by grouping
21.3Factoring difference of squares: x2−y2x^2 - y^2
21.4Factoring trinomials

22Quadratic Functions

22.1Introduction to quadratic functions (free lessons)
22.2Transformations of quadratic functions
22.3Quadratic function in general form: y=ax2+bx+cy = ax^2 + bx+c
22.4Quadratic function in vertex form: y=a(x−p)2+qy = a(x-p)^2 + q
22.5Completing the square (free lessons)
22.6Converting from general to vertex form by completing the square
22.7Shortcut: Vertex formula (free lessons)
22.8Graphing quadratic functions: General form VS. Vertex form
22.9Finding the quadratic functions for given parabolas (free lessons)
22.10Applications of quadratic functions

23Solving Quadratic Equations

23.1Solving quadratic equations by factoring
23.2Solving quadratic equations by completing the square
23.3Using quadratic formula to solve quadratic equations
23.4Nature of roots of quadratic equations: The discriminant
23.5Applications of quadratic equations

24Radicals

24.1Square and square roots (free lessons)
24.2Evaluating and simplifying radicals
24.3Operations with radicals (free lessons)
24.4Conversion between entire radicals and mixed radicals
24.5Adding and subtracting radicals (free lessons)
24.6Multiplying radicals
24.7Rationalize the denominator
24.8Solving radical equations

25Rational Expressions

25.1Simplifying rational expressions and restrictions
25.2Adding and subtracting rational expressions (free lessons)
25.3Multiplying rational expressions
25.4Dividing rational expressions
25.5Solving rational equations
25.6Applications of rational equations
25.7Simplifying complex fractions
25.8Partial fraction decomposition

26Polynomial Functions

26.1What is a polynomial function? (free lessons)
26.2Remainder theorem
26.3Factor theorem
26.4Rational zero theorem
26.5Characteristics of polynomial graphs
26.6Multiplicities of polynomials
26.7Imaginary zeros of polynomials
26.8Determining the equation of a polynomial function
26.9Applications of polynomial functions
26.10Solving polynomial inequalities
26.11Fundamental theorem of algebra
26.12Descartes’ rule of signs

27Exponential Functions

27.1Graphing exponential functions
27.2Graphing transformations of exponential functions
27.3Finding an exponential function given its graph
27.4Exponential growth and decay by percentage

28Logarithmic Functions

28.1What is a logarithm?
28.2Converting from logarithmic form to exponential form (free lessons)
28.3Evaluating logarithms without a calculator
28.4Common logarithms
28.5Natural log: ln
28.6Evaluating logarithms using change-of-base formula
28.7Converting from exponential form to logarithmic form (free lessons)
28.8Solving exponential equations with logarithms
28.9Product rule of logarithms (free lessons)
28.10Quotient rule of logarithms
28.11Combining product rule and quotient rule in logarithms
28.12Evaluating logarithms using logarithm rules
28.13Solving logarithmic equations (free lessons)
28.14Graphing logarithmic functions
28.15Finding a logarithmic function given its graph

29Conics

29.1Conics - Parabola
29.2Conics - Ellipse
29.3Conics - Circle
29.4Conics - Hyperbola

30Imaginary and Complex Numbers

30.1Introduction to imaginary numbers (free lessons)
30.2Complex numbers and complex planes (free lessons)
30.3Adding and subtracting complex numbers
30.4Complex conjugates
30.5Multiplying and dividing complex numbers

31Sequences, Series, and Binomial Theorem

31.1Arithmetic sequences (free lessons)
31.2Arithmetic series (free lessons)
31.3Geometric sequences
31.4Geometric series
31.5Infinite geometric series
31.6Sigma notation
31.7Binomial theorem
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