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1Understanding Integers

1.1Place values
1.2Comparing and ordering numbers
1.3Rounding numbers

2Adding and Subtracting Integers

2.1Introduction to integer addition
2.2Adding integers
2.3Introduction to integer subtraction
2.4Subtracting integers
2.5Application of integer operations

3Multiplying and Dividing Integers

3.1Understanding integer multiplication
3.2Multiplying integers
3.3Understanding integer division
3.4Dividing integers
3.5Applications of integer operations

4Number Theory

4.1Divisibility Rules
4.2Determining Common Factors
4.3Determining Common Multiples
4.4Introduction to exponents

5Adding and Subtracting Fractions

5.1Using models to add and subtract fractions
5.2Adding fractions with like denominators
5.3Subtracting fractions with like denominators
5.4Adding and subtracting fractions with unlike denominators
5.5Adding and subtracting mixed numbers

6Multiplying and Dividing Fractions

6.1Multiplying fractions and whole numbers (free lessons)
6.2Dividing fractions with whole numbers
6.3Multiplying proper fractions
6.4Multiplying improper fractions and mixed numbers
6.5Dividing fractions and mixed numbers
6.6Applications of fraction operations

7Operation with Decimals

7.1Adding and subtracting decimals
7.2Multiplying decimals
7.3Dividing decimals
7.4Order of operations (BEDMAS)

8Fractions, Decimals, and Percents

8.1Percent of a number
8.2Taxes, discounts, tips and more

9Ratios, Rates, and Proportions

9.1Ratios (free lessons)
9.2Rates
9.3Proportions

10Introduction to Variables and Expressions

10.1Evaluating algebraic expressions

11Solving Linear Equations

11.1Solving linear equations using multiplication and division (free lessons)
11.2Solving two-step linear equations: ax+b=cax + b = c, xa+b=c{x \over a} + b = c
11.3Solving linear equations using distributive property: a(x+b)=ca(x + b) = c (free lessons)
11.4Solving linear equations with variables on both sides
11.5Solving literal equations

12Linear Inequalities

12.1Express linear inequalities graphically and algebraically (free lessons)
12.2Solving one-step linear inequalities (free lessons)
12.3Solving multi-step linear inequalities (free lessons)
12.4Graphing linear inequalities in two variables (free lessons)

13Measuring Systems

13.1Metric systems (free lessons)
13.2Imperial systems
13.3Conversions between metric and imperial systems
13.4Conversions involve squares and cubic

14Number System

14.1Understanding the number systems (free lessons)
14.2Prime factorization
14.3Greatest Common Factors (GCF)
14.4Least Common Multiple (LCM) (free lessons)
14.5Rational vs. Irrational numbers
14.6Converting repeating decimals to fractions

15Radicals

15.1Operations with radicals (free lessons)
15.2Conversion between entire radicals and mixed radicals
15.3Adding and subtracting radicals (free lessons)
15.4Multiplying radicals
15.5Solving radical equations

16Exponents

16.1Exponents: Product rule (ax)(ay)=a(x+y) (a^x)(a^y)=a^{(x+y)} (free lessons)
16.2Exponents: Division rule axay=a(x−y){a^x \over a^y}=a^{(x-y)}
16.3Exponents: Power rule (ax)y=a(x⋅y) (a^x)^y = a^{(x\cdot y)} (free lessons)
16.4Exponents: Negative exponents
16.5Exponents: Zero exponent: a0=1 a^0 = 1
16.6Exponents: Rational exponents
16.7Scientific notation
16.8Convert between radicals and rational exponents (free lessons)
16.9Solving for exponents
16.10Solving exponential equations using exponent rules

17Operations of Polynomials

17.1What is a polynomial? (free lessons)
17.2Polynomial components
17.3Multiplying monomial by monomial
17.4Multiplying monomial by binomial
17.5Multiplying binomial by binomial (free lessons)
17.6Multiplying polynomial by polynomial
17.7Applications of polynomials

18Introduction to Relations and Functions

18.1Relationship between two variables (free lessons)
18.2Understand relations between x- and y-intercepts
18.3Domain and range of a function (free lessons)
18.4Identifying functions
18.5Function notation (free lessons)

19Linear Functions

19.1Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} (free lessons)
19.2Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2) (free lessons)
19.3Slope equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}
19.4Slope intercept form: y = mx + b (free lessons)
19.5General form: Ax + By + C = 0 (free lessons)
19.6Point-slope form: y−y1=m(x−x1)y - y_1 = m (x - x_1) (free lessons)
19.7Rate of change
19.8Graphing linear functions using table of values
19.9Graphing linear functions using x- and y-intercepts (free lessons)
19.10Graphing from slope-intercept form y=mx+b
19.11Graphing linear functions using a single point and slope
19.12Word problems of graphing linear functions
19.13Parallel and perpendicular lines in linear functions (free lessons)
19.14Applications of linear relations

20Systems of Equations

20.1Determining number of solutions to linear equations (free lessons)
20.2Solving systems of linear equations by graphing
20.3Using elimination method to solve systems of linear equations
20.4Using substitution method to solve systems of linear equations
20.5System of linear-quadratic equations (free lessons)

21Factoring Polynomials

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
21.5Factoring difference of cubes
21.6Factoring sum of cubes

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
23.6Solving quadratic inequalities

24Rational Expressions

24.1Simplifying rational expressions and restrictions
24.2Adding and subtracting rational expressions (free lessons)
24.3Multiplying rational expressions
24.4Dividing rational expressions
24.5Solving rational equations
24.6Applications of rational equations
24.7Simplifying complex fractions
24.8Partial fraction decomposition

25Function Notation

25.1Function notation (free lessons)
25.2Operations with functions
25.3Adding functions
25.4Subtracting functions
25.5Multiplying functions
25.6Dividing functions
25.7Composite functions (free lessons)
25.8Inequalities of combined functions
25.9Inverse functions (free lessons)
25.10One to one functions
25.11Difference quotient: applications of functions

26Transformations of Functions

26.1Transformations of functions: Horizontal translations
26.2Transformations of functions: Vertical translations
26.3Reflection across the y-axis: y=f(−x)y = f(-x) (free lessons)
26.4Reflection across the x-axis: y=−f(x)y = -f(x)
26.5Transformations of functions: Horizontal stretches
26.6Transformations of functions: Vertical stretches
26.7Combining transformations of functions
26.8Even and odd functions

27Polynomial Functions

27.1What is a polynomial function? (free lessons)
27.2Polynomial long division (free lessons)
27.3Polynomial synthetic division
27.4Remainder theorem
27.5Factor theorem
27.6Rational zero theorem
27.7Characteristics of polynomial graphs
27.8Multiplicities of polynomials
27.9Imaginary zeros of polynomials
27.10Descartes’ rule of signs

28Trigonometry with Right Triangles

28.1Use sine ratio to calculate angles and side (Sin = oh \frac{o}{h} ) (free lessons)
28.2Use cosine ratio to calculate angles and side (Cos = ah \frac{a}{h} )
28.3Use tangent ratio to calculate angles and side (Tan = oa \frac{o}{a} )
28.4Combination of SohCahToa questions (free lessons)
28.5Solving expressions using 45-45-90 special right triangles (free lessons)
28.6Solving expressions using 30-60-90 special right triangles
28.7Word problems relating ladder in trigonometry
28.8Word problems relating guy wire in trigonometry
28.9Other word problems relating angles in trigonometry

29Trigonometric Ratios and Angle Measure

29.1Standard angles
29.2Coterminal angles (free lessons)
29.3Reference angles
29.4Find the exact value of trigonometric ratios
29.5ASTC rule in trigonometry (All Students Take Calculus) (free lessons)
29.6Unit circle (free lessons)
29.7Converting between degrees and radians
29.8Trigonometric ratios of angles in radians
29.9Radian measure and arc length

30Law of Sines and Cosines

30.1Law of sines
30.2Law of cosines
30.3Applications of the sine law and cosine law

31Imaginary and Complex Numbers

31.1Introduction to imaginary numbers (free lessons)
31.2Adding and subtracting complex numbers
31.3Complex conjugates
31.4Multiplying and dividing complex numbers

32Angles, Lines, and Transversals

32.1Pairs of lines and angles
32.2Parallel lines and transversals
32.3Parallel line proofs
32.4Perpendicular line proofs (free lessons)

33Circles

33.1Circle and circumference
33.2Angles in a circle (free lessons)
33.3Arcs of a circle
33.4Areas and sectors of circles
33.5Conics - Circle

34Surface Area and Volume

34.1Surface area and volume of prisms (free lessons)
34.2Surface area and volume of pyramids
34.3Surface area and volume of cylinders
34.4Surface area and volume of cones (free lessons)
34.5Surface area and volume of spheres

35Statistics

35.1Median and mode
35.2Mean
35.3Range and outliers
35.4Application of averages

36Data and Graphs

36.1Reading and drawing histograms
36.2Reading and drawing line graphs
36.3Box-and-whisker plots and scatter plots
36.4Stem-and-leaf plots
36.5Reading and drawing Venn diagrams

37Probability

37.1Determining probabilities using tree diagrams and tables (free lessons)
37.2Probability of independent events
37.3Probability with Venn diagrams
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