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Arithmetic, Elementary Algebra, College-Level Math, Advanced Algebra, and Quantitative Reasoning. We cover all sections comprehensively.

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1. Numbers and Relations

1.1

Place value

1.2

Comparing and ordering numbers

1.3

Rounding numbers

2. Number Theory

2.1

Divisibility Rules

2.2

Prime factorization

2.3

Determining Common Factors

2.4

Determining Common Multiples

2.5

Introduction to exponents

3. Adding and Subtracting Integers

3.1

Introduction to integer addition

3.2

Adding integers

3.3

Introduction to integer subtraction

3.4

Subtracting integers

3.5

Application of integer operations

4. Multiplying and Dividing Integers

4.1

Understanding integer multiplication

4.2

Multiplying integers

4.3

Understanding integer division

4.4

Dividing integers

4.5

Applications of integer operations

5. Operations with Decimals

5.1

Adding and subtracting decimals

5.2

Multiplying decimals

5.3

Dividing decimals

5.4

Order of operations (PEMDAS)

6. Fractions, Decimals, and Percents

6.1

Representing percents

6.2

Percent of a number

6.3

Converting among decimals, fractions, and percents

6.4

Adding and multiplying percents

6.5

Applications of percents

6.6

Taxes, discounts, tips and more

6.7

Simple interest

7. Adding and Subtracting Fractions

7.1

Using models to add and subtract fractions

7.2

Adding fractions with like denominators

7.3

Subtracting fractions with like denominators

7.4

Adding and subtracting fractions with unlike denominators

7.5

Adding and subtracting mixed numbers

8. Multiplying and Dividing Fractions

8.1

Multiplying fractions and whole numbers

8.2

Dividing fractions with whole numbers

8.3

Multiplying proper fractions

8.4

Multiplying improper fractions and mixed numbers

8.5

Dividing fractions and mixed numbers

8.6

Applications of fraction operations

9. Introduction to Variables and Expressions

9.1

Evaluating algebraic expressions

10. Introduction to Equations

10.1

Solving one - step equations: x + a = b

11. Solving Linear Equations

11.1

Solving linear equations using multiplication and division

11.2

Solving two-step linear equations: ax + b = c, x/a + b = c

11.3

Solving linear equations using distributive property: a(x + b) = c

11.4

Solving linear equations with variables on both sides

11.5

Solving literal equations

12. Ratios, Rates, and Proportions

12.1

Ratios

12.2

Rates

12.3

Proportions

13. Angles, Lines, and Transversals

13.1

Pairs of lines and angles

13.2

Parallel lines and transversals

13.3

Parallel line proofs

13.4

Perpendicular line proofs

14. Circles

14.1

Circles and circumference

14.2

Arcs of a circle

14.3

Areas and sectors of circles

14.4

Angles in a circle

14.5

Chord properties in circles

14.6

Tangent properties in circles

14.7

Central and inscribed angles in circle

15. Surface Area of 3D Shapes

15.1

Introduction to surface area of 3-dimensional shapes

15.2

Nets of 3-dimensional shapes

15.3

Surface area of prisms

15.4

Surface area of cylinders

16. Symmetry and Surface Area

16.1

Line symmetry

16.2

Rotational symmetry and transformations

16.3

Surface area of 3-dimensional shapes

17. Scale Factors and Similarity

17.1

Enlargements and reductions with scale factors

17.2

Scale diagrams

17.3

Similar triangles

17.4

Similar polygons

18. Pythagorean Theorem

18.1

Squares and square roots

18.2

Pythagorean theorem

18.3

Estimating square roots

18.4

Using the pythagorean relationship

18.5

Applications of pythagorean theorem

19. Statistics

19.1

Median and mode

19.2

Mean

19.3

Range and outliers

19.4

Application of averages

20. Data and Graphs

20.1

Reading and drawing bar graphs

20.2

Reading and drawing histograms

20.3

Reading and drawing line graphs

20.4

Box-and-whisker plots and scatter plots

20.5

Reading and drawing Venn diagrams

20.6

Stem-and-leaf plots

20.7

Frequency tables and dot plots

21. Linear Inequalities

21.1

Express linear inequalities graphically and algebraically

21.2

Solving one-step linear inequalities

21.3

Solving multi-step linear inequalities

21.4

Compound inequalities

22. Introduction to Relations and Functions

22.1

Relationship between two variables

22.2

Understand relations between x- and y-intercepts

22.3

Domain and range of a function

22.4

Identifying functions

22.5

Function notation

23. Linear Functions

23.1

Distance formula:

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

23.2

Midpoint formula:

M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)

23.3

Slope equation:

m = \frac{y_2-y_1}{x_2- x_1}

23.4

Slope intercept form: y = mx + b

23.5

General form: Ax + By + C = 0

23.6

Point-slope form:

y - y_1 = m (x - x_1)

23.7

Rate of change

23.8

Graphing linear functions using table of values

23.9

Graphing linear functions using x- and y-intercepts

23.10

Graphing from slope-intercept form y=mx+b

23.11

Graphing linear functions using a single point and slope

23.12

Word problems of graphing linear functions

23.13

Parallel and perpendicular lines in linear functions

23.14

Applications of linear relations

24. Linear Equations

24.1

Introduction to linear equations

24.2

Introduction to nonlinear equations

24.3

Special case of linear equations: Horizontal lines

24.4

Special case of linear equations: Vertical lines

24.5

Parallel line equation

24.6

Perpendicular line equation

24.7

Combination of both parallel and perpendicular line equations

24.8

Applications of linear equations

25. Solving Systems of Linear Equations

25.1

Determining number of solutions to linear equations

25.2

Solving systems of linear equations by graphing

25.3

Using elimination method to solve systems of equations

25.4

Using substitution method to solve systems of equations

25.5

25.6

Unknown number related questions in linear equations

25.7

Distance and time related questions in linear equations

25.8

Rectangular shape related questions in linear equations

26. Exponents

26.1

Product rule of exponents

26.2

Quotient rule of exponents

26.3

Power of a product rule

26.4

Power of a quotient rule

26.5

Power of a power rule

26.6

Negative exponent rule

26.7

Combining the exponent rules

26.8

Scientific notation

26.9

Convert between radicals and rational exponents

26.10

Solving for exponents

27. Operations with Polynomials

27.1

What is a polynomial?

27.2

Polynomial components

27.3

Multiplying monomial by monomial

27.4

Multiplying monomial by binomial

27.5

Multiplying binomial by binomial

27.6

Multiplying polynomial by polynomial

27.7

Applications of polynomials

28. Factoring Polynomial Expressions

28.1

Common factors of polynomials

28.2

Factoring polynomials by grouping

28.3

Solving polynomials with the unknown "b" from x^2 + bx + c

28.4

Solving polynomials with the unknown "c" from x^2 + bx + c

28.5

Factoring polynomials: x^2 + bx + c

28.6

Applications of polynomials: x^2 + bx + c

28.7

Solving polynomials with the unknown "b" from

ax^2 + bx + c

28.8

Factoring polynomials:

ax^2 + bx + c

28.9

Factoring perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2

28.10

Find the difference of squares: (a - b)(a + b) = (a^2 - b^2)

28.11

Evaluating polynomials

28.12

Using algebra tiles to factor polynomials

28.13

Solving polynomial equations

28.14

Word problems of polynomials

29. Factoring Trinomials (Advanced)

29.1

Factor by taking out the greatest common factor

29.2

Factor by grouping

29.3

Factoring difference of squares: x^2 - y^2

29.4

Factoring trinomials

29.5

Factoring difference of cubes

29.6

Factoring sum of cubes

30. Rational Expressions

30.1

Simplifying rational expressions and restrictions

30.2

Adding and subtracting rational expressions

30.3

Multiplying rational expressions

30.4

Dividing rational expressions

30.5

Solving rational equations

30.6

Applications of rational equations

30.7

Simplifying complex fractions

30.8

Partial fraction decomposition

31. Reciprocal Functions

31.1

Graphing reciprocals of linear functions

31.2

Graphing reciprocals of quadratic functions

32. Radicals

32.1

Square and square roots

32.2

Cubic and cube roots

32.3

Evaluating and simplifying radicals

32.4

Converting radicals to mixed radicals

32.5

Converting radicals to entire radicals

32.6

Adding and subtracting radicals

32.7

Multiplying and dividing radicals

32.8

Rationalize the denominator

33. Radicals (Advanced)

33.1

Operations with radicals

33.2

Conversion between entire radicals and mixed radicals

33.3

Adding and subtracting radicals

33.4

Multiplying radicals

33.5

Solving radical equations

34. Quadratic Functions

34.1

Introduction to quadratic functions

34.2

Transformations of quadratic functions

34.3

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

34.4

Quadratic function in vertex form: y = a(x-p)^2 + q

34.5

Completing the square

34.6

Converting from general to vertex form by completing the square

34.7

Shortcut: Vertex formula

34.8

Graphing quadratic functions: General form VS. Vertex form

34.9

Finding the quadratic functions for given parabolas

34.10

Applications of quadratic functions

35. Quadratic Equations and Inequalities

35.1

Solving quadratic equations by factoring

35.2

Solving quadratic equations by completing the square

35.3

Using quadratic formula to solve quadratic equations

35.4

Nature of roots of quadratic equations: The discriminant

35.5

Applications of quadratic equations

35.6

Solving quadratic inequalities

36. Right Triangle Trigonometry

36.1

Use sine ratio to calculate angles and sides (Sin =

\frac{o}{h}

)

36.2

Use cosine ratio to calculate angles and sides (Cos =

\frac{a}{h}

)

36.3

Use tangent ratio to calculate angles and sides (Tan =

\frac{o}{a}

)

36.4

Combination of SohCahToa questions

36.5

Solving expressions using 45-45-90 special right triangles

36.6

Solving expressions using 30-60-90 special right triangles

36.7

Word problems relating ladder in trigonometry

36.8

Word problems relating guy wire in trigonometry

36.9

Other word problems relating angles in trigonometry

37. Laws of sines and cosines

37.1

Law of sines

37.2

Law of cosines

37.3

Applications of the sine law and cosine law

38. Bearings

38.1

Introduction to bearings

38.2

Bearings and direction word problems

38.3

Angle of elevation and depression

39. Sequences and Series

39.1

39.2

39.3

39.4

39.5

Infinite geometric series

39.6

Sigma notation

39.7

Arithmetic mean vs. Geometric mean

40. Functions

40.1

Function notation

40.2

Operations with functions

40.3

Adding functions

40.4

Subtracting functions

40.5

Multiplying functions

40.6

Dividing functions

40.7

Composite functions

40.8

Inequalities of combined functions

40.9

Inverse functions

40.10

One to one functions

40.11

Difference quotient: applications of functions

41. Exponential Functions

41.1

Exponents: Product rule (a^x)(a^y) = a^(x+y)

41.2

Exponents: Division rule (a^x / a^y) = a^(x-y)

41.3

Exponents: Power rule (a^x)^y = a^(x * y)

41.4

Exponents: Negative exponents

41.5

Exponents: Zero exponent: a^0 = 1

41.6

Exponents: Rational exponents

41.7

Solving exponential equations using exponent rules

41.8

Graphing exponential functions

41.9

Graphing transformations of exponential functions

41.10

Finding an exponential function given its graph

42. Logarithmic Functions

42.1

What is a logarithm?

42.2

Converting from logarithmic form to exponential form

42.3

Evaluating logarithms without a calculator

42.4

Common logarithms

42.5

Natural log: ln

42.6

Evaluating logarithms using change-of-base formula

42.7

Converting from exponential form to logarithmic form

42.8

Solving exponential equations with logarithms

42.9

Product rule of logarithms

42.10

Quotient rule of logarithms

42.11

Combining product rule and quotient rule in logarithms

42.12

Evaluating logarithms using logarithm rules

42.13

Solving logarithmic equations

42.14

Graphing logarithmic functions

42.15

Finding a logarithmic function given its graph

43. Applications of Exponential and Logarithmic Functions

43.1

Exponential growth and decay by a factor

43.2

Exponential decay: Half-life

43.3

Exponential growth and decay by percentage

43.4

Finance: Compound interest

43.5

Continuous growth and decay

43.6

Logarithmic scale: Richter scale (earthquake)

43.7

Logarithmic scale: pH scale

43.8

Logarithmic scale: dB scale

43.9

Finance: Future value and present value

44. Graphs of Trigonometric Functions

44.1

Sine graph: y = sin x

44.2

Cosine graph: y = cos x

44.3

Tangent graph: y = tan x

44.4

Cotangent graph: y = cot x

44.5

Secant graph: y = sec x

44.6

Cosecant graph: y = csc x

44.7

Graphing transformations of trigonometric functions

44.8

Determining trigonometric functions given their graphs

45. Trigonometric Identities

45.1

Quotient identities and reciprocal identities

45.2

Pythagorean identities

45.3

Sum and difference identities

45.4

Cofunction identities

45.5

Double-angle identities

46. Solving Trigonometric Equations

46.1

Solving first degree trigonometric equations

46.2

Determining non-permissible values for trig expressions

46.3

Solving second degree trigonometric equations

46.4

Solving trigonometric equations involving multiple angles

46.5

Solving trigonometric equations using pythagorean identities

46.6

Solving trigonometric equations using sum and difference identities

46.7

Solving trigonometric equations using double-angle identities

47. Permutations and Combinations

47.1

Fundamental counting principle

47.2

Factorial notation

47.3

Path counting problems

47.4

Permutation vs. Combination

47.5

Permutations

47.6

Combinations

47.7

Problems involving both permutations and combinations

47.8

Pascal's triangle

47.9

Binomial theorem

48. Conics

48.1

48.2

48.3

48.4

49. Imaginary and Complex Numbers

49.1

Introduction to imaginary numbers

49.2

Complex numbers and complex planes

49.3

Adding and subtracting complex numbers

49.4

Complex conjugates

49.5

Multiplying and dividing complex numbers

49.6

Distance and midpoint of complex numbers

49.7

Angle and absolute value of complex numbers

49.8

Polar form of complex numbers

49.9

Operations on complex numbers in polar form

50. Introduction to Matrices

50.1

Notation of matrices

50.2

Adding and subtracting matrices

50.3

Scalar multiplication

50.4

Matrix multiplication

50.5

The three types of matrix row operations

50.6

Representing a linear system as a matrix

50.7

Solving a linear system with matrices using Gaussian elimination

51. Determinants and Inverses of Matrices

51.1

The determinant of a 2 x 2 matrix

51.2

The determinant of a 3 x 3 matrix (General & Shortcut Method)

51.3

The inverse of a 2 x 2 matrix

51.4

The inverse of 3 x 3 matrices with matrix row operations

51.5

The inverse of 3 x 3 matrix with determinants and adjugate

51.6

2 x 2 invertible matrix

51.7

Solving linear systems using Cramer's Rule

51.8

Solving linear systems using 2 x 2 inverse matrices

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