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### Algebra I

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### Analylitical Geometry

- Translate word problems and solve equations
- Solving the average speed problem
- One variable equation example
- Example of word problem solving
- Example of two variable one degree equation
- Example of number problem solving 3
- Example of number problem solving 1
- Example of number problem solving 2
- Example of number problem solving 4
- Example of number problem solving 5
- Example of inequality problem solving 1
- Example of inequality problem solving 2
- Example of word problem solving 2
- Example of simply polynomial and solving equation
- Example of proving a square root equality
- Example of solving a fraction equation
- Example of using the difference of two squares
- Prove that the value of 3x^2 - 2x + 5 is larger than 0
- One variable equation example 1
- One variable equation example 2
- Polynomial concept
- One variable one degree equation
- Two variables one degree equation

- How to find the domain of a function?
- How to find the domain of a function involved in logarithm?
- How to find the quadratic equation when given two solutions?
- Variable substitution example 1
- Variable substitution example 2
- How to find the value of an inverse function?
- How to find the inverse function?
- Solve a function equation to find f(x)

- Find interior angles in a triangle
- Rectangle problem solving example
- Right triangle example
- Circle example
- Example involving Parallel lines, angle bisector and triangle
- Line segments example
- Find the area of an obtuse triangle
- Isosceles triangles example
- Lines and angles example
- Lines, triangle and angles example
- Example of simple circle problem solving 1
- Example of ratio problem solving 1
- Example of solving a right triangle
- Example of cylinder and sphere problem solving

- How to draw the graph of y = cos2x?
- Simplify sin(2x/3 + 3pi/2)
- Given the angle a, find sin(a)
- Draw graph of y = -cos(2/3)x
- Given cos(a) = -3/5, find tan(a)
- Given tan(A) = -4/3, find sin(A)
- Draw graph of y = 1 + cos(x)
- Given cos100
^{o}, find sin10^{o} - Draw graph of y = sin(x) x in [-pi, pi]
- Draw graph of y = cos(x) x in [-pi, pi]
- Draw graph of y = sin2x
- draw graph of y = sin(x/2)
- draw y = sin(x + pi/4) and y = sin(x - pi/2)
- Draw graph of y = sin(2x - pi/4)
- Draw graph of y = sin(2x + pi/4)
- Transform graph y = sin(x) to y = sin(x/2 - pi/6)
- Write functions based on wave transformation
- Given graph, find its function f(x)
- f(x) = sin(2x + pi/4) is symmetry to
- Decrease interval of y = sin(2x + pi/4)
- Given graph, write the its function
- Given y = Asin(Bx + C), find A, B and C
- Given y = Asin(Bx + C) + b, find A, B, C and b
- Shift and shrink y = sin(2x - pi/6), find function
- Write function based on given sine graph
- Solving a simple harmonic motion problem
- How to find domain of a function?
- Find domain of y = log(2sin x - square root of 3)
- Find the monotonic increase intervalof a function
- Values of special angles and y = cos(x)
- Draw the graph of y = -cos(x pi/2)
- Any angle trigonometry function

What is the algebra expression? In arithmetic, the basic operation are sum, difference, product and quotient. In algebra, use letters such as a, b, c, x or y to represent particular numbers. The expression that use the basic operation symbol to connect number and letter is called algebra expression. In algebra, the basic operation symbol also include power which can be possible, negative or fraction. How to write the algebra expression? We need to find those words that related to quantity. We use number, letter and operation symbol to express those words sentence. When you do these examples, you will think what math principle should used to solve each problem. This process will help you understand the math principles.

Geometry is the study of the relationship among the shape, size and position of an object. In this section, the geometry we study is the plane geometry. There are many concepts and properties in plane geometry. We need to study them one by one. The best way to master geometry is to practice. When solve a geometry problem, you need to analyze which math principle can be applied to solve the problem. The more practice, the more understanding math you have.

The function section is for those students who are interested in high school mathematics. Help students more understand trigonometry and help students ready for college study. If you have a well understand trigonometry, you should finish college study not more than four years which will save expensive tuition.

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