Learn math by understanding examples

- Serve as a math learning tool for all students, parents and teachers
- Learning mathematics by understanding principle and examples
- Apply math concepts to solve real world problems
- Help middle school students prepare for high school
- Help high school students prepare for college
- Improve student’s math testing score in standard tests
- Help student’s success in college study

- Do each example and exercise yourself and check the answer
- Draw a diagram for each question, label the known and mark the unknown in the diagram
- Practice logic inference, from known to unknown, step by step
- Apply geometry concepts and algebra skill to each step
- Summarize what geometry principles you learned when solve a problem

- Identify which category the given problem belongs to
- Find the right method to solve the given problem
- Write solution step by step and check the solution
- Summarize what algebra skills you used to solve the given problem

- Understand the trigonometry concepts
- Learn how to use trigonometry formulas
- Identify the trigonometry category for a given problem
- Find the right trigonometry formula to solve the given problem
- Summarize which trigonometry principle used to solve this problem

- Learning and practice reasoning and write the solution step by step
- Master geometry, algebra and trigonometry problem solving skills
- Help students improve PSAT, SAT and ACT scores in math
- Build a good habit on math study
- Preparing for college study

**Goal of this math website:** This math website is designed to help all middle and high school students to better understand algebra, geometry and trigonometry. There are multiple examples
designed for students to practice how to analyze math problems and solve them. Help students build a very solid background for college study and improve students testing scores in the standard test.

**Most importantly,** mathematics can train our brain. By learning mathematics, we can obtain the logical thinking skills which can be apply to our life. For example
to make a physical product, we need at least to know its principles of mathematics. Learning mathematics will help students have more options for their career and help them build self-confidence.

**Prealgebra** prime numbers, prime factoring, common factors, greatest common factor (GCF), simplify fraction, equivalent fractions, complex fraction when numerator is a fraction,
complex fraction when denominator is a fraction, complex fraction when both numerator and denominator are fractions, least common multiple (LCM), least common denominator (LCD),
compare fractions with common denominators, compare fractions with different denominators, compare fractions with same numerators and different denominators,
improper fraction to mixed number, mixed number to fraction, add fractions with the same denominator, add fractions with different denominators, add mixed numbers with the same denominator,
add mixed number with different denominators, subtract fraction with the same denominator, subtract fractions width different denominators, subtract mixed number with the same denominator,
subtract mixed number with different denominators, multiply fractions, multiply fraction by mixed number, multiply mixed numbers, divide a whole number by a fraction,
divide a fraction by a fraction, divide a fraction by a mixed number, divide mixed number by mixed number, rational numbers, positive exponents and zero exponent, negative exponents

**Algebra **translate words into algebra expression, first degree equation examples, polynomials, polynomial multiplication, polynomial divide by monomial,
algebra of fractions, complex fractions, one variable equations, two variables equations, inequalities, absolute value equation, first degree inequality, absolute value inequality,
quadratic equation, radical equation, sequence, inverse function, quadratic absolute value inequality

**Geometry** points, midpoint, lines, parallel lines, perpendicular lines, angle and angle pairs, angle measure, right angle, acute angle, obtuse angle, straight angle, adjacent angles,
vertical angles, complementary angles, supplementary angles, corresponding angles, alternate interior angles, consecutive interior angles, testing parallel lines, testing perpendicular lines,
triangle, interior angles of a triangle, exterior angle of a triangle, equilateral triangle, isosceles triangle, scalene triangle, right triangle, obtuse triangle, acute triangle, equiangular triangle,
altitudes, medians and angle bisectors of a triangle, congruent triangles, similar triangles, triangle inequality theorem, quadrilaterals, parallelogram, special parallelogram, square, polygon

**Trigonometry** quadrant angles, degree, radian and sector, any angle trigonometric functions, values of trigonometric function of special angles, graphs of Sine function and transformation,
graphs of Cosine function and transformation, trigonometry function examples, find the maximum value of a function in an interval, sine function properties, graph of a sine function examples,
logarithms definition example, logarithms equation example, parabola example, analytical geometry examples, application of parabola and hyperbola

**Asked Queations** algebra expression, algebra equation, remove square root, quadratic equation, adjacent angle pairs, adjacent angles formed by perpendicular lines,
adjacent angles formed by intersected lines, interior and exterior points of circle, graph of sine and cosine function, graph of y = sin (x - pi), draw the graph of y = -2 sin (x - pi/4),
draw the graph of Sine square x, draw the graph of y = sin (3pi x), draw the graph of y = sin (x/3), draw the graph of y = 1/2sin (x pi/2), graph of y=2sin(x) and y=2cos(x),
graph of y = cos (2 x pi/2), graph of y = 1 - cos (pi/4 - x), draw the graph of y = cos2x, graphs of y = sin(x) and y = csc(x), graph of y = csc4(x 3pi/2),
graph of y = cot (x - pi/4), -cotangent(2(pi/4)), finding the value of tan (-945 degree), what is the formula of the tangent angles sum?

**Probability** probability event, probability definition, formula to solve probability problems, using table to solve probability problems, using tree to solve probability problems

**Solid Geometry** plane line and points, plane line and angles, find longest diagonal in a rectangle prism, find the altitude of a tetrahedron, find the angle between a line segment and a plane,
find the relation between a triangle plane and a segment

**Algebra 1 Video Lessons** translate word sentence into algebra expressions, translate word problems and solve equations, examples of word problem solving,
one variable equation examples, two variables one-degree equations, number problem solving, inequality problem solving, polynomial, fraction equation, polynomial concept

**Geometry Video Lessons** line segments, line and angles, parallel and angles, lines, triangle and angles, parallel lines, angle bisector and triangle, interior angles in a triangle,
exterior angle of a triangle, isosceles triangles, triangles, right triangles, circles, circle triangle, rectangles, area of an obtuse triangle, area of an equilateral triangle,
area of a triangle, area of a bow, congruent triangles, similar triangles, ratio, cylinder and sphere, orthogonal plane, coordinate plane, shortest segment

**Algebra 2 Video Lessons** quadratic functions, proving a square root equality, find the quadratic equation when given two solutions, solve quadratic equation by root extraction method,
solve quadratic equation by factoring method, solve quadratic equation by completing square method, solve quadratic equation using formula method, variable substitution,
prove that the value of a polynomial is always larger than zero, solve a function equation to find f(x), draw the graph of the quadratic function y = x^{2} - 4x + 5,
draw the graph of the quadratic function y = -2x^{2} - 8x + 1, relationship between the graph of a quadratic function and is coefficients, transform the graph of y = (1/2) x^{2} to y = (1/2) (x - 3)^{2} - 2,
transform the graphs of y = -x^{2} - 2x to y = -x^{2} + 4x - 3, transform the graph of y = 2x^{2} to y = 2x^{2} + 12x + 17, find the quadratic function from graph,
domain of a function, domain of a function involved in logarithm, inverse function, value of an inverse function

**Trigonometry Video Lessons** any angle trigonometry functions, given the angle a and find sin(a), given cos (a) = -3/5 and find tan(a), given tan (A) = -4/3 and find sin(A),
given cos100^{o} and find sin10^{o}, given angle a and find tan (pi/4 - 2a), given tan (pi - 2a) = -13/12 and find tan a, given tan a = -3/4 and find cos a, given P (-1, y) and sin a and find y,
draw the graph of sine functions, draw the graph of y = sin x when x is from -pi to pi, draw the graph of y = sin x and x is from 0 to 2pi, 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), draw the graph of y = sin (2x - pi/3), simplify sin (2x/3 + 3pi/2),
draw the graph of y = cos (x) sin(x), draw graph of y = sin (2x + pi/6) - cos^{2}x, property of a Sine Graph, f(x) = sin (2x + pi/4) is symmetry to, decrease interval of y = sin (2x + pi/4),
find the monotonic increase interval of a function, find properties of y = 2 sin (x/2 + pi/4), transform graph y = sin (x) to y = sin (x/2 - pi/6), write functions based on wave transformation,
shift and shrink y = sin (2x - pi/6) and find the function, write analytical expression of a sine graph, solving a simple harmonic motion problem, angle between the positive x-axis and a line,
draw the graph of cosine functions, draw the graph of tan x, find maximum and minimum values of a function, trigonometry equation, find the angle a

**Analytical Geometry Video Lessons** Ellipse examples, Hyperbola examples, Parabola examples