Playing With Surveyors Math

Law of Cosines:

Check out: Ies-math

Cliffs Notes Trigonometry

To find square root:
Cosine calculator
Square root calculator
FInding square roots on a calculator

Check out the Aviation math for Kids to practice more awesome math! Remember math is so much fun if we can use it in real life! Read Examples of Math in Real Life and try to discover math opportunities surrounding your typical life or interests! Maybe you know a friend or a relative that uses a certain kind of math in their lives. You might develop an interest for math discussing and observing them work with it. Aviation and geography are of constant interest for us. 

The problem we set up. We want to know the distance of side "x" of the given triangle using surveyors math 


Imagining it using the azimuth

Azimuth picture by Developer.mozilla.org

With this problem we can practice how to find the unknown interior angles and also the unknown distance (x)

We want to know the solution as if this problem had to do with orienteering.  So we imagine a real place and try to position ourselves in the location virtually and eventually physically. 
We can pretend to be surveyors. We can even pretend with aviation as well since both practices use geography and topography. 

Have fun trying to figure it out!



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Algebra 2 Khan Academy numbered

Unit 1
Solving systems of equations for the king

  1. Trolls, tolls, and systems of equations
  2. Solving the troll riddle visually
  3. Solving systems graphically
  4. Graphing systems of equations
  5. King's cupcakes: Solving systems by elimination
  6. Simple elimination practice
  7. Systems of equations with simple elimination
  8. How many bags of potato chips do people eat?
  9. Systems with elimination practice
  10. Systems of equations with elimination
  11. Talking bird solves systems with substitution
  12. Practice using substitution for systems
  13. Systems of equations with substitution
  14. Systems of equations
  15. Systems of equations word problems
  16. Inconsistent systems of equations
  17. Infinite solutions to systems
  18. Consistent and inconsistent systems
  19. Independent and dependent systems
  20. Practice thinking about number of solutions to systems
  21. Graphing systems with one, zero, or infinite solutions
  22. Systems with one, zero, or infinite solutions

Systems of inequalities

  1. Visualizing the solution set for a system of inequalities
  2. Graphing systems of inequalities
  3. Graphing systems of inequalities 2
  4. Graphing systems of inequalities
  5. Graphing and solving systems of inequalities
  6. Modeling constraints with two-variable inequalities

Systems with three variables

  1. Systems of three variables
  2. Systems of three variables 2
  3. Solutions to three variable system
  4. Solutions to three variable system 2
  5. Three equation application problem

Non-linear systems of equations


  1. Estimating a solution to nonlinear system with calculator
  2. Estimating a solution to nonlinear system with calculator part 2
  3. Intersecting functions
  4. Non-linear systems of equations 1
  5. Non-linear systems of equations 2
  6. Non-linear systems of equations 3
  7. Systems of nonlinear equations 1
  8. Systems of nonlinear equations 2
  9. Systems of nonlinear equations 3
  10. Systems of nonlinear equations
Total: 43

Unit 2
Function introduction
  1. What is a function?
  2. Difference between equations and functions
  3. Relations and functions
  4. Evaluating with function notation
  5. Understanding function notation (example 1)
  6. Understanding function notation (example 2)
  7. Understanding function notation (example 3)
  8. Understanding function notation
Function expressions

  1. Sum of functions
  2. Difference of functions
  3. Product of functions
  4. Quotient of functions
  5. Evaluating expressions with function notation
  6. Modeling with combined functions
  7. Modeling with combined functions
Domain and range

  1. Domain of a function
  2. Domain and range of a relation
  3. Domain and range from graph
  4. Domain and range of a function given a formula
  5. Domain and range 1
  6. Domain of a radical function
  7. Domain of a function
  8. Domain and range 2
  9. Domain and range of a function
  10. Range of a function
Recognizing functions
  1. Testing if a relationship is a function
  2. Graphical relations and functions
  3. Functions as graphs
  4. Recognizing functions (example 1)
  5. Recognizing functions (example 2)
  6. Functional relationships 1
  7. Recognizing functions (example 3)
  8. Recognizing functions
  9. Recognizing functions (example 4)
  10. Recognizing functions (example 5)
  11. Recognizing functions 2
Composing functions
  1. Introduction to function composition
  2. Creating new function from composition
  3. Evaluating composite functions example
  4. Evaluating composite functions
  5. Modeling with function composition
  6. Modeling with composite functions
Function inverses
  1. Introduction to function inverses
  2. Function inverse example 1
  3. Function inverses example 2
  4. Function inverses example 3
  5. Inverses of linear functions
  6. Algebraically finding inverses
  7. Domain and range with inverse functions
  8. Understanding inverses of functions
Piecewise functions
  1. What is a function?
  2. Graphs of absolute value functions
  3. Absolute value graphing exercise example
  4. Graphs of absolute value functions
  5. Graphs of piecewise linear functions
  6. Matching expressions to define intervals of functions example
  7. Finding a piecewise function definition from graph
  8. Graphs of piecewise nonlinear functions
Shifting and reflecting functions
  1. Shifting and reflecting functions
  2. Shifting functions
  3. Shifting and reflecting functions
  4. Flipping and shifting radical functions
  5. Equations for radical functions example
  6. Matching radical functions with graphs exercise example
  7. Graphs of square root functions
Properties and features of functions
  1. When a function is positive or negative
  2. Positive and negative parts of functions
  3. Recognizing odd and even functions
  4. Connection between even and odd numbers and functions
  5. Even and odd functions
  6. Recognizing features of functions (example 1)
  7. Recognizing features of functions (example 2)
  8. Recognizing features of functions (example 3)
  9. Recognizing features of functions
Comparing and interpreting functions
  1. Interpreting features of functions (example 1)
  2. Interpreting features of functions (example 2)
  3. Interpreting features of functions
  4. Comparing features of functions (example 1)
  5. Comparing features of functions (example 2)
  6. Comparing features of functions (example 3)
  7. Comparing features of functions
Undefined and indeterminate answers

  1. Why dividing by zero is undefined
  2. Why zero divided by zero is undefined/indeterminate
  3. Undefined and indeterminate
More mathy functions
  1. A more formal understanding of functions
  2. Introduction to the inverse of a functiom
Total: 86

Unit 3

Factoring quadratics

  1. Factoring quadratic expressions
  2. Examples: Factoring simple quadratics
  3. Factoring quadratics 1
  4. Solving a quadratic equation by factoring
  5. Recognizing a perfect square quadratic
  6. Solving quadratics by factoring
  7. Example 1: Factoring trinomials with a common factor
  8. Factoring quadratics 2
  9. Solving quadratics by factoring 2
  10. Factoring special products
  11. Example 1: Factoring difference of squares
  12. Factoring difference of squares 1
  13. Example 2: Factoring difference of squares
  14. Factoring difference of squares 2
  15. Factoring to produce difference of squares
  16. Factoring difference of squares 3
  17. Example 5: Factoring by grouping
  18. Example 6: Factoring by grouping
  19. Factoring polynomials by grouping
Completing the square and the quadratic formula
  1. Solving quadratic equations by square roots
  2. Solving quadratics by taking the square root
  3. Solving quadratic equations by completing the square
  4. Solving quadratics by completing the square 1
  5. Solving quadratics by completing the square 2
  6. How to use the quadratic formula
  7. Proof of quadratic formula
  8. Using the quadratic formula
  9. Example: Complex roots for a quadratic
  10. Quadratic formula with complex solutions
  11. Discriminant of quadratic equations
  12. Discriminant for types of solutions for a quadratic
  13. Solutions to quadratic equations
Quadratic inequalities
  1. Quadratic inequalities
  2. Quadratic inequalities (visual explanation)
Adding and multiplying polynomials
  1. Terms coefficients and exponents in a polynomial
  2. Addition and subtraction of polynomials
  3. Adding and subtracting polynomials
  4. Multiplying polynomials example
  5. Multiplying polynomials example 2
  6. Multiplying polynomials
  7. Equivalent forms of polynomial expressions
  8. Polynomial identities
Dividing polynomials
  1. Polynomial division
  2. Polynomial divided by monomial
  3. Dividing multivariable polynomial with monomial
  4. Dividing polynomials 1
  5. Dividing polynomials with remainders
  6. Dividing polynomials with remainders example
  7. Dividing polynomials with remainders
Synthetic division
  1. Synthetic division
  2. Synthetic division example 2
  3. Why synthetic division works
Polynomial remainder theorem
  1. Polynomial remainder theorem
  2. Polynomial remainder theorem example
  3. Polynomial remainder theorem to test factor
  4. Constructing a polynomial that has a certain factor
  5. Remainder theorem of polynomials
  6. Polynomial remainder theorem proof
Factoring and roots of higher degree polynomials

  1. Factoring sum of cubes
  2. Difference of cubes factoring
  3. Example: Factoring a fourth degree expression
  4. Factoring 5th degree polynomial to find real zeros
  5. Identifying graph based on roots
  6. Using zeros to graph polynomials
Polynomial graphs and end behavior
  1. Polynomial end behavior
  2. Polynomial end behavior example
  3. Another polynomial end behavior example
  4. Polynomial end behavior exercise example
  5. Graphs of polynomials
Binomial theorem
  1. Binomial theorem
  2. Pascal's triangle for binomial expansion
  3. Determining coefficient in binomial expansion
  4. Binomial theorem
  5. Intuitive connection between binomial expansion and combinatorics
  6. Connecting Pascal's triangle to binomial combinatorics
  7. Algorithm for mentally computing binomial expansion coefficients
  8. Binomial theorem combinatorics connection
Simplifying rational expressions
  1. Simplifying rational expressions introduction
  2. Simplifying rational expressions 1
  3. Simplifying rational expressions 2
  4. Simplifying rational expressions 3
Rational functions
  1. Adding and subtracting rational expressions
  2. Adding and subtracting rational expressions 2
  3. Adding and subtracting rational expressions 3
  4. Rational equations
  5. Solving rational equations 1
  6. Solving rational equations 2
  7. Solving rational equations 3
  8. Subtracting rational expressions
  9. Applying rational equations 1
  10. Applying rational equations 2
  11. Applying rational equations 3
  12. Multiplying and simplifying rational expressions
  13. Multiplying and dividing rational expressions 1
  14. Multiplying and dividing rational expressions 2
  15. Multiplying and dividing rational expressions 3
  16. Extraneous solutions to rational equations
  17. Rational inequalities
  18. Rational inequalities 2
Asymptotes and graphing rational functions
  1. Asymptotes of rational functions
  2. Another rational function graph example
  3. A third example of graphing a rational function
Partial fraction expansion
  1. Partial fraction expansion 1
  2. Partial fraction expansion 2
  3. Partial fraction expansion 3
  4. Partial fraction expansion
Advanced structure in expressions
  1. Structure in rational expression
  2. Structure in exponential expression
  3. Advanced structure in expressions
Fundamental Theorem of Algebra
  1. Fundamental theorem of algebra
  2. Fundamental theorem of algebra for quadratic
  3. Possible number of real roots
  4. The fundamental theorem of algebra
Total:113

Unit 4

Simplifying rational expressions
  1. Simplifying rational expressions introduction
  2. Simplifying rational expressions 1
  3. Dividing polynomials by binomials 1
  4. Simplifying rational expressions 2
  5. Dividing polynomials by binomials 2
  6. Simplifying rational expressions 2
  7. Simplifying rational expressions 3
  8. Simplifying rational expressions example 2
  9. Dividing polynomials by binomials 3
  10. Simplifying rational expressions 3
  11. Simplifying rational expressions 4
Adding and subtracting rational expressions
  1. Adding and subtracting rational expressions 1
  2. Adding and subtracting rational expressions 2
  3. Adding and subtracting rational expressions 3
  4. Adding and subtracting rational expressions 2
  5. Subtracting rational expressions
  6. Simplifying first for subtracting rational expressions
  7. Adding and subtracting rational expressions 4
  8. Adding and subtracting rational expressions 5
  9. Adding and subtracting rational expressions
  10. Adding and subtracting rational expressions 3
  11. Adding and subtracting rational expressions 6
  12. Adding and subtracting rational expressions 7
  13. Rationalizing denominators of expressions
Graphing rational functions
  1. Horizontal and vertical asymptotes of function
  2. Matching rational functions to their graphs
  3. Another rational function graph example
  4. Asymptotes of rational functions
  5. A third example of graphing a rational function
  6. Finding horizontal and vertical asymptotes
  7. Graphs of rational functions
Partial fraction expansion
  1. Partial fraction expansion 1
  2. Partial fraction expansion 2
  3. Partial fraction expansion 3
  4. Partial fraction expansion
Solving rational equations
  1. Ex 1: Multi step equation
  2. Solving rational equations 1
  3. Rational equations
  4. Solving rational equations 1
  5. Solving rational equations 2
  6. Solving rational equations 3
  7. Applying rational equations 1
  8. Applying rational equations 2
  9. Applying rational equations 3
  10. Solving rational equations 2
  11. Extraneous solutions to rational equations
  12. Extraneous solutions to rational equations
  13. Rational inequalities
  14. Rational inequalities 2
Multiplying and dividing rational expressions
  1. Multiplying and simplifying rational expressions
  2. Multiplying and dividing rational expressions 1
  3. Multiplying and dividing rational expressions 2
  4. Multiplying and dividing rational expressions 3
  5. Multiplying and dividing rational expressions 1
  6. Multiplying and dividing rational expressions 2
  7. Multiplying and dividing rational expressions 3
  8. Multiplying and dividing rational expressions 4
  9. Multiplying and dividing rational expressions 5
Total: 58
Unit 5

Exponential growth and decay
  1. Exponential growth functions
  2. Graphing exponential functions
  3. Understanding linear and exponential models
  4. Understanding linear and exponential models
  5. Comparing exponential and quadratic models
  6. Comparing growth rates of exponentials and polynomials
  7. Constructing linear and exponential functions from data
  8. Constructing linear and exponential functions from graph
  9. Equivalent forms of exponential expressions
  10. Constructing linear and exponential functions
Modeling with exponential functions
  1. Exponential growth and decay word problems
  2. Decay of cesium 137 example
  3. Modeling ticket fines with exponential function
  4. Rewriting and interpreting exponential functions
  5. Modeling with exponential functions
  6. Solving exponential equation
  7. Using logarithms to solve exponential equations
Logarithmic functions
This tutorial shows you what a logarithmic function is. It will then go on to show the many times in nature and science that these type of functions are useful to describe what is happening.
  1. Comparing exponential and logarithmic functions
  2. Graphing logarithmic functions
  3. Matching functions to their graphs
  4. Graphs of logarithmic functions
  5. Graphs of exponentials and logarithms
  6. Vi and Sal explore how we think about scale
Logarithmic equations
  1. Solving logarithmic equations
  2. Solving logarithmic equations
Continuous compounding and e
  1. Introduction to interest
  2. Interest (part 2)
  3. Introduction to compound interest and e
  4. Compound interest and e (part 2)
  5. Compound interest and e (part 3)
  6. Compound interest and e (part 4)
Total: 31
Unit 6

The imaginary unit i
  1. Introduction to i and imaginary numbers
  2. Calculating i raised to arbitrary exponents
  3. Imaginary unit powers
  4. Imaginary roots of negative numbers
  5. i as the principal root of -1 (a little technical)
Complex numbers
  1. Introduction to complex numbers
  2. The imaginary unit and complex numbers
  3. Plotting complex numbers on the complex plane
  4. The complex plane
  5. Adding complex numbers
  6. Subtracting complex numbers
  7. Adding and subtracting complex numbers
  8. Multiplying complex numbers
  9. Multiplying complex numbers
  10. Complex conjugates example
  11. Dividing complex numbers
  12. Dividing complex numbers
  13. Absolute value of a complex number
  14. Absolute value of complex numbers
  15. Example: Complex roots for a quadratic
  16. Algebra II: Imaginary and complex numbers
Total:21

Unit 7

Conic section basics
  1. Introduction to conic sections
  2. Recognizing conic sections
Circles
  1. Pythagorean theorem and the equation of a circle
  2. Radius and center for a circle equation in standard form
  3. Equation of a circle in factored form
  4. Graphing circles
  5. Completing the square to write equation in standard form of a circle
  6. Equation of a circle in non-factored form
  7. Graphing circles 2
Ellipses
  1. .Conic sections: Intro to ellipses
  2. Equation of an ellipse
  3. Foci of an ellipse
  4. Exploring the foci of an ellipse
Parabolas
  1. Parabola intuition example 1
  2. Parabola intuition 1
  3. Focus and directrix introduction
  4. Using the focus and directrix to find the equation of a parabola
  5. Equation for parabola from focus and directrix
  6. Finding focus and directrix from vertex
  7. Parabola intuition 2
  8. Parabola intuition 3
Hyperbolas
  1. Conic sections: Intro to hyperbolas
  2. Conic sections: Hyperbolas 2
  3. Conic sections: Hyperbolas 3
  4. Asymptotes of a hyperbola
  5. Foci of a hyperbola
  6. Proof: Hyperbola foci
Conics from equations
  1. Identifying an ellipse from equation
  2. Identifying a hyperbola from an equation
  3. Identifying circles and parabolas from equations
  4. Hyperbola and parabola examples
Conics in the IIT JEE
  1. Tangent line hyperbola relationship (very optional)
  2. IIT JEE circle hyperbola common tangent part 1
  3. IIT JEE circle hyperbola common tangent part 2
  4. IIT JEE circle hyperbola common tangent part 3
  5. IIT JEE circle hyperbola common tangent part 4
  6. IIT JEE circle hyperbola common tangent part 5
  7. IIT JEE circle hyperbola intersection

Total: 38

Unit 9
Basic matrix operations
  1. Introduction to the matrix
  2. Matrix dimensions
  3. Representing data with matrices
  4. Representing relationships with matrices
  5. Scalar multiplication
  6. Scalar matrix multiplication
  7. Matrix addition and subtraction
  8. Matrix addition and subtraction
  9. Transpose of a matrix
  10. Matrix transpose
Matrix multiplication
  1. Matrix multiplication introduction
  2. Multiplying a matrix by a matrix
  3. Multiplying a matrix by a matrix
  4. Defined and undefined matrix operations
  5. Defined and undefined matrix operations
Total:15
Total of all : 406

 406items /100 days=4 items a day
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