Algebra Two



1 |Absolute value |

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|2 |Complex Fraction |A fraction that contains a fraction in the numerator, denominator or both |

|3 |Linear Regression |A line of best fit |

|4 |Direct Variation | |

| | |, x and y increase or decrease together |

| | | |

|5 |Inverse Variation | |

| | |as x increases y decreases and vice versa |

| | | |

|6 |Consistent Dependent System |A system of equations with an infinite number of solutions |

|7 |Consistent Independent System |A system of equations with exactly one solution |

|8 |Constraints |Boundaries used in Linear Programming |

|9 |Feasible region |The area of intersection of a system of inequalities |

|10 |Inconsistent System |A system of equations with no solution |

|11 |Matrix |An organization of numbers or variables in columns and rows |

|12 |Objective Function |The function being maximized or minimized in Linear Programming |

|13 |Zero product property |If ab=0, then a=0, b=0, or both a and b = 0 |

|14 |Complex conjugate | |

|15 |Complex Number | |

| | |Any number of the form where a,b are real numbers |

| | | |

|16 |Imaginary Number | |

|17 |Axis of Symmetry |The line that splits a graph into symmetrical parts |

|18 |Circle |[pic] |

|19 |Discriminant | |

| | |, used to determine the number and type of solutions to a quadratic |

| | |equation |

| | | |

|20 |Parabola | |

|21 |Vertex |Maximum or minimum of a parabola |

|22 |Zeros/Roots |The x - intercepts of a function |

|23 |Asymptote |The line that a curve approaches |

|24 |Composition | |

|25 |Inverse functions |A reflection over the line y = x |

|26 |Iteration |A function in which the output becomes the next input |

|27 |Recursive Formula |In a sequence, shows how to find the nth term from the terms before or after it |

|28 |Radical Expression |An expression with variables inside/under the radical |

|29 |Rational Expression |A polynomial divided by a polynomial |

|30 |Arithmetic sequence |A pattern of numbers where the common difference of consecutive terms is the same |

|31 |Arithmetic series |The sum of the elements of an arithmetic sequence |

|32 |Geometric Sequence |A sequence of numbers where each term is found by multiplying by a constant |

|33 |Geometric Series |The sum of n terms of a geometric sequence |

L to J Concepts

Algebra II

Essential Learning Example Problem with Solution

1. Point slope form of a line

2. Linear Regression Write equation of line of best fit through (1,1), (2,1),(3,3), and (4,4)

3. Solve for Specified Variable solve for [pic] given

4. Graphing Linear Equations

[pic]

5. Graphing Linear Inequalities

[pic]

6. Direct Variation y varies directly as x, when x = 5, y = 25 find y when x = 7

7. Inverse Variation x varies inversely as y, when y = 12, x = 10

find x when y = 4

x=30

8. Graphing Absolute Value Functions

9. Solve Absolute Value Equations

[pic]

10. Graphing Greatest Integer Functions

11. Solve Compound Inequalities

12. Solve systems of equations by substitution.

13. Solve systems of equations by graphing.

And identify the type of solution

Consistent

Dependent

(3,-1)

Consistent

Independent

No solution

Inconsistent

14. Solve systems of equations by elimination. [pic]

15. Graphing Systems of Inequalities

16. Simplifying with Rule of Exponents

17. Multiply Polynomials [pic]

18. Divide Polynomials

19. Factor Polynomials

20. Add/Subtract Polynomials

21. A third degree equation

22. A fourth degree equation

23. Simplification of complex number

24. Addition of complex numbers (2 + 3i ) + ( 5 + 2i ) = 7 + 5i

(3 – 5i ) + ( 6 + i ) = 9 – 4i

25. Subtraction of complex numbers (2 + 3i ) - ( 5 + 2i ) = -3 + i

(3 – 5i ) - ( 6 + i ) = -3 – 6i

26. Multiplication of complex numbers ( 6 + 2i )( 3 – 5i ) = 28 - 4i

( 3 + 2i )[pic]= 5 + 12i

27. Division of complex numbers

28. Cyclic Powers of i

29. Solve by completing square [pic]

30. Solve by using square roots

31. Solving by quadratic formula

32. Solve using Quadratic Techniques

33. Use the Discriminant to Find the Type discriminant = -191 of Roots and Number 2 imaginary roots

34. Graph [pic]

Graph [pic]

35. Determine if a relation is a function {(0,2), (3,4), (0,5), (-12,-1)} --no

y = 3x – 1 --yes

vertical line test for functions

36. Find [pic] [pic]

37. Identify the domain and range of a function Domain

Range

38. Determine if a function has an inverse, if so y = 3x+2

find it and graph it [pic]

39. Recursion and Iteration Find the first three iterates

40. Addition of radicals

41. Subtraction of radicals

42. Multiplication of radicals

43. Division of radicals

44. Radical equations [pic] x = 33/2

[pic] x = 9/2

[pic] x = 4 or 1

45. Simplify Rational Expressions

[pic]

46. Rational Equations

47. Arithmetic Sequences

48. Arithmetic Series

49. Geometric Sequence

50. Geometric Series

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