Essential Learningexample Problem with Solution
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 /
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 LearningExample Problem with Solution
1. Point slope form of a line
2. Linear RegressionWrite equation of line of best fit through (1,1), (2,1),(3,3), and (4,4)
3. Solve for Specified Variablesolve for given
4. Graphing Linear Equations
5. Graphing Linear Inequalities
6. Direct Variationy varies directly as x, when x = 5, y = 25 find y when x = 7
7. Inverse Variationx 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
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.
15. Graphing Systems of Inequalities
16. Simplifying with Rule of Exponents
17. Multiply Polynomials
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 )= 5 + 12i
27. Division of complex numbers
28. Cyclic Powers of i
29. Solve by completing square
30. Solve by using square roots
31. Solving by quadratic formula
32. Solve using Quadratic Techniques
33. Use the Discriminant to Find the Typediscriminant = -191 of Roots and Number 2 imaginary roots
34. Graph
Graph
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
37. Identify the domain and range of a functionDomain
Range
38. Determine if a function has an inverse, if soy = 3x+2
find it and graph it
39. Recursion and IterationFind the first three iterates
40. Addition of radicals
41. Subtraction of radicals
42. Multiplication of radicals
43. Division of radicals
44. Radical equations x = 33/2
x = 9/2
x = 4 or 1
45. Simplify Rational Expressions
46. Rational Equations
47. Arithmetic Sequences
48. Arithmetic Series
49. Geometric Sequence
50. Geometric Series