Algbra II Midterm
Terms
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- Commutative Property
-
ab = ba
a+b = b+a - Associative Property
-
3+(5+2) = 5+(3+2)
3(5*2)= 5(3*2) - Distributive
- 3(5+2) = (3*5)+(3*2)
- When solving inequalities...
- solve like a regular equation.
- When solving absolute value inequalities...
-
ex. /2x-1/<15
turns into
15</2x-1/<15 - A relation is a function
- all of the x's are unique
- When solving absolute value inequalities with an "or-equal-to" sign...
-
The answer will be:
Either a or b. - to find slope...
- the change in y over the change in x
- Formula for direct variation
- y=kx
- When graphing peicewise functions...
- graph the top equations as one line and the bottom equations as another line.
- when graphing absolute value functions...
-
vertex = (h,k)
when /x-h/+k - when solving Linear Systems...
- substitute or complete the square
- To tell how many solutions there are...
-
same line= infinite solutions
undetermined= no solution
determined solution= one solution - When graphing linear inequalities
- shade in the different lines. Where the darkest shading is, is the solution area.
- When finding max and min...
- graph all of the constraints until you have the darkest shaded region. Plug the vertices of that region (crooked line) into the orinal equation.
- When finding matrices Determinants...
- cross multiply the matrix and add the two products together
- When multiplying two matrices together...
- top row * first column, first row * second column, etc.
- Performing operations with matrices
- follow PEMDAS, and multiply a regular number by every number in the matrix when necessary
- Cramer's Rule
- when you have ax+by=c and dx+cy=f, put it into the matrix a-b-d-e (left to right, top to bottom)
- To find an inverse
- switch the top left and bottom right, and negate the top right and bottom left.
- When completing the square...
- put it in ax(squared)+bx=-c form. Add 25 to both sides of the equation. Factor the side without the "C". Find the square rool of both sides of the equation. Solve.
- When solving with the quadratic formula.
- substitute the standard equation into the quadratic formula and solve.
- Finding the discriminant of a standard equation
- Use Cramer's Rule and then find the determinant.
- When solving an absolute value inequality...
-
ex /2x-5/<9
becomes
9</2x-5/<9 - When solving for an absolute value equation...
- Solve for case #1 (positive answer in the origional equation) and case #2 (negative answer in the origional equation)