SOL STUDY GUIDE
I. PROPERTIES
Commutative:
Associative:
Transitive:
II. CONICS: Formulas can also be found in #9 on the Casio!!
Parabola: or
Circle:
Ellipse:
Hyperbola:
III. GRAPHS AND THEIR EQUATIONS:
Linear: y = x
Quadratic:
Absolute value:
Greatest Integer (Step Function): y = [x]
Square Root:
Exponential:
Logarithmic:
IV. SOLVING
Quadratics
1)Get all pieces on the left side
2)Try to factor (Pull out a GCF or T-table)
3)If it won’t work, use the quadratic formula
(Given on the SOL formula sheet)
Discriminant: helps determine the roots ()
> 0 gives 2 real solutions
< 0 gives 2 complex (imaginary) solutions
= 0 gives 1 real solution
Absolute Value: *TWO POSSIBLE SOLUTIONS*
1) Get absolute value by itself
2) The inside = positive right side and inside = negative right side
Square Root: Creates TWO Solutions
Squaring: ONE SOLUTION, Check your answer!
**ROOTS = ZEROS = SOLUTIONS = X-INTERCEPTS**
V. FACTORING: Always look for a GCF first!!
Difference of squares:
Difference of cubes:
Sum of cubes:
Basic trinomial: T-table method
Harder trinomial: T-table, replace the middle term, group factor
VI. SEQUENCE AND SERIES
Arithmetic: add the same difference to make the next term
Geometric: multiply the same factor to make the next term
Series; plug in the numbers from the first to the last into the expression, then add their values
VII. INVERSE
Switch x and y and re-solve for y!
VIII. COMPOSITION OF FUNCTIONS
Take the function listed second and substitute it in the function listed first
IX. VARIATION
Direct: y = kx Inverse:Joint: y = kxz
1)Pay attention to order and terms being squared or cubed
2)Use the same equation for every part of a problem you are solving
3)K is the constant and is in all variation problems!
Ex: If n varies directly with the cube of g and n = 32 when g = 2, find g when n = 108.
Formula:
X: COMPLEX NUMBERS (IMAGINARY)
MEMORIZE!!!!