Algebra II SOL Review
What % are four S.D. of the mean?
0.15%
Define "standard deviation"
A calculated quantity to indicate deviation from the mean
What does a not perfect square discriminant mean?
Quadratic formula to solve
Rational Numbers
Ration = Ratio Any number can be written as a fraction Decimals can go on and on forever as long as the repeat EX: -3, -2, -2, -1, -1/2, 0, 1/2, 1, 2, 3
How do you find asymptotes?
Set the denominator equal to zero, then solve
X ≤ number
Solid dot on number, shade left
X ≥ number
Solid dot on number, shade right
Define "mean"
The average of the data points
What is the Exp. Function?
The horizontal asymptote
What is the log function?
The vertical asymptote
What two methods are used for solving radicals?
Tree method and Perfect Square method
What does "k" in a graphing equation represent?
Vertical translation (+k = moves up, -K = moves down)
What is CSC SOPAS?
When factoring difference of cubes, use CSC SOPAS. C: cube the first term S: same sign C Cube the second term S: square of the first cube O: Opposite sign P: product of the first and second cubes A: always positive S: square of the second cube
Guess and check easiest?
When the leading coefficient is 1
When is Multiply and Divide easiest?
When the leading coefficient is not equal to 1
What is the Axis of Symmetry?
When x=h
What is the standard form of a complex number?
a+bi
What is (a^n)^m equal to?
a^mn
What is the standard form of a quadratic?
ax^2+bx+c
Equation for Graphing Radical Functions
a√b(x-h) +k
What does "b" in a graphing equation represent?
horizontal stretch (Vertical compression) or horizontal compression (Vertical stretch)
What does "h" in a graphing equation represent?
horizontal translation (-h = moves right, +h= moves left)
What does "a" in a graphing equation represent?
vertical stretch or vertical compression
What does the product rule look like?
x^m times x^n = x^m+n IF the bases are the same
What does the quotient rule look like?
x^m/x^n = x^m-n IF x doesn't equal 0
What is the quadratic graphing equation?
y= a(x-h)^2+k
What does "i" equal?
√-1
What does [ ] mean?
"Can equal" or "actually touches on a number line or graph."
What does ( ) mean?
"Does not = this value" or "approaches but never touches."
What does U mean?
"In union with" or "As well as."
< and ≤ create what sort of statements?
"and"
> and ≥ create what sort of statements?
"or"
Solve 27x^3 + 8
(3x+2)(9x^2-6x+4)
What is a difference of squares?
(a+b)(a-b) = a^2 - b^2
What is the focus?
(h, k+1/4a)
What does "i^2" equal?
-1
What is the quadratic formula?
-b±√b^2-4ac/2a
What does "i^3" equal?
-i
What does "i^4" equal?
1
What are the 3 main % of the Bell Curve?
1. 68% 2. 95% 3. 97.5%
How do you simplify rational expressions by adding?
1. Factor First 2. Find a common denominator 3. Reduce
How do you simplify rational expressions by subtracting?
1. Factor First 2. Find a common denominator 3. Reduce
How do you simplify rational expressions by multiplying?
1. Factor anything that can be factored 2. Reduce
How do you simplify rational expressions by dividing?
1. Flip the term on the right of the division sign 2. Solve like multiplying
How do you find the vertex form of a quadratic?
1. Move "c" to the other side 2. find a GCF and factor out that GCF 3. Divide "b" by 2 then square 4. Multiply both sides by the GCF 5. Factor 6. Add "c" back over
What are the two ways to write the series, means, sums?
1. Sn=n/2 ( a1+an ) (n, and 1 in subscript for both) 2. Sn=n/2[2a1+(n-1)d]
When is a radical in its simplest form?
1. When no factor pairs 2. No radicals in the denominator 3. No fractions/decimals/negatives under the radical 4. Fraction is in lowest terms
What are the 4 ways to do compositions? (only two variables)
1. f(g(x)) 2. (f∘g)(x) 3. g(f(x)) 4. (g∘f)
What are other names for solutions of quadratic functions?
1. x-intercept 2. root 3. x-value 4. zero
What % are two S.D. of the mean?
13.6%
Absolute Value inequalities have how many answers?
2
What % are three S.D. of the mean?
2.35%
What % are one S.D. of the mean?
34%
Define a bell curve
A graph of a normal distribution
Absolute Value
Absolute Value is the distance between that number and zero on the number line. EX: l3l = 3, so if lxl =3, x= plus or minus 3
What are the 4 ways to do combinations?
Adding: (f+g)(x) Subtracting: (f-g)(x) Multiplying: (fg)(x) Dividing: (f/g)(x)
Solve 4+3i+7-13i
Answer: 11-10i
How do you find holes?
Anything that was crossed off in reducing
Irrationals
Decimals will go on and on forever w/o repeating EX: -1, 0, 1, √3, 2, e, 3, π, 4
What is the Even-Even-Odd Absolute Value Role?
Even power under an even index and you get an odd power answer, put an absolute value around the variable.
Whole Numbers
Exactly the same as Natural #s plus 0 No negative values No fractions
What does a perfect square discriminant mean?
Factor to solve
What are the two methods for foiling trinomials?
Guess and Check or Multiply and Divide
X < number
Hollow dot on number, shade left
X > number
Hollow dot on number, shade right
What is the second rule of dividing radicals?
If the radical doesn't have a factor in common, "rationalize the denominator."
What is the first rule of dividing radicals?
If the radical terms have a factor in common, combine them as one big radical and reduce.
What is the third rule of dividing radicals?
If there is a sum or difference in the denominator, rationalize the denominator by multiplying the conjugate pairs.
What does the degree of the polynomial do?
It determines the number of solutions
How do you solve systems by graphing?
Look for the intersecting point(s)
What does a negative discriminant mean?
No real solutions (use Quadratic formula to solve)
What does a discriminant of zero mean?
One solution (Double Root)
Real Numbers
Only numbers on the number line EX: -1, 0, 1, 2, e, 3, π...
Natural Numbers
Our counting numbers No negative values No fractions Ex: 1, 2, 3, 4......
What does "i^25" equal?
Process: (i^4)^6 times i Answer: i
What does a positive discriminant mean?
There are two solutions
What happens when the index is even?
There is no real root to a negative root
How are logarithmic and exponential functions related?
They are the inverses to each other
Integers
Think "Number Line" No fractions EX: -2, -1, 0, 1, 2...
What is the solution for quadratic functions?
Where it crosses @ the x-axis
What do you do if a rational exponent is negative?
You put a one over it.
How can rational exponents be written as?
a ^ m/n or ( n√a )^m or n√a^m
What is the discriminant and what does it do?
b^2-4ac The discriminant tells how many solutions, what kind of solution, and how we should solve
What does logb(a)=c equal? (b is in subscript)
b^c=a
What does log(x) stand for?
log10^x (the 10 is in subscript)
What is the Directrix?
y= k- 1/4a
