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