Algebra 2 Final Basic Study Guide (read description)

question

Velocity Problems Formula
answer

FEET PER SECOND=Height(H)= velocity(v) x Time(T) – 16 x (T squared) METERS PER SECOND= Height(h)=velocity(v) x Time(T) -4.9 x (T squared)
question

Quadratic Formula (This was mostly covered semester 1, but it’s almost always applicable in algebra so you should definitely still know it). Btw remember that variables nect to each other mean multiplied (I had to do this a little with this formula to format it correctly).
answer

x = -b ± (√b² – 4ac) ÷ 2a
question

Standard Quadratic Form (this is when you would use quadratic formula, so you should be able to recognize this)
answer

ax² + bx + c = 0
question

Quadratic Vertex Form
answer

y = a(x-h)² + K If a>0 then the parabola opens up with minimum vertex. If a<0 then parabola opens down with maximum vertex Vertex will always be (h,k), note that it is ALWAYS a positive \"h\" Axis of symmetry will always be x=h, again note the positive \"h\"
question

Standard Form
answer

y = ax² + bx + c
question

To find vertex from standard form
answer

(-b ÷ 2a, plug x coordinate in and solve for y) In standard form y intercept is always (0,c)
question

Discriminant
answer

b² – 4ac If discrimant0 then zeros will be real numbers, 2 x intercepts. If discriminant=0 then one zero, and will be real number. x intercept=vertex. If positive and perfect square it will be rational If positive but not perfect square it will be irrational.
question

Degree
answer

The greatest exponent of a polynomial’s terms. If the polynomial has more than one variable you need to add the exponents in each term, the greatest value of these sums is the degree.
question

Polynomial Expression
answer

Where the degree of each term is a whole number.
question

Leading Coefficient
answer

The constant of the term with the highest degree.
question

Multiplication rule for monomials
answer

a(to the power of m) x a(to the power of n) = a(to the power of m +n)
question

List of ways to factor
answer

1. GCF 2. Special Case a.Difference of 2 squares b. Sum/Difference of 2 cubes 3. 2 binomials 4. Grouping
question

Dividing variables
answer

You subtract the exponents Example: x³ ÷ × = x²
question

Rules for when synthetic division works
answer

1. Divisor is linear (no exponents in bottom) 2. Have to be able to put divisor in \”x-a\” form How to set it up: a| coefficients of dividends in descending order Example: (x² – x – 6) ÷ (x – 3) 3| 1 -1 -6 ↓ ↓ ↓ + 0 3 6 ———————— 1 2 0 first degree coefficient, constant, remainder.
question

Rational Root Theorem
answer

Tells possible rational roots (solutions effectively). Once you find one that works via synthetic division you just have to factor to find all answers. P (Factors of Constant) ÷ Q (Factors of Lead Coefficient)
question

Sum/Product of Quadratic Roots Btw personally I didn’t understand this totally, but there’s a good youtube video to explain it (first one when you look it up)
answer

Sum = -b ÷ a Product = c ÷ a Basically, when condense everything down you can solve quadratic equations by utilizing this concept like this: a² + (-sum of roots) + (product of roots) It’s actually very useful, and can be used in place of the quadratic formula.
question

Division Rule for Monomials
answer

x(to the power of m) ÷ x(to the power of n = x(to the power of m-n)
question

Power Rule
answer

(a to the power of m)(raised to the power of n) = a( to the power of m x n) Example: (x²)³ = x⁶
question

Power of a Product
answer

(a x b)(to the power of m) = a(to the power of m) x b(to the power of n)
question

Power of a Quotient
answer

(x÷y)(to the power of m)= x(to the power of m) ÷ y(to the power of m)
question

Zero Power
answer

x⁰ ALWAYS = 1
question

Negative Power
answer

x⁻¹ = 1 ÷ x
question

Adding/Subtracting Radicals/Exponents
answer

You can only add if radicals/exponents are the same. Remember that you can never have radical in denominator.
question

Solving Equations with Radicals
answer

1. Isolate radical. 2. Square/cube/etc. to eliminate radical 3. Solve 4. Check. or 1. Isolate radical 2. Raise to power of reciprocal. 3. Solve 4. Check.
question

Variables as exponents
answer

Make coefficients the same and set exponents equal to each other.
question

Interest Problems
answer

Formulas: Simple: Principal x Rate = Interest Compound: Balance = Principal(1 + interest rate ÷ number of times per year compounded)(to the power of number of times per year compounded x time in years) Continuously compounding: P x e(to the rate of growth/decay percentage x time in years)
question

Common logarithm
answer

Base 10.
question

Natural Logarithm
answer

Base \”e\”.
question

Matrices Basic Information
answer

How do you name a matrix? Name it a variable. Dimensions of a matrix? # of rows by # of columns. Types of matrices? 1. Square Matrix- # of roms = # of columns. 2. Row Matrix- 1 row. 3. Column Matrix- 1 column. 4. Zero Matrix- All entries are 0. 5. Identity Matrix- All entries are zero except diagonal 1’s.
question

Adding and Subtracting Matrices
answer

1. Dimensions must match. 2. Add of subtract corresponding entries.
question

Multiplying Matrices (by other matrices not scalar)
answer

1. Inner Dimensions must match. 2. Outer dimensions will tell dimensions of product.
question

Determinants
answer

Shown by: | a b| (lines would be connected however) |c d| Criss cross multiply and subtract bottom minus top (ad-bc) With non-square matrices you rewrite the first two columns to side, criss-cross multiply and add, and subtract bottom minus top. |a b c d| a b |e f g h | e f |i g k z| i g
question

Cramer’s Rule
answer

This is based off of this format: Coefficient matrix x variable matrix = constant matrix Denominator of x answer is always the determinant of coefficient while for the numerator you sub in constants for x column and find discriminant. For y denominator is also determinant of coefficient and numerator is determinant of coefficient with constants in y column.
question

The Matrix
answer

A sick movie.
question

Singular Matrix
answer

If determinant of coefficient is 0.
question

Finding the inverse of a matrix
answer

A⁻₁ = 1 ÷ Discriminant of A x |d -b| |-c a| This is useful because in the typical equation you can just multiply constants by inverse of coefficient and get your solution.
question

Solving Linear Inequalities
answer

1. Simplify each side by distributing or combining like terms 2. Move the variables to the same side of the equation/inequality 3. Isolate the term with the variable. 4. Isolate the variable. IF YOU MULTIPLY OR DIVIDE BOTH SIDES OF AN INEQUALITY BY A NEGATIVE NUMBER YOU MUST SWITCH THE INEQUALITY SIGN!! (sorry for yelling).
question

Unions and Intersections.
answer

The union of two sets is all the numbers in the two sets. It’s symbol is a \”U\” (The U of Miami). It’s word is \”or\”. The intersection of two sets is all the numbers that belong to both of the sets (which are in both, not all). It is symbolized by an upside down U. It’s word is \”and\”.
question

Absolute Value inequalities
answer

example: |y|>5 y>5 or y<-5
question

Absolute values in Combined Inequalities
answer

1. Break it down (if needed) 2. Do both + and – of 2 sides. 3. Do graphs for both. 4. Find intersects. 5. Graph and state answer.
question

Absolute Value Inequalities Pattern
answer

|x|>a then it’s an \”or\” statement. |x|<a then it's an \"and\" statement.
question

Probability
answer

favorable outcomes over total outcomes.
question

Mutually Exclusive Events
answer

2 events that have no outcomes in common.
question

The Addition Principle
answer

1. If two events A and B are mutually exclusive, then P(A) +P(B) 2. If two events A and B are not mutually exclusive, then P(A or B) = P(A) + P(B) – P(A and B)
question

Independent Events
answer

Two or more events in which the occurrence of one event does not affect the probability of the occurrence of the next event.
question

Multiplication Rule for Probabilities
answer

1. When two events A and B are independent, the probability of both occurring is P(A and B) = P(A) x P(B). 2. When two events A and B are dependent, the probability of both ocurring is P(A and B) = P(A) x P(B happening after A).
question

Dependent Events
answer

Two or more events in which the occurrence of one event affects the probability of the occurrence of the next event.

Get instant access to
all materials

Become a Member