Algebra

Question 1

Many problems with two or more inequalities can be combined…

1. What must inequalities have to be combined

– What is the process?

2. What do you do if variables do not combine?

Answer 1

One common term to align

1. Simplify
2. Ensure signs point the same way
3. Stack

*Note: inequalities w/ multiple variables may not combine, if so:
A) combine what you can
B) Find common term through multiplying or dividing

Question 2

Inequalities (Compare QTY’s w/ different values)

1. Translating Graph Formula
2. Dividing or Multiplying inequality by a negative

Answer 2

1. | x - midpoint | ≤ distance from end to mid point
   –– shaded = included / equal to
   –– open = excluded / more or less than
2. diving or multiplying inequality by a negative…flip the sign!!

Question 3

What to consider?

AV | means two end solutions, both not always valid!

Answer 3

Two scenarios and plug extreme values into x

Scenario #1: (positive) = positive

Scenario #2: (positive) = (negative)

The most difficult Q’s involve multiple brackets on one side….you must test numbers (try strat guide Q #15)

Question 4

• Exponents & Roots…how are they related?

- Even Exponents…why are they significant?

Answer 4

Opposite equations, which cancel one another out.

ie: a square cancels a square root (vice versa)
ie: cube root cancels out cube exponent

Solve for x under radical:
Isolate & multiply or divide by corresponding exponent

Solve for variable with an exponent:
Isolate, take corresponding root on both sides

Root of a term with EVEN exponent always results in the AV of that term.

Question 5

Quadratic Equations (variables to 1st & 2nd power)…how do you solve?

Answer 5

– Factor to solve
– Ensure x^2 term is positive
– Set #’s equal to zero

It is possible for a quadratic to have only one solution.

– Given as quadratic, consider factoring
–– Given with factors, consider FOILING
–––If factors already set to zero…DO NOT FOIL…instead set each factor equal to zero

Question 6

Hidden Quadratics

Answer 6

ax^2 + bx + c = 0

Discriminat = b^2 - 4ac

Question 7

Quadratic Formulas (3)

Answer 7

1. ) x² – y² = (x-y)(x+y)
2. ). x² + 2xy + y² = (x+y)²
3. ) x² – 2xy + y² = (x-y)²

Question 8

Quadratic Inequalities

Answer 8

Must be factored to be solved.

Question 9

Multiple Equations (2)

Answer 9

1.) Stack and eliminate (only works when addition or subtraction can cause one to cancel out thus must have opposite coefficients.

2. ) Isolate and substitute.
   - - Isolate opposite of ask to solve

Three or more equations can use either or both! Substitution often easiest.

Question 10

Multiple Equations with Addition or Subtraction and Multiplication =

Answer 10

Quadratics

Plugging addition or subtraction eq into multiplication eq produces a quadratic

eg) x + y = 20 and xy = 64
plugging x = 20- y into xy = 64 gives you a Quadratic

Question 11

Inequalities & Equations combined…what do you do?

Answer 11

Isolate variable in common

Substitute the equation into the inequality