Algebra

Question 1

Linear equations

Answer 1

• Solve/simplify/manipulate one-variable questions or multi-variable systems of equations.
• When are 2 equations not enough? (they’re copies of each other, or at least one of them has multiplied variables, creating a quadratic)
• When is 1 equation enough? (solving for COMBO, or variables = pos int’s)

Question 2

Exponents/Roots Overview

Answer 2

• can’t distribute across addition or subtraction
• if bases are the same, combine exponents
• if exponents are the same, combine bases (never combine both) - if bases are different and exponents are different, you can’t do anything!

12^5 * 12^3 = 12^5+3
(12^5)^3 = 12^15
12^5 /12^3 = 12^5-3

12^5 * 3^5 = 36^5
4^3 * 4^3 = 16^3 or 4^3 * 4^3 = 4^6

Question 3

Adding Or Subtracting Exponents/Roots

Answer 3

factor out and calculate what’s left
e.g. 12^5 + 12^7 = 12^5 (1 + 12^2) = 12^5 (145)

Question 4

Multiplying or Dividing Exponents/Roots

Answer 4

multiplying or dividing: break down bases until they match

e.g. 12^5 * 10^4 = 2^x * 3^y * 5^z –> (2^52^53^5 ) * (2^4 * 5^4 ) = 2^x * 3^y * 5^z

Question 5

Approximate Square Root

Answer 5

√40 is between 6 and 7, because √36 < √40 < √49

Question 6

Simplify Square Root

Answer 6

√40 = √(4*10) = √4 * √10 = 2√10

Question 7

Quadratics

Answer 7

• Even power? Beware: multiple solutions!
• Set equal to 0 and find possible values
• 3 Special Quadratics
  x^2 - y^2 = (x+y)(x-y)
  (x+y)^2 = x^2 + 2xy + y^2
  (x-y)^2 = x^2 - 2xy + y^2

Question 8

Formulas/Functions

Answer 8

• Don’t panic. They’re just inventing some translation process.
  Each time we see this function symbol they’ve invented and defined,
  we have to perform that translation process

Question 9

Sequences

Answer 9

Question 10

Inequalities

Answer 10

Think about: negatives and fractions! Don’t multiply or divide by a
variable if you don’t know its sign. If they tell you variables are positive,
they want you to manipulate the algebra.
- Test Weird/Extreme cases (ZONEF)
- If you have two inequalities, add them up.
- “ > 0” or “ < 0” is really testing positive/negative rules
- if we’re given |x – 5| < 8
we write (x-5) < 8 or -(x-5) < 8