Chapter 1
Chapter 1
Solving compound inequalities
Solving absolute value equations and inequalities
Remember to flip sign when multiplying or dividing by a negative!
Solving for a variable.
Chapter 2
Know how to graph lines in general (Vertical and Horizontal lines also)
Knowing how to find equations of lines will help with graph problems where you need to match a graph to an equation.
Quick graphs will also help with graphing problems (graphing using intercepts: x-intercept is y = 0, y-intercept is x=0)
Graphing absolute value functions
Graph piecewise functions
Evaluate piecewise functions
Chapter 3
Solve systems of equations graphically
Understand the meaning of infinitely many solutions, one solution, and no solutions graphically.
Solve systems of equations algebraically
Substitution method versus Linear Combination or Elimination method (making opposites)
Graphing a system of linear inequalities
Solve 3 variables
Chapter 5
Graph parabolas
Vertex form
Standard form
Intercept form
Know how to find all vertices
Know which way it opens, the max or min, and how to find max or min
How to find x-intercepts (y = 0) and y-intercept (x = 0)
Know axis of symmetry (x = “x-value of the vertex”)
Complex numbers
Operations
Add, subtract
Multiply – Remember i2 = -1
Divide – Multiply top and bottom by conjugate of the denominator
Plotting – Real part is like x, imaginary part is like y.
Absolute value
Remember, i is NOT a part of that formula, you should NOT have a negative number inside the root as an answer
Solving quadratics
Factor – COMMON TERM FIRST
Square root both sides – REMEMBER PLUS\MINUS
Completing the square, (b/2)2
Quadratic formula
Know what the discriminant means. Intercepts versus solutions
Remember, roots, solutions, x-interecept, factors, they all pretty much mean try to solve it, though they have different meanings in a sense.
Applications, using the dropped ball and thrown ball formula
Simplify by dividing by a number if possible.
If it’s a dropped ball, it’s root both sides most likely
If it’s a thrown object, quadratic formula is most likely (though it may factor)
Chapter 6
Simplify exponent expressions, properties
Know all exponent rules.
Remember, 2x-1 power is (2/x), NOT (1/2x) That mistake is still being made
Also (3/x-1) = 3x, NOT (x/3)
Know all exponent rules.
Look at Pg 327: 48-51
Graphing
END BEHAVIOR AND DEGREES
Polynomial Operations
Add, subtract, multiply
Patterns for multiplication
Division, synthetic versus long
Need to know what the remainder means
If the remainder is zero, what that means for what you got, factors wise, synthetic substitution wise
Solving\Simplifying polynomial equations
Solving
Factoring
COMMON TERM
x-factor, x-box, grouping
Factoring by grouping if you have four things
Synthetic division and rational root test
PLACE HOLDERS!!!
Quadratic Formula
Square rooting both sides
Simplify
Given a factor, or a f(k) = 0, or a solution, how to break things down using synthetic division. Also know what f(k) = 0 means
Understand what find zeros, all solutions, real solutions, x-intercept, factors, and what it means (pretty much synthetic, break things down until you have an x2, then solve)
Chapter 7
Remember how to rationalize and simplify with fractional exponents
Not as crazy for test, but review all basic problems for sure
Know how to simplify roots
Know when you add exponents (same base) and when to multiply (different bases)
Function operations
Add, subtract, multiply, divide
COMPOSITE FUNCTIONS ALSO
KNOW HOW TO FIND DOMAIN!!!!
How to find inverse, how the inverse is represented graphically
Solving Functions
Raising or rooting both sides to the correct power
CHECK EXTRANEOUS SOLUTIONS
Don’t stress for final, but need to know generally:
Linear Programming
Graphing roots and cubes
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