##### Rick Hobbs, Mission College, Santa Clara, CA

Mr. Hobbs' Math Corner Math 903 main page

# MATH 903 TOPIC SUMMARY

Below is a summary of the main topics from Math 903. You should review all of these while studying for your final exam.

# Solve:

• Linear equations (isolate the variable)
• Linear inequalities
• simple
• compound
• Systems of linear equations
• solve by graphing
• solve by substitution
• solve by addition method
• Systems of linear inequalities
• Quadratic equations (set equal to zero and factor)
• Rational equations
• Proportions (cross-multiply)
• Non-proportions (multiply boths sides by LCD)

• Applications

• Formulas
• Geometry
• Area and perimeter
• Square
• Circle
• Rectangle
• Triangle
• Similar figures (sides are proportional)
• Pythagorean theorem
• Simple interest (I= PRT)
• Solve for a variable in a formula

• Applications (word problems):

• Read and understand the problem.
• Draw an appropriate picture, diagram or table.
• Define a variable or variables. Be explicit.
• Set up a linear, quadratic or rational equation, or system of linear equations, to model the problem.
• Solve the equation or system of equations.
• Check the solution(s) to the equation(s), and check the reasonableness of the solution(s). Watch for extraneous solutions.
• Include correct measurement units in the solution(s).

Types of problems and puzzles:

• Geometry
• Motion
• Dry mixture
• Wet mixture
• Work
• Number
• Percent change
• Money & interest
• Projectile motion
• Miscellaneous

# Perform operations (Add, Subtract, Multiply and Divide):

• Fractions
• Signed numbers
• Polynomials
• Rational expressions
• Functions
• Order of operations
• Scientific notation
• Evaluate: functions and expressions

# Simplify:

• Linear expressions (remove parentheses and combine like terms)
• Exponential expressions (final answers has only positive exponents)
• Rational expressions (factor and cancel common factors)
• Complex fractions

# Properties:

• Real numbers
• Commutative property of addition (order)
• Commutative property of multiplication (order)
• Associative property of addition (grouping)
• Associative property of multiplication (grouping)
• Identity element of addition (zero)
• Identity element of multiplication (one)
• Inverse property of addition (opposite)
• Inverse property of multiplication (reciprocal)
• Distributive property
• Absolute value of real numbers
• Equations
• Addition property of equality
• Multiplicaiton property of equality
• Exponents
• product rule
• quotient rule
• power rule
• zero exponent rule
• negative exponent rule
• expanded power rule

# Polynomials:

• Add
• Subtract
• Multiply
• Divide
• Factor
• Factor out common monomial factors
• Four terms: factor by grouping
• Three terms (quadratic trinomial): use AC test or trial/error method
• Two terms
• Difference of two squares
• Difference of two cubes
• Sum two cubes
• Sum two squares is not factorable unless there is a common monomial factor

# Lines:

• Graphing
• Components of the Cartesian Coordinate System
• x and y coordinates
• x and y axes
• quadrants
• Given the equation of a line:
• Plot points on the line
• Find the x and y intercepts of the line
• Find the slope of the line:
• by solving the equation for y
• by using to points to find the ratio of vertical change to horizontal change
• Graph the line accurately on a coordinate system
• Use a straight-edge
• Label a scale on your coordinate system
• Plot integer points accurately
• Extend the line to the edges of your graph paper
• Types of lines:
• slanted: y = mx + b
• horizontal: y = k
• vertical: x = k
• Slope
• Find the slope of the line by two methods
• Types of slopes
• positive
• negative
• zero (horizontal line)
• undefined (vertical line)
• Slopes of parallel and perpendicular lines
• Intercepts
• x-intercept: y = 0
• y-intercept: x = 0
• Forms of equations of lines
• Standard form
• Point-slope form
• Slope-intecept form
• Function form
• Find the equation of a line
• Given one point and the slope
• Given two points
• Put the equation in any or all of the four forms

# Vocabulary and Notation

• Know the definitions of the vocabulary words written in bold letters throughout each chapter
• Know how to use and interpret the variety of notations and symbols used in algebra
• Operations
• Absolute value
• Minus sign
• subtraction
• part of a negative numeral
• opposite of
• negative exponent means reciprocal
• negative signs in front of exponents with and without parentheses
• Exponents
• positive
• negative
• zero
• Fraction bar
• Parentheses
• Scientific notation
• Interval notation
• set-builder notation
• number line (graphing)
• interval notation
• Function notation
• function vs relation
• domain
• range
• vertical line test

# Checking:

• We have discussed ways to check virtually all of the exercises and problems we have done this semester.
• Check each problem.
• Look for careless mistakes such as sign errors and arithmetic errors.
• Mistakes are your friends: searching for and finding errors make your math skills stronger.
• You should be confident whether or not your solutions are correct: if you know there is an error, find the mistake and correct it.

Mr. Hobbs' Math Corner Math 903 main page
 Instructor: Rick Hobbs Email: rick_hobbs@wvm.edu Phone/voicemail: (408) 855-5325 Office hours: Click here

last update: 5/20/09