Mr. Hobbs' Math Corner •Math 903 main page
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MATH 903 TOPIC SUMMARY |
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| 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
- 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
- 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.
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last update: 5/20/09