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Mathematics

ALGEBRA GUIDE

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Formula Sheet for College Algebra Final Exam Properties of Exponents p p mp npp m n mpnppmn nmmn mn m n mnmn bb b a b a baba aa aa a aaa 1.6 .5 )(.4 )(.3 .2 .1 = =??? ? ??? ? = = = = ? ? + Quadratic Formula a acbbx 2 42 ???= Circle rradius khcenter rkyhx = = =?+? ),( )()( 222 Vertex of Parabola ),( )()( 2 , 2 2 khatVertex khxaxf a bfa b +?= ??? ???? ? ?? ??? ? ?? Standard Form of Equation of Parabola phxdirectrix kphfocus khvertex hxpky pkydirectrix pkhfocus khvertex kyphx ?= += = ?=? ?= += = ?=? : ),( ),( )(4)( : ),( ),( )(4)( 2 2 Properties of Logarithms pb pb b xbiffxy p b p b b y b b = = = = == log.5 01log.4 log.3 1log.2 log.1 nm n m nm mn mpm bb b bb b b p b loglog

UPDATED EXAM INTERMEDIATE ALGEBRA

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MATH EXAM 1 THRU 3 1 MATH EXAM #1 1. Determine whether the diagram defines y as a function of x. if it does not, indicate a value x that is assigned more than one value of y X y -4 5 -3 7 4 9 4 11 2. GRAPH THE FUNCTION: h(x) =|4-x| X h(x) 3 1 4 0 5 1 6 2 2 2 1 3 3. Determine the graph of the solution of the given system. X + Y > 2 X - Y < 2 MATH EXAM 1 THRU 3 2 3 Determine whether the graph is a function 4. THE GRAPH OF A SYSTEM OF 2 LINEAR INEQUALITES IS SHOWN. TELL WHICH POINT IS A SOLUTION OF THE SYSTEM. MATH EXAM 1 THRU 3 3 6. FIND THE SOLUTION OF THE SYSTEM. X > -2 Y > -4

FORMULAS AND FUNCTIONS/RADICAL EXP AND EQUATION/ QUAD EQU, FUNCTION& INEQU

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MATH EXAM 1 1 MATH EXAM #1 1. Determine whether the diagram defines y as a function of x. if it does not, indicate a value x that is assigned more than one value of y X y -4 5 -3 7 4 9 4 11 2. GRAPH THE FUNCTION: h(x) =|4-x| X h(x) 3 1 4 0 5 1 6 2 2 2 1 3 3. Determine the graph of the solution of the given system. X + Y > 2 X - Y < 2 MATH EXAM 1 2 3 Determine whether the graph is a function 4. THE GRAPH OF A SYSTEM OF 2 LINEAR INEQUALITES IS SHOWN. TELL WHICH POINT IS A SOLUTION OF THE SYSTEM. MATH EXAM 1 3 6. FIND THE SOLUTION OF THE SYSTEM. X > -2 Y > -4 7. GRAPH THE SOLUTIONS OF THE SYSTEM

RADICAL EXPRESSIONS AND EQUATIONS

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Exam 2 CH 9 Exam 2 COMPLETE THE TABLE OF VALUES FOR f(x) = ?x + 1, and then graph the function. Give the domain and range of the function X F(x) 0 1 4 9 Domain: _____________ Range:______________ The graph of a square root function f is shown below. Find the value(s) of x for which f(x) =1 Evaluate the square root ; if possible 4. Simplify the expression. Assume that x is unrestricted and use the absolute value symbols of necessary. Simplify SIMPLIFY assume all variables are unrestricted and use absolute value symbols when necessary EVALUATE THE EXPRESSION SIMPLLIFY THE EXPRESSION Perform the indicated operation. Simplify if possible. Assume all are positive.

FORMULAS/LITERAL EQUATIONS, INEQUALTIES AND FUNCTIONS

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MATH EXAM 1 MATH EXAM #1 Determine whether the diagram defines y as a function of x. if it does not, indicate a value x that is assigned more than one value of y X y -4 5 -3 7 4 9 4 11 2. GRAPH THE FUNCTION: h(x) =|4-x| X h(x) 3 1 4 0 5 1 6 2 2 2 1 3 3. Determine the graph of the solution of the given system. X + Y > 2 X - Y < 2 3 Determine whether the graph is a function 4. THE GRAPH OF A SYSTEM OF 2 LINEAR INEQUALITES IS SHOWN. TELL WHICH POINT IS A SOLUTION OF THE SYSTEM. 6. FIND THE SOLUTION OF THE SYSTEM. X > -2 Y > -4 7. GRAPH THE SOLUTIONS OF THE SYSTEM 2x ? 4y > -6 3x + y > 5 8. find the solutions of the system X ? Y < 5 Y < 0 X > 0

FINAL EXAM- FORMULAS/EQUATION/INEQUALTIES/EXPONENTIAL AND LOG FUNCTIONS/SYSTEMS OF EQUATIONS,QUADRATIC EQUATIONS,FUNCTIONS,INEQU

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MATH EXAM 1 THRU 4 1 MATH EXAM #1 1. Determine whether the diagram defines y as a function of x. if it does not, indicate a value x that is assigned more than one value of y X y -4 5 -3 7 4 9 4 11 2. GRAPH THE FUNCTION: h(x) =|4-x| X h(x) 3 1 4 0 5 1 6 2 2 2 1 3 3. Determine the graph of the solution of the given system. X + Y > 2 X - Y < 2 MATH EXAM 1 THRU 4 2 3 Determine whether the graph is a function 4. THE GRAPH OF A SYSTEM OF 2 LINEAR INEQUALITES IS SHOWN. TELL WHICH POINT IS A SOLUTION OF THE SYSTEM. MATH EXAM 1 THRU 4 3 6. FIND THE SOLUTION OF THE SYSTEM. X > -2 Y > -4

FINAL EXAM- FORMULAS/EQUATION/INEQUALTIES/EXPONENTIAL AND LOG FUNCTIONS/SYSTEMS OF EQUATIONS,QUADRATIC EQUATIONS,FUNCTIONS,INEQU

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MATH EXAM 1 THRU 4 MATH EXAM #1 Determine whether the diagram defines y as a function of x. if it does not, indicate a value x that is assigned more than one value of y X y -4 5 -3 7 4 9 4 11 2. GRAPH THE FUNCTION: h(x) =|4-x| X h(x) 3 1 4 0 5 1 6 2 2 2 1 3 3. Determine the graph of the solution of the given system. X + Y > 2 X - Y < 2 3 Determine whether the graph is a function 4. THE GRAPH OF A SYSTEM OF 2 LINEAR INEQUALITES IS SHOWN. TELL WHICH POINT IS A SOLUTION OF THE SYSTEM. 6. FIND THE SOLUTION OF THE SYSTEM. X > -2 Y > -4 7. GRAPH THE SOLUTIONS OF THE SYSTEM 2x ? 4y > -6 3x + y > 5 8. find the solutions of the system X ? Y < 5 Y < 0 X > 0

EXPONENTIAL AND LOGARITHMIC FUNCTIONS REVIEW

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Exam 4 Which of the following ordered pairs is a solutuion of (-2,-36) c. (-2,1/36) (-2,1/12) d. (-2,-12) Use composition to show that the pair of functions are inverses. Let find f-g the graph represents a function use the horizontal line test to decide where function is one to one If the function is one to one, find its inverse Find the inverse of the function. Then graph the function and its inverse on one coordinate system. Show line of symmetry on graph Let find the composition (f ? g)(x) Write in exponential form Evulatate the expression Evaluate the expression. Evualtae the expression Write the logarithm as a sum/ difference of logarithms of a single quanity. Then simplify if possible

TEST GUIDE FOR FORMULAS/LITERAL EQUATIONS, INEQUALTIES AND FUNCTIONS

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Math 1270 Exam #3 Solve using elimination a. b. c. Solve by substitution Determine whether the given ordered triple is a solution of the given system (7,1,1) Find the equation of the form y= for the parabola shown in the illustration. Points: (1,-2) , (-1,-6), (3,-6) An artist makes three types of ceramic status at a monthly cost of $655 for 180 status. The manufacturing costs for the three types are $5, $4 and $3. If the statues sell for $20, $12 and $9 respectively, how many of each type should be made to produce $ 2,100 in monthly revenue? _________________expensive _________________middle- priced _________________inexpensive

Practice Test on Algebraic Equations and Functions

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An equivalent expression to the algebraic expression 9x2 ? 4y2 is: A) 3x ? 2y B) 6(3x2 ? 2y2) C) (3x + 2y)(3x ? 2y) D) (2y + 3x)(2y ? 3x) Correct. Your answer=C, Correct answer=C Explanation: 9x2 ? 4y2 = (3x + 2y)(3x ? 2y) Factor the trinomial x2 ? 2x ? 15: A) (x ? 3)(x ? 5) B) (x + 3)(x ? 5) C) (x ? 3)(x + 5) D) (x + 3)(x + 5) Correct. Your answer=B, Correct answer=B Explanation: The numbers ?5 and 3 multiply to give ?15 and add to give ?2. x2 ? 2x ? 15 = x2 ? 5x +3x ? 15 = x (x ? 5) + 3 (x ? 5) = (x ? 5)(x + 3) Fully factored, the quadratic function y = 2x2 + 10x + 12 can be expressed as: A) y = 2(x + 6)(x + 2) B) y = 2(x + 3)(x + 2) C) y = 2(x + 6)(x + 1) D) y = 2(x + 3)(x + 1) Correct. Your answer=B, Correct answer=B Explanation: y = 2x2 + 10x + 12 y = 2(x2 + 5x + 6)

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