Find the distance between the pair of points. 2) (7, 7) and (3, 5) A) 12 3 units B) 2 5 units C) 6 units D) 12 units B) 8 C) 63 2


 Laurence Hoover
 9 months ago
 Views:
Transcription
1 Sample Departmental Final  Math 9 Write the first five terms of the sequence whose general term is given. 1) a n = n 2  n 0, 2,, 12, 20 B) 2,, 12, 20, 30 C) 0, 3, 8, 1, 2 D) 1,, 9, 1, 2 Find the distance between the pair of points. 2) (7, 7) and (3, ) 12 3 units B) 2 units C) units D) 12 units Solve the equation. 3) log 8 ( + 2)  log 8 = B) 8 C) 3 2 D) 2 3 Simplif. ) B) + 2 C) + 2 D)  2 Solve the equation. ) = B) 22 C) D) 8 ) = 83 B)  3 C) 3 D) 3 Using the change of base formula, rewrite the following epression using common logarithms. 7) log 2 log 2 log B) log log 2 C) log 2 D) log 2 Solve. 8) Jim can run miles per hour on level ground on a still da. One wind da, he runs miles with the wind, and in the same amount of time runs miles against the wind. What is the rate of the wind? mph B) mph C) mph D) 3 mph 1
2 9) = + 3 B) 2 C) 3 D) 8 ) = 0 1, 1 B) 1, 1, , C) 1, 1, i, i D) i, i, i, i 11) = B) 3 C) 9 D) 12) A painter can finish painting a house in 7 hours. Her assistant takes 9 hours to finish the same job. How long would it take for them to complete the job if the were working together? hours B) hours C) 8 hours D) 1 3 hours 13) How man real solutions are possible for a sstem of equations whose graphs are a parabola and a circle? 1, 2, or 3 real solutions B) 0, 1, 2, or 3 real solutions C) 0, 1, 2, 3, or real solutions D) 1, 2, 3, or real solutions Use the square root propert to solve the equation. 1) ( + 2) 2 = 11 9 B) 211, C)  11, 11 D) 211, Solve. 1) One number is 2 less than a second number. Twice the second number is 8 less than 3 times the first. Find the two numbers. 12 and 1 B) 1 and 12 C) 11 and 13 D) 13 and 1 1) = B) 37 C) 18 D) 17) The cost in millions of dollars for a compan to manufacture thousand automobiles is given b the function C() = Find the number of automobiles that must be produced to minimize the cost. 1 thousand automobiles B) thousand automobiles C) thousand automobiles D) 2 thousand automobiles Find the eact value. 18) ln e B) 1 C) e D) e 2
3 19) log,000 2 B) 0 C) D) 1 Identif whether the equation, when graphed, will be a parabola, circle, ellipse, or hperbola. 20) 2 = parabola B) circle C) ellipse D) hperbola 21) = 1 parabola B) circle C) ellipse D) hperbola Graph the function. 22) = log 2 B) C) D) Use the quadratic formula to solve the equation. 23) (  8) = 313, + 13 B) , C)  19, + 19 D) ,
4 2) =   i 7,  + i C)  i 7,  + i B)  i 7, + i D)   i 7, + i Sketch the graph of the equation. Find its verte. 2) = 2  verte (, 0) B) verte (0, ) C) verte (0, ) D) verte (, 0) Rationalize the denominator and simplif. Assume that all variables represent positive real numbers. 2) B) C) D) Perform the indicated operation. Write the result in the form a + bi. 27) ( + i)  (2 + i) 83i B) 8 + 3i C) + i D) 83i
5 Find the indicated term for the sequence whose general term is given. 28) a n = (1)n n + 9 ; a B)  7 C) 1 21 D) Sketch the graph of the equation. Find its center and radius. 29) ( + ) = 1 center (0, ); radius = B) center (, 0); radius = C) center (0, ); radius = D) center (, 0); radius = Rationalize the denominator and simplif. Assume that all variables represent positive real numbers. 30) B) 7 3 C) 21 D) Multipl, and then simplif if possible. 31) ( 2  ) 22 B) 72 C) 32 D) 7 + 2
6 Solve the sstem. 32) z = z = 2 z = 3 (3,, ) B) (,, 3) C) (, 3, ) D) Find the value of the logarithmic epression. 33) log B) 1 2 C) 2 D)  1 Find the power of i. 3) i 28 i B) i C) 1 D) 1 Solve the equation for. Give an eact solution. 3) ln = e B) 3.2 C) 3.2 D) e 3.2 3) log = 3. e 3. B) 3. C) 3. D) 3. e Match the function with its graph. 37) f() = B) (3, ) (3, ) C) D) (3, ) (3, ) 
7 Graph the solution of the sstem of linear inequalities. 38)  < + < 3 B) C) D) Solve the equation. Give an eact solution. 39) e ( + 2) = e + 2 B) ln 7 C) e D) ln  2 Solve the equation for the specified variable. 0) V r 2 h = 1 3 ; for h h = V r2 B) h = V 3r 2 C) h = Vr 2 3 D) h = 3V r 2 Epress as the logarithm of a single epression. 1) log 2 + log 2 log 2 3 B) log 2 12 C) log 12 D) log 3 Write the series with summation notation. 2) (9) 9i B) i = 1 (9i + 3) C) i = 1 9i D) i = 1 i = 1 (9i + ) 7
8 Write the first five terms of the geometric sequence whose first term, a 1, and common ratio, r, are given. 3) a 1 = ; r = 1 3, 3, 9, 27, 81 B) 3, 9, 27, 81, 23 C), 12, 3, 8, 32 D), 13 3, 1,, Find the inverse of the onetoone function. ) f() = 3 + f 1 () =  B) f 1 () = C) f 1 () = D) f 1 () = 3  ) f() = f 1 () = B) f 1 () = C) f 1 () = 73 D) f 1 () = 73 For the given functions f and g, find the composition. ) f() = 3  ; g() = 2 Find (f g)() B) C) D) Find the indicated term of the sequence. 7) If the second term of an arithmetic progression is 11 and the sith term is 9, find the fifteenth term. 9 B) 1 C) D) Epress as the logarithm of a single epression. Assume that variables represent positive numbers. 8) log b q  log b r log b q r B) log b (q  r) C) log b q log b r D) log b q r 8
9 Determine which graph is the graph of a onetoone function. 9) B) C) D) Write an equation to describe the variation. Use k for the constant of proportionalit. 0) w varies directl as the square of and inversel as the cube of. w = k2 3 B) w = k3 2 C) w = k D) w 2 3 = k For the given functions f and g, find the composition. 1) f() = 2 + ; g() = + 2 Find (g f)(3). 2 B) 28 C) 120 D) 0 Write in terms of i. 2) i B) ±20 C) 20i D) i 20 Find the indicated term of the sequence. 3) The fifteenth term of the arithmetic sequence whose first term is  and whose common difference is 3 B) 9 C) 38 D)  9
10 ) Find the seventh term of the geometric sequence 1, 2,,... 1 B) 128 C) 12 D) Write as a logarithmic equation. ) 3 2 = 9 log 3 9 = 2 B) log 2 9 = 3 C) log 3 2 = 9 D) log 9 3 = 2 Match the equation with its graph. ) = (  2) ( + 3) B) C) 8 2 D)
11 Identif the domain and then graph the function. 7) f() =  3 [0, ) B) [0, ) C) [3, ) D) [3, ) Use the graph of the following function f() to find the value. 8) Find such that f() = B) 3 C) 7 D) 11
12 Write an equation of the circle with the given center and radius. 9) (, 1); 13 (  1) 2 + ( + ) 2 = 19 B) (  ) 2 + ( + 1) 2 = 13 C) ( + 1) 2 + (  ) 2 = 19 D) ( + ) 2 + (  1) 2 = 13 Given the matri in echelon form, find the solution for the sstem. 0) (12, 1, 2) B) (, 7, 2) C) (2, 1, 12) D) (9, 3, 2) Find the surface area of the figure. 1) 3 m m 7 m 1 m2 B) 18 m2 C) 122 m2 D) 8 m2 Find the variation equation for the variation statement. 2) z varies jointl as and the cube of ; z = 90 when = and = 3 = 3 B) = 3 C) = 3 D) = 3 Use the given right triangle to find the trigonometric function. 3) cos A B) 3 C) 3 D) 3 Use the properties of eponents to simplif the epression. ) 3/ 1/ 3/ B) C) 1/2 D) 1 12
13 The graph of an eponential function is given. Match the graph to one of the following functions. ) f() = 21 B) f() = 2 (  1) C) f() = 2 D) f() = Simplif. Assume that all variables represent an real number. ) B) + C)  + D) + Complete the indicated row operation. 7) Replace R2 in with 3R1 + R2. B) C) D) Solve the problem. 8) A bacteria culture starts with units and triples ever da. Write the general term of the sequence that describes the growth of this culture. Find the number of bacteria units there will be at the beginning of the fourth da. an = 3() n  1 ; 192 units B) an = (3) n ; 32 units C) an = (3) n  1 ; 8 units D) an = () n ; 2 units 9) At a certain time of da, the angle of elevation of the sun is 0. Find the height of a pole whose shadow at that time is 13 feet long ft (13 3)/3 feet B) 13 2 feet C) 13 3 feet D) 2 feet 70) Find the sum of the first nine negative integers.  3 B)  C)  D)  13
14 Simplif the radical epression. Assume that all variables represent positive real numbers. 71) 320k7q8 8k7q8 k B) 8q k7 C) 8k3q k D) 8k3q Use the partial sum formula to find the partial sum of the given geometric sequence. 72) Find the sum of the first five terms of the geometric sequence 1, 2,, B) 279 C) 2 D) 31 Use radical notation to write the epression. Simplif if possible. 73) 1 1/2 2  B) 1 C)  1 D) Find the unknown side of the right triangle. 7) B) 1 C) 2 3 D) 1 Provide an appropriate response. 7) How do ou find Dz when solving a sstem of equations using Cramer's Rule? Replace the column values with the constantcolumn values. B) Replace the column and column values with the constantcolumn values. C) Replace the zcolumn values with the constantcolumn values. D) Replace the column values with the constantcolumn values. 1
15 Graph the equation. 7) (  1) ( + 1) 2 9 = 1 B) C) D) Find the volume of the figure. 77) 2 in. 1π/3 in.3 B) 8π/3 in.3 C) 32π/3 in.3 D) π in.3 If the function is onetoone, list the inverse function. 78) f = {(3, 1), (3, 1), (2, 1), (2, 1)} f 1 = {(1, 3), (3, 3), (1, 2), (1, 2)} B) f 1 = {(1, 3), (1, 3), (1, 2), (1, 2)} C) f 1 = {(1, 3), (1, 3), (1, 3), (1, 2)} D) not onetoone 1
16 Graph the equation. 79) = 1 B) C) D) Find the square root. Assume that all variables represent positive real numbers. 80) B) 2 C) 12 D) Complete the square b adding the proper constant to the binomial so that the resulting trinomial is a perfect square trinomial. Then factor the trinomial. 81) (1) = (  )2 B) = (  )2 C) = (  8)2 D) () = (  8)2 Add. 82) B) 1 C) D) 72 1
17 Solve the nonlinear sstem of equations for real solutions. 83) 222 = = 1 (2, 3), (2,  3), (2, 3), (2,  3) B) ( 3, 2), ( 3, 2), ( 3, 2), ( 3, 2) C) ( 3, 2), ( 3, 2) D) ( 3, 2), ( 3, 2) Solve the inequalit. Graph the solution set and write the solution set in interval notation. 8)  + < 0 (, ) B) (, ) (, ) C) (, ) D) (, ) ) > 0 (7, 3) B) (3, ) C) (, 7) (3, ) D) (, 7) Find the sum of the terms of the infinite geometric sequence. 8) 3, 3, 3 1,... 3 B) C) 1 D) 3 Use the product rule to multipl. 87) B) 1 C) 12 D) 2 17
18 Write with positive eponents. Simplif if possible. 88) 1 / B) 32 C) 1 32 D) not a real number Find the volume of the figure. 89) Cone 8 in. 3 in. 2π in.3 B) 72π in.3 C) 8π in.3 D) 1π in.3 Sketch the graph of the quadratic function. Give the verte and ais of smmetr. 90) f() =  1 ( + 2)21 verte (1, 2); ais = 1 B) verte (1, 2); ais = C) verte (2, 1); ais = 2 D) verte (2, 1); ais =
19 Answer Ke Testname: MATH 9 1) A 2) B 3) D ) D ) D ) A 7) B 8) B 9) C ) B 11) B 12) A 13) C 1) B 1) A 1) D 17) D 18) B 19) C 20) D 21) C 22) D 23) C 2) B 2) D 2) C 27) B 28) C 29) B 30) B 31) B 32) B 33) A 3) D 3) D 3) C 37) C 38) A 39) D 0) D 1) A 2) D 3) A ) D ) D ) A 7) C 8) D 9) D 19
20 Answer Ke Testname: MATH 9 0) A 1) A 2) C 3) D ) D ) A ) B 7) C 8) C 9) B 0) A 1) C 2) C 3) D ) C ) C ) B 7) D 8) C 9) C 70) C 71) C 72) D 73) B 7) D 7) C 7) D 77) C 78) B 79) B 80) D 81) B 82) D 83) B 8) C 8) C 8) B 87) C 88) C 89) A 90) C 20
MAT 1033C  MartinGay Intermediate Algebra Chapter 8 (8.1, 8.2, 8.5, 8.6) Practice for the Exam
MAT 33C  MartinGa Intermediate Algebra Chapter 8 (8.1 8. 8. 8.6) Practice for the Eam Name Date Da/Time: SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
More informationSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Practice for the Final Eam MAC 1 Sullivan Version 1 (2007) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Find the distance d(p1, P2) between the points
More informationMATH 115: Final Exam Review. Can you find the distance between two points and the midpoint of a line segment? (1.1)
MATH : Final Eam Review Can ou find the distance between two points and the midpoint of a line segment? (.) () Consider the points A (,) and ( 6, ) B. (a) Find the distance between A and B. (b) Find the
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Final Eam Review MAC 1 Fall 011 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve and check the linear equation. 1) ( + )  = (  7) A)
More information25) x x + 30 x2 + 15x ) x Graph the equation. 30) y =  x  1
PreAP Algebra Final Eam Review Solve. ) A stone is dropped from a tower that is feet high. The formula h =  t describes the stoneʹs height above the ground, h, in feet, t seconds after it was dropped.
More informationTO THE STUDENT: To best prepare for Test 4, do all the problems on separate paper. The answers are given at the end of the review sheet.
MATH TEST 4 REVIEW TO THE STUDENT: To best prepare for Test 4, do all the problems on separate paper. The answers are given at the end of the review sheet. PART NONCALCULATOR DIRECTIONS: The problems
More informationChapters 8 & 9 Review for Final
Math 203  Intermediate Algebra Professor Valdez Chapters 8 & 9 Review for Final SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the formula for
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. B) x y =
Santa Monica College Practicing College Algebra MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Write the standard equation for the circle. 1) Center
More information9 (0, 3) and solve equations to earn full credit.
Math 0 Intermediate Algebra II Final Eam Review Page of Instructions: (6, ) Use our own paper for the review questions. For the final eam, show all work on the eam. (6, ) This is an algebra class do not
More informationLast modified Spring 2016
Math 00 Final Review Questions In problems 6, perform the indicated operations and simplif if necessar.. 8 6 8. 7 6. ( i) ( 4 i) 4. (8 i). ( 9 i)( 7 i) 6. ( i)( i) In problems 7, solve the following applications.
More informationMath 110 Final Exam Review Revised December 2015
Math 110 Final Exam Review Revised December 2015 Factor out the GCF from each polynomial. 1) 60x  15 2) 7x 8 y + 42x 6 3) x 9 y 5  x 9 y 4 + x 7 y 2  x 6 y 2 Factor each fourterm polynomial by grouping.
More informationUnit 2 Notes Packet on Quadratic Functions and Factoring
Name: Period: Unit Notes Packet on Quadratic Functions and Factoring Notes #: Graphing quadratic equations in standard form, verte form, and intercept form. A. Intro to Graphs of Quadratic Equations: a
More informationInstructor: Imelda Valencia Course: A3 Honors Pre Calculus
Student: Date: Instructor: Imelda Valencia Course: A3 Honors Pre Calculus 01 017 Assignment: Summer Homework for those who will be taking FOCA 017 01 onl available until Sept. 15 1. Write the epression
More informationMTH 112 Practice Test 3 Sections 3.3, 3.4, 3.5, 1.9, 7.4, 7.5, 8.1, 8.2
MTH 112 Practice Test 3 Sections 3.3, 3., 3., 1.9, 7., 7., 8.1, 8.2 Use properties of logarithms to epand the logarithmic epression as much as possible. Where possible, evaluate logarithmic epressions
More informationSECTION 87 De Moivre s Theorem. De Moivre s Theorem, n a Natural Number nthroots of z
87 De Moivre s Theorem 635 B eactl; compute the modulus and argument for part C to two decimal places. 9. (A) 3 i (B) 1 i (C) 5 6i 10. (A) 1 i 3 (B) 3i (C) 7 4i 11. (A) i 3 (B) 3 i (C) 8 5i 12. (A) 3
More informationMATH College Algebra Review for Test 2
MATH 4  College Algebra Review for Test Sections. and.. For f (x) = x + 4x + 5, give (a) the xintercept(s), (b) the intercept, (c) both coordinates of the vertex, and (d) the equation of the axis of
More informationLesson 9.1 Using the Distance Formula
Lesson. Using the Distance Formula. Find the eact distance between each pair of points. a. (0, 0) and (, ) b. (0, 0) and (7, ) c. (, 8) and (, ) d. (, ) and (, 7) e. (, 7) and (8, ) f. (8, ) and (, 0)
More informationAlgebra 2. Chapter 4 Exponential and Logarithmic Functions. Chapter 1 Foundations for Functions. Chapter 3 Polynomial Functions
Algebra 2 Chapter 1 Foundations for Chapter 2 Quadratic Chapter 3 Polynomial Chapter 4 Exponential and Logarithmic Chapter 5 Rational and Radical Chapter 6 Properties and Attributes of Chapter 7 Probability
More informationAccuplacer College Level Math Study Guide
Testing Center Student Success Center Accuplacer Study Guide The following sample questions are similar to the format and content of questions on the Accuplacer College Level Math test. Reviewing these
More information( ) 2 + 2x 3! ( x x ) 2
Review for The Final Math 195 1. Rewrite as a single simplified fraction: 1. Rewrite as a single simplified fraction:. + 1 + + 1! 3. Rewrite as a single simplified fraction:! 4! 4 + 3 3 + + 5! 3 3! 4!
More informationApplied Algebra II Semester 2 Practice Exam A DRAFT. 6. Let f ( x) = 2x A. 47 B. 92 C. 139 D. 407
Applied Algebra II Semester Practice Eam A. Find the solution set of { + 0, 0} { + i 0, i 0} { + i, i } { +, } + = 9.. Let f ( ) = and ( ) 0 g =. Which epression is equivalent to f g? ( ) ( ). What is
More informationIntermediate Algebra 100A Final Exam Review Fall 2007
1 Basic Concepts 1. Sets and Other Basic Concepts Words/Concepts to Know: roster form, set builder notation, union, intersection, real numbers, natural numbers, whole numbers, integers, rational numbers,
More information3.1 Graph Quadratic Functions
3. Graph Quadratic Functions in Standard Form Georgia Performance Standard(s) MMA3b, MMA3c Goal p Use intervals of increase and decrease to understand average rates of change of quadratic functions. Your
More informationAlgebra 2 (2006) Correlation of the ALEKS Course Algebra 2 to the California Content Standards for Algebra 2
Algebra 2 (2006) Correlation of the ALEKS Course Algebra 2 to the California Content Standards for Algebra 2 Algebra II  This discipline complements and expands the mathematical content and concepts of
More informationDiagnostic Tests Study Guide
California State Universit, Sacramento Department of Mathematics and Statistics Diagnostic Tests Stud Guide Descriptions Stud Guides Sample Tests & Answers Table of Contents: Introduction Elementar Algebra
More information( ) ( ) ( )( ) Algebra II Semester 2 Practice Exam A DRAFT. = x. Which expression is equivalent to. 1. Find the solution set of. f g x? B.
Algebra II Semester Practice Eam A. Find the solution set of 5 5 +, 9 9 +, 5 5 +, =.. Let f ( ) = and g( ) =. Which epression is equivalent to f g? ( ) ( ) + ( ) 9 9 +, 5. If h( ) = 0 and j( ) h( ) + j
More informationNational 5 Mathematics
St Andrew s Academ Mathematics Department National 5 Mathematics UNIT 4 ASSESSMENT PREPARATION St Andrew's Academ Maths Dept 01617 1 Practice Unit Assessment 4A for National 5 1. Simplif, giving our answer
More informationUse Properties of Exponents
4. Georgia Performance Standard(s) MMAa Your Notes Use Properties of Eponents Goal p Simplif epressions involving powers. VOCABULARY Scientific notation PROPERTIES OF EXPONENTS Let a and b be real numbers
More informationClasswork #40: Final Review: Solving Equations, Word Problems, Linear Equations, Systems of Linear Equations
Classwork #0: Final Review: Solving Equations, Word Problems, Linear Equations, Sstems of Linear Equations Solving Equations: Isolate the variable! Things to watch for: when ou have parentheses the inequalit
More informationAlgebra/Precalc Review
Algebra/Precalc Review The following pages contain various algebra and precalculus topics that are used in the stud of calculus. These pages were designed so that students can refresh their knowledge
More informationMath 101 chapter six practice exam MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Math 1 chapter si practice eam MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Which equation matches the given calculatorgenerated graph and description?
More informationQuadratic Function. Parabola. Parent quadratic function. Vertex. Axis of Symmetry
Name: Chapter 10: Quadratic Equations and Functions Section 10.1: Graph = a + c Quadratic Function Parabola Parent quadratic function Verte Ais of Smmetr Parent Function =  1 0 1 1 Eample 1: Make a table,
More informationUnit 9: Rational Functions
Date Period Unit 9: Rational Functions DAY TOPIC Direct, Inverse and Combined Variation Graphs of Inverse Variation Page 484 In Class 3 Rational Epressions Multipling and Dividing 4 Adding and Subtracting
More informationAlgebra 1 Skills Needed for Success in Math
Algebra 1 Skills Needed for Success in Math A. Simplifing Polnomial Epressions Objectives: The student will be able to: Appl the appropriate arithmetic operations and algebraic properties needed to simplif
More informationBRONX COMMUNITY COLLEGE of the City University of New York DEPARTMENT OF MATHEMATICS & COMPUTER SCIENCE. MTH06 Review Sheet y 6 2x + 5 y.
BRONX COMMUNITY COLLEGE of the Cit Universit of New York DEPARTMENT OF MATHEMATICS & COMPUTER SCIENCE MTH06 Review Sheet. Perform the indicated operations and simplif: n n 0 n +n ( 9 )( ) + + 6 + 9ab a+b
More informationPreCalculus and Trigonometry Capacity Matrix
PreCalculus and Capacity Matri Review Polynomials A1.1.4 A1.2.5 Add, subtract, multiply and simplify polynomials and rational epressions Solve polynomial equations and equations involving rational epressions
More informationLesson 7.1 Polynomial Degree and Finite Differences
Lesson 7.1 Polnomial Degree and Finite Differences 1. Identif the degree of each polnomial. a. 1 b. 0. 1. 3. 3 c. 0 16 0. Determine which of the epressions are polnomials. For each polnomial, state its
More informationMath 102 Final Exam Review
. Compute f ( + h) f () h Math 0 Final Eam Review for each of the following functions. Simplify your answers. f () 4 + 5 f ( ) f () + f ( ). Find the domain of each of the following functions. f( ) g (
More informationMath 2412 Pre Calculus TEST 2 Prep Fall 2011
Math 41 Pre Calculus TEST Prep Fall 011 Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Find the eact value under the given conditions. 1) sin α
More informationSECONDDEGREE INEQUALITIES
60 (40) Chapter Nonlinear Sstems and the Conic Sections 0 0 4 FIGURE FOR EXERCISE GETTING MORE INVOLVED. Cooperative learning. Let (, ) be an arbitrar point on an ellipse with foci (c, 0) and ( c, 0)
More informationAlgebra 2 with Trigonometry Correlation of the ALEKS course Algebra 2 with Trigonometry to the Tennessee Algebra II Standards
Algebra 2 with Trigonometry Correlation of the ALEKS course Algebra 2 with Trigonometry to the Tennessee Algebra II Standards Standard 2 : Number & Operations CLE 3103.2.1: CLE 3103.2.2: CLE 3103.2.3:
More informationFinal Exam Review Part 2 #4
Final Eam Review Part # Intermediate Algebra / MAT 135 Fall 01 Master (Prof. Fleischner) Student Name/ID: 1. Solve for, where is a real number. + = 8. Solve for, where is a real number. 9 1 = 3. Solve
More informationInfinite Limits. Let f be the function given by. f x 3 x 2.
0_005.qd //0 :07 PM Page 8 SECTION.5 Infinite Limits 8, as Section.5, as + f() = f increases and decreases without bound as approaches. Figure.9 Infinite Limits Determine infinite its from the left and
More informationa = B. Examples: 1. Simplify the following expressions using the multiplication rule
Section. Monomials Objectives:. Multiply and divide monomials.. Simplify epressions involving powers of monomials.. Use epressions in scientific notation. I. Negative Eponents and Eponents of Zero A. Rules.
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
MAT 10 Test 2 Review (chapters 6,7,11) Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Multipl both sides of each equation b a common denominator
More informationy x+ 2. A rectangular frame for a painting has a perimeter of 82 inches. If the length of the frame is 25 inches, find the width of the frame.
. Simplif the complex fraction x 4 4 x. x 4 x x 4 x x 4 x x 4 x x E) 4 x. A rectangular frame for a painting has a perimeter of 8 inches. If the length of the frame is inches, find the width of the frame.
More informationMATH 2  PROBLEM SETS
MATH  PROBLEM SETS Problem Set 1: 1. Simplify and write without negative eponents or radicals: a. c d p 5 y cd b. 5p 1 y. Joe is standing at the top of a 100foot tall building. Mike eits the building
More informationChapter 5: Quadratic Equations and Functions 5.1 Modeling Data With Quadratic Functions Quadratic Functions and Their Graphs
Ch 5 Alg Note Sheet Ke Chapter 5: Quadratic Equations and Functions 5.1 Modeling Data With Quadratic Functions Quadratic Functions and Their Graphs Definition: Standard Form of a Quadratic Function The
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Eam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A ceramics workshop makes serving bowls, platters, and bread baskets to sell at its Winter
More informationChapter 1 Notes: Quadratic Functions
19 Chapter 1 Notes: Quadratic Functions (Textbook Lessons 1.1 1.2) Graphing Quadratic Function A function defined by an equation of the form, The graph is a Ushape called a. Standard Form Vertex Form
More informationName Class Date. Quadratic Functions and Transformations. 4 6 x
 Quadratic Functions and Transformations For Eercises, choose the correct letter.. What is the verte of the function 53()? D (, ) (, ) (, ) (, ). Which is the graph of the function f ()5(3) 5? F 6 6 O
More informationINTRODUCTION GOOD LUCK!
INTRODUCTION The Summer Skills Assignment for has been developed to provide all learners of our St. Mar s Count Public Schools communit an opportunit to shore up their prerequisite mathematical skills
More informationSummary and Vocabulary
Chapter 2 Chapter 2 Summar and Vocabular The functions studied in this chapter are all based on direct and inverse variation. When k and n >, formulas of the form = k n define directvariation functions,
More informationReview Topics for MATH 1400 Elements of Calculus Table of Contents
Math 1400  Mano Table of Contents  Review  page 1 of 2 Review Topics for MATH 1400 Elements of Calculus Table of Contents MATH 1400 Elements of Calculus is one of the Marquette Core Courses for Mathematical
More informationPRACTICE FINAL EXAM. 3. Solve: 3x 8 < 7. Write your answer using interval notation. Graph your solution on the number line.
MAC 1105 PRACTICE FINAL EXAM College Algebra *Note: this eam is provided as practice onl. It was based on a book previousl used for this course. You should not onl stud these problems in preparing for
More informationRational Exponents and Radical Functions
.1..... Rational Eponents and Radical Functions nth Roots and Rational Eponents Properties of Rational Eponents and Radicals Graphing Radical Functions Solving Radical Equations and Inequalities Performing
More informationM122 College Algebra Review for Final Exam
M1 College Algebra Review for Final Eam Revised Fall 017 for College Algebra  Beecher All answers should include our work (this could be a written eplanation of the result, a graph with the relevant feature
More informationIntermediate Algebra
Intermediate Algebra The purpose of this course is to strengthen students foundational conceptual and procedural skills in order to prepare students for collegeandcareer readiness. The course textbook,
More informationESCONDIDO UNION HIGH SCHOOL DISTRICT COURSE OF STUDY OUTLINE AND INSTRUCTIONAL OBJECTIVES
ESCONDIDO UNION HIGH SCHOOL DISTRICT COURSE OF STUDY OUTLINE AND INSTRUCTIONAL OBJECTIVES COURSE TITLE: Algebra II A/B COURSE NUMBERS: (P) 7241 / 2381 (H) 3902 / 3903 (Basic) 0336 / 0337 (SE) 5685/5686
More informationCenterville High School Curriculum Mapping Algebra II 1 st Nine Weeks
Centerville High School Curriculum Mapping Algebra II 1 st Nine Weeks Chapter/ Lesson Common Core Standard(s) 11 SMP1 1. How do you use a number line to graph and order real numbers? 2. How do you identify
More informationHonors Algebra 2 ~ Spring 2014 Name 1 Unit 3: Quadratic Functions and Equations
Honors Algebra ~ Spring Name Unit : Quadratic Functions and Equations NC Objectives Covered:. Define and compute with comple numbers. Operate with algebraic epressions (polnomial, rational, comple fractions)
More informationCHAPTER 3 Applications of Differentiation
CHAPTER Applications of Differentiation Section. Etrema on an Interval.............. 0 Section. Rolle s Theorem and the Mean Value Theorem. 07 Section. Increasing and Decreasing Functions and the First
More informationUNCORRECTED. To recognise the rules of a number of common algebraic relations: y = x 1 y 2 = x
5A galler of graphs Objectives To recognise the rules of a number of common algebraic relations: = = = (rectangular hperbola) + = (circle). To be able to sketch the graphs of these relations. To be able
More informationSample Problems For Grade 9 Mathematics. Grade. 1. If x 3
Sample roblems For 9 Mathematics DIRECTIONS: This section provides sample mathematics problems for the 9 test forms. These problems are based on material included in the New York Cit curriculum for 8.
More informationUsing Intercept Form
8.5 Using Intercept Form Essential Question What are some of the characteristics of the graph of f () = a( p)( q)? Using Zeros to Write Functions Work with a partner. Each graph represents a function of
More informationEXPONENT REVIEW!!! Concept Byte (Review): Properties of Exponents. Property of Exponents: Product of Powers. x m x n = x m + n
Algebra B: Chapter 6 Notes 1 EXPONENT REVIEW!!! Concept Byte (Review): Properties of Eponents Recall from Algebra 1, the Properties (Rules) of Eponents. Property of Eponents: Product of Powers m n = m
More informationcorrelated to the Virginia Standards of Learning Algebra II with Trigonometry
correlated to the Virginia Standards of Learning Algebra II with Trigonometry AII/T.1 The student will identify field properties, axioms of equality and inequality, and properties of order that are valid
More informationMAT Intermediate Algebra  Final Exam Review Textbook: Beginning & Intermediate Algebra, 5th Ed., by MartinGay
MAT0  Intermediate Algebra  Final Eam Review Tetbook: Beginning & Intermediate Algebra, 5th Ed., by MartinGay Section 2. Solve the equation. ) 9  (  ) = 2 Section 2.8 Solve the inequality. Graph the
More informationDiagnostic Tests. (c) (sa sb )(sa sb ) Diagnostic Test: Algebra
Diagnostic Tests Success in calculus depends to a large etent on knowledge of the mathematics that precedes calculus: algebra, analtic geometr, functions, and trigonometr. The following tests are intended
More informationAnswer Explanations. The SAT Subject Tests. Mathematics Level 1 & 2 TO PRACTICE QUESTIONS FROM THE SAT SUBJECT TESTS STUDENT GUIDE
The SAT Subject Tests Answer Eplanations TO PRACTICE QUESTIONS FROM THE SAT SUBJECT TESTS STUDENT GUIDE Mathematics Level & Visit sat.org/stpractice to get more practice and stud tips for the Subject Test
More informationAPPENDIX D Rotation and the General SecondDegree Equation
APPENDIX D Rotation and the General SecondDegree Equation Rotation of Aes Invariants Under Rotation After rotation of the  and aes counterclockwise through an angle, the rotated aes are denoted as the
More information2.1 Evaluate and Graph Polynomial
2. Evaluate and Graph Polnomial Functions Georgia Performance Standard(s) MM3Ab, MM3Ac, MM3Ad Your Notes Goal p Evaluate and graph polnomial functions. VOCABULARY Polnomial Polnomial function Degree of
More informationPrecalculus Fall Final Exam REVIEW Evaluate the function at the specified value(s) of the independent variable and simplify.
Precalculus Fall Final Eam EVIEW 016017 1. Model the following situation with a linear equation in slopeintercept form. 4 The gas tank in a truck holds 15 gallons. The truck uses gallon per mile. 7.
More informationCalculus w/applications Prerequisite Packet Paint Branch High School Math Department
Updated 6/014 The problems in this packet are designed to help you review topics from previous math courses that are important to your success in Calculus with Applications. It is important that you take
More information2. Use your graphing calculator to graph each of the functions below over the interval 2, 2
MSLC Math 0 Final Eam Review Disclaimer: This should NOT be used as your only guide for what to study. if 0. Use the piecewise defined function f( ) to answer the following: if a. Compute f(0), f(), f(),
More informationPreCalculus. Curriculum (447 topics additional topics)
PreCalculus This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet curricular needs.
More information1.9 CC.912.A.REI.4b graph quadratic inequalities find solutions to quadratic inequalities
1 Quadratic Functions and Factoring 1.1 Graph Quadratic Functions in Standard Form 1.2 Graph Quadratic Functions in Vertex or Intercept Form 1.3 Solve by Factoring 1.4 Solve by Factoring 1.5 Solve Quadratic
More informationPRECALCULUS FINAL EXAM REVIEW
PRECALCULUS FINAL EXAM REVIEW Evaluate the function at the indicated value of. Round our result to three decimal places.. f () 4(5 ); 0.8. f () e ; 0.78 Use the graph of f to describe the transformation
More informationNEXTGENERATION Advanced Algebra and Functions
NEXTGENERATIN Advanced Algebra and Functions Sample Questions The College Board The College Board is a missiondriven notforprofit organization that connects students to college success and opportunit.
More information3) Find the distance for each set of ordered pairs (remember to provide EXACT answers): 5) x 2 + y 2 + 6x 6y + 9 = 0 A) Ellipse (x 1) 2
Algebra Chapter Review 1) State the Midpoint Formula: State the Distance Formula: ID: 1 Name Date ) Find the midpoint for each set of ordered pairs: a) (1, ), (, ) b) (, 0), (, 3) Period c) (, ), (,
More informationState whether the following statements are true or false: 27.
Cumulative MTE 9 Review This packet includes major developmental math concepts that students ma use to prepare for the VPT Math (Virginia Placement Test for Math or for students to use to review essential
More informationAlgebra II. A2.1.1 Recognize and graph various types of functions, including polynomial, rational, and algebraic functions.
Standard 1: Relations and Functions Students graph relations and functions and find zeros. They use function notation and combine functions by composition. They interpret functions in given situations.
More informationAlgebra Review C H A P T E R. To solve an algebraic equation with one variable, find the value of the unknown variable.
C H A P T E R 6 Algebra Review This chapter reviews key skills and concepts of algebra that you need to know for the SAT. Throughout the chapter are sample questions in the style of SAT questions. Each
More informationWAYNESBORO AREA SCHOOL DISTRICT CURRICULUM ALGEBRA II
UNIT: Review of Basic Algebra Skills as Needed SR1 and any Supplemental Materials UNIT : What skills from Algebra I are used in Algebra II? Review Algebra I Skills as Needed SR1 and any additional resources
More informationMuskogee Public Schools Curriculum Map
Muskogee Public Schools Curriculum Map 200920010 Course: Algebra II Grade Level: 912 Nine 1 st Nine Standard 1: Number Systems and Algebraic Operations  The student will perform operations with rational,
More informationAlgebra Notes Quadratic Functions and Equations Unit 08
Note: This Unit contains concepts that are separated for teacher use, but which must be integrated by the completion of the unit so students can make sense of choosing appropriate methods for solving quadratic
More informationLaw of Sines, Law of Cosines, Heron s Formula:
PreAP Math Analsis nd Semester Review Law of Sines, Law of Cosines, Heron s Formula:. Determine how man solutions the triangle has and eplain our reasoning. (FIND YOUR FLOW CHART) a. A = 4, a = 4 ards,
More informationPreCalculus and Trigonometry Capacity Matrix
Information PreCalculus and Capacity Matri Review Polynomials A1.1.4 A1.2.5 Add, subtract, multiply and simplify polynomials and rational epressions Solve polynomial equations and equations involving
More informationState whether the following statements are true or false: 30. 1
Cumulative MTE 9 Review This packet includes major developmental math concepts that students ma use to prepare for the VPT Math (Virginia Placement Test for Math or for students to use to review essential
More informationMATH 108 REVIEW TOPIC 6 Radicals
Math 08 T6Radicals Page MATH 08 REVIEW TOPIC 6 Radicals I. Computations with Radicals II. III. IV. Radicals Containing Variables Rationalizing Radicals and Rational Eponents V. Logarithms Answers to Eercises
More informationMath 0240 Final Exam Review Questions 11 ( 9) 6(10 4)
Math 040 Final Eam Review Questions 11 ( 9) 6(10 4) 1. Simplif: 4 8 3 + 8 ( 7). Simplif: 34 3. Simplif ( 5 7) 3( ) 8 6 4. Simplif: (4 3 ) 9 5. Simplif: 6. Evaluate 4 7 3 3 4 5 when and 3 Write each of
More informationHomework. Basic properties of real numbers. Adding, subtracting, multiplying and dividing real numbers. Solve one step inequalities with integers.
Morgan County School District Re3 A.P. Calculus August What is the language of algebra? Graphing real numbers. Comparing and ordering real numbers. Finding absolute value. September How do you solve one
More information(x a) (a, b, c) P. (z c) E (y b)
( a). FUNCTIONS OF TWO VARIABLES 67 G (,, ) ( c) (a, b, c) P E ( b) Figure.: The diagonal PGgives the distance between the points (,, ) and (a, b, c) F Using Pthagoras theorem twice gives (PG) =(PF) +(FG)
More informationExam practice Disclaimer. The actual test does not mirror this practice. This is meant as a means to help you understand the material.
Eam 3 24 practice Disclaimer. The actual test does not mirror this practice. This is meant as a means to help ou understand the material. Graph the function. 1) f() = 2 2 + 4 + 3 1) Sketch the graph of
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Rationalize the denominator and simplify. 1 1) B) C) 1 D) 1 ) Identify the pair of like
More information54. Focus and Directrix of a Parabola. Key Concept Parabola VOCABULARY TEKS FOCUS ESSENTIAL UNDERSTANDING
5 Focus and Directri of a Parabola TEKS FOCUS VOCABULARY TEKS ()(B) Write the equation of a parabola using given attributes, including verte, focus, directri, ais of smmetr, and direction of opening.
More informationMath 0320 Final Exam Review
Math 0320 Final Exam Review SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Factor out the GCF using the Distributive Property. 1) 6x 3 + 9x 1) Objective:
More informationLesson 10.1 Solving Quadratic Equations
Lesson 10.1 Solving Quadratic Equations 1. Sketch the graph of a quadratic equation with each set of conditions. a. One intercept and all nonnegative yvalues b. The verte in the third quadrant and no
More information+ = + + = x = + = + = 36x
Ch 5 Alg L Homework Worksheets Computation Worksheet #1: You should be able to do these without a calculator! A) Addition (Subtraction = add the opposite of) B) Multiplication (Division = multipl b the
More informationMATH98 Intermediate Algebra Practice Test Form A
MATH98 Intermediate Algebra Practice Test Form A MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the equation. 1) (y  4)  (y + ) = 3y 1) A)
More information