MAT 00 GROUP FINAL EXAM HOMEWORK SHOW ALL WORK DO NOT USE A CALCULATOR The problems come from the following final eams: W0, F, F0, W, W, F, W, f Adding/Subtracting Algebraic Epressions Simplif b adding (or subtracting) like terms wherever possible: a) b) 9 9 7 + + + + + π + 8 c) + + π + + + d) + + + + + e) + + π f) 7 + 7 + π g) π + + Simplifing Radical Epressions m n p m n p 0 7 Simplif completel: 8 mn Multipl and simplif completel: ( )( + ) ( ) Simplif completel: Multipl and simplif: ( )( + ) 7 z 7 Simplif completel: z 0 z 7 Multipl and simplif completel: ( + 8) 8 Simplif completel: ( ) z 9 Let ( ) f ( ) = Find and simplif f () 0 z 0 p 0 Simplif completel: ( mn ) 0 m n m
Multipl and simplif: ( + )( ) Multipl and simplif: ( ) Simplif completel: (a b c 0 ) a b Negative Eponent Epressions Simplif completel: ( ) Simplif completel: ( ) Simplif completel: 7 Simplif completel: 8 Simplif completel: + + 9 8 9 9 Simplif completel: 8 + 8 0 Simplif completel: (7 7 ) Simplif completel: 7 7 9 + 9 Absolute Value Equations and/or Inequalities Solve: + < 0 Solve: 7 7 > 9 Let f ( ) = + Find all numbers, for which f ( )
+ Solve: 9 Solve: + + > 7 Solve: + = 8 Solve: + 9 Solve: + 8 = 0 Solve: + < Solve: + Let f() = and g() = 7 + Find all for which f() = g() Solve: < Solve: Let f ( ) = + Find all for which f() = Two Variable Stor Problems (Linear) In a triangle, one side is twice as long as the shortest side and another is two inches less than four times the shortest side If the perimeter of the triangle is inches, what are the side lengths? 7 Two cars leave Detroit, travelling in opposite directions One travels at a speed of 80 km/hour and the other at a speed of 9 km/hour In how man hours will the be 8 km apart? 8 In the ear 009, Baltimore had one-half the snowfall of Washington, D C and Philadelphia had inches more than one-third the snowfall of Washington, D C If the total snowfall in the three cities combined was 77 inches, what was the snowfall in each of the cities? 9 The length of a rectangular picture is more than twice the width The perimeter is 8 inches Find the dimensions of the picture 0 Jamie has $0 in nickels and pennies in his pocket If he has a total of coins, how man nickels and how man pennies does he have? Solving Formulas Solve for b : = ab b
Solve for a c b : = c a + a a + Solve for : 7 b a + = a ab Solve for + c b : + = a b Solve for b: ab + = b Solve for b: a + a b = c 7 Solve for b: acb ab + = b Finding the Domain of Functions 8 Let f be the function given b f ( ) = + What is the domain of f? 9 Let f be the function given b f ( ) = What is the domain of f? t 9 0 Let g be the function given b g ( t) = t + 9 What is the domain of g? Let f be the function given b f ( ) = + What is the domain of f? + Let f be the function given b f ( ) = What is the domain of f? Let g be the function given b g() = + What is the domain of g? Let g be the function given b g ( ) = What is the domain of g?
Evaluating Functions f ( ) = + Let f be the function given b ( ) Find and simplif 9 ( ) f ( ) f (7 pts) Let f be the function given b ( ) = ( + ) Find and simplif f ( ) f ( ) f 7 Let r be the function given b r ( ) = a) Find and simplif r () b) Find and simplif r( a) + 8 Let q be the function given b q ( ) = + Find and simplif q ( + h) q( ) 9 Let f be the function given b f ( ) = Find and simplif f ( ) f ( ) h 0 Let f be the function given b ( ) = ( + ) f f Find and simplif ( + ) f ( ) Let f be the function given b f ( ) + = f + [ f ] Find and simplif ( ) ( ) Let f be the function given b f ( ) = f Find and simplif ( + h ) f ( h ) Let g be the function given b g ( ) = + a) Find and simplif g ( ) b) Find and simplif g ( a) Let f be the function given b f ( ) = + f ( + h) f ( ) Find and simplif h Let h be the function given b h() = + a) Find and simplif h() b) Find and simplif h(a + ) h
Let f be the function given b f() = 7 Find and simplif f(a+h)f(a) h 7 Let f be the function given b f ( ) = + 7 a) Find and simplif f () b) Find and simplif f ( a + ) 8 Let f be the function given b f ( ) = f ( + h) f ( ) Find and simplif h Finding Equations of Lines 9 Find the equation of the line that is perpendicular to = and passes through the point(, ) 70 Find the equation of the line that is parallel to = 7 and passes through the point(,) 7 Find the equation of the line that has undefined slope and passes through the point (, ) 7 Find the equation of the line that is perpendicular to the line 7 = and passes through the point (, ) 7 Find the equation of the line shown here (,) - - - - - - (-,-) - - 7 Find the equation of the line that is perpendicular to + = 0 7 Find the equation of the line through the points (, ) and (,) and passes through the point (, 7) 7 Find the equation of the line that is perpendicular to the line = 8 and passes through the point (,) 77 Find the equation of the line that has slope, m = 0, and passes through the point (, )
78 Find the equation of the line that is perpendicular to the line + = and passes through the point (,) 79 Find the equation of the line that is perpendicular to the -ais and passes through the point, 80 Find the equation of the line that has -intercept (,0) and -intercept (0,) 8 Find the equation of the line that is parallel to the line = and passes through the point (, ) 8 Find the equation of the line that is perpendicular to the line = 0 and passes through the point (,) Radical Equation Stor Problems 8 The length of a rectangle is twice its width If the diagonal measures 0 inches, what is the area of the rectangle? 8 The foot of an etension ladder is 0 feet from a wall, while the top of the ladder reaches the top of the wall The ladder is feet longer than the height of the wall What is the height of the wall? 8 A rectangle has a diagonal measuring 0 cm The length of the rectangle is three times the width of the rectangle Find the eact perimeter of the rectangle 8 The area of a triangle is square feet The height of the triangle is feet longer than its base Find the base and the height of the triangle 87 The length of a rectangle is inches more than the width If the diagonal is 0 inches, find the AREA of the rectangle 88 The sum of the two numbers is 0 and the sum of their squares is 8 Find the numbers 89 A rectangle has a diagonal measuring cm The length of the rectangle is cm more than the width of the rectangle Find the length and the width 90 In a right triangle, the length of the long leg is inch less than twice the length of the short leg The hpotenuse is inch more than twice the length of the short leg Find the length of each side of the triangle Solving Quadratic Equations 9 Solve, writing an non-real solutions in the form bi 7 a + : = ( + ) 9 Solve, writing an non-real solutions in the form a ± bi : ( )( ) = 9 Solve, writing an non-real solutions in the form bi 9 Solve, writing an non-real solutions in the form a + bi : 9 Solve, writing an non-real solutions in the form bi a + : ( + + )( 7) = 0 + = a + : ( ) = 9 Solve, writing an non-real solutions in the form a + bi: = 7
97 Solve, writing an non-real solutions in the form bi a ± : 7 = ( + )( ) Graphing Quadratic Equations 98 Graph, labeling the verte and all and intercepts: f ( ) = + 99 Graph, labeling the verte and all and intercepts: f ( ) = + 00 Graph, labeling the verte and all and intercepts: f ( ) = + + 0 Graph, labeling the verte and all and intercepts: g( ) = + 8 0 Graph, labeling the verte and all and intercepts: f ( ) = 0 Graph, labeling the verte and all or intercepts: f() = + + 0 Graph, labeling the verte and all and intercepts: f ( ) = + 9 Simplifing Rational Epressions 0 Simplif completel: + 0 Simplif completel: + 07 Simplif completel: + + 08 Simplif completel: + Comple Fractions 7 09 Simplif completel: 0 Simplif completel: + + + Simplif completel: 9 8
Simplif completel: a b a b ab Solving Radical Equations Solve: + + + = Solve: + = Solve: = Solve: + 7 = 7 Let f ( ) = 0 Find all such that f ( ) = 8 Solve: + = 9 Solve: + + 7 = Nonlinear Inequalities 0 Let g ( ) = Find all inputs,, such that ( ) < + Solve: ( ) 0 Solve: + + 8 > 0 g Solve: Let f ( ) = ( + )( ) Find all inputs,, such that ( ) > 0 + 8 Solve: + Solve: 7 Solve: > + 8 Solve: ( )( + ) 0 f + 0 Solve: 9 Solve: ( ) 0 9
Solve: Reading Graphs of Functions The graph of a function, f, is shown here a) What is the domain of f? b) What is the range of f? c) Find all such that f ( ) = - - - - - - - The graph of a function, f, is shown here a) What is the domain of f? b) What is the range of f? c) What is f ()? d) Find all numbers, such that f ( ) = - - - - - - - - - - - The graph of a function, f, is shown here a) What is the domain of f? b) What is the range of f? c) Find all such that f ( ) = - - - - - - 0
The graph of a function, f, is shown here a) What is the domain of f? b) What is the range of f? c) What is f (0)? d) Find all such that f ( ) = 0 - - - - - - - - - - - The graph of a function, f, is shown here a) What is the domain of f? b) What is the range of f? c) What is f (0)? d) Find all numbers,, such that f ( ) = - - - - - - 7 The graph of a function, f, is shown here a) What is the domain of f? b) What is the range of f? c) What is f()? d) Find all numbers,, such that f() = 0 -- -- -- - - -- - - -- - -
Solving Quadratic-like Equations 8 Solve: + + 0 = 0 9 Solve: w w 8 = 0 0 Solve: ( + ) ( + ) = Solve: + = Solve: + 8 + = 0 8 8 Solve: = + Solve: t = t + Evaluating Logarithms Find: a) ( ) log b) 00 log 0 c) ( ) log Using the approimate values log (0) = 7 and log () = find: a) log ( ) b) ( ) log c) log (0) 7 Find: a) log ( ) b) log ( ) c) ( 0) log 0 8 Using the approimate values log () = and log (0) = 7 find: log b) log c) log () a) ( 0) 9 Find: a) ( ) log b) log 9 c) log 0 7 000 0 Using the approimate values log 7 () = 0 7 and log 7 () = find: log 7 b) log 7 c) log 7 (8) a) ( ) Find: a) ( 7) log b) log c) ( ) log
Using the approimate values log () = and log () = 9 find: a) log ( ) b) ( 0) log c) log ( ) Find: a) log ( ) b) log c) log 8 Given the approimate values log () = and log () = find: a) log ( 0) b) ( ) log c) log Find: a) log 9 (7) b) log () c) log () Given the approimate values log () = 0 and log () = find: a) log (0) b) log () c) log Solving Logarithmic Equations 7 Solve: log 7 ( ) = log 7( + ) 8 Solve: log (7 ) log ( ) = 9 Solve: log ( + ) = log ( ) 0 Solve: log ( + ) + log ( ) = Solve: log ( ) = ( ) log Solve: log ( ) = log ( ) Solve: ( ) + log ( ) 0 log = Conic Sections Sketch the curve given b + = 0 Sketch the curve given b ( ) + 9( + ) = Sketch the curve given b + = 7 Sketch the curve given b = 8 Sketch the curve given b = 9
9 Sketch the curve given b + + 8 + = 0 Evaluating Trigonometric Functions 70 Arrange the following numbers in order from smallest to largest: π cos ( ) ( ) sin log 7 Arrange the following numbers in order from smallest to largest: tan(π ) log ( ) sin ( ) cos( ) 7 Arrange the following numbers in order from smallest to largest: log () ) sin( cos ( ) π 7 Arrange the following numbers in order from smallest to largest: tan( π ) ( π ) sin log cos ( ) ( ) 7 Arrange the following numbers in order from smallest to largest: π cos ( ) sin ( ) log 7 Arrange the following numbers in order from smallest to largest: tan(π) cos() sin() log () 7 Arrange the following numbers in order from smallest to largest: tan(π ) cos ( ) sin ( ) log ( ) Converting Degrees to Radians and vice versa 77 a) Convert to radians: π 8 o π b) Convert to degrees: radians 8 78 a) Convert ( π ) o to radians b) Convert 8 radians to degrees 79 a) Convert to radians: o 0 π π b) Convert to degrees: radians 9 80 a) Convert to radians: o b) Convert to degrees: π radians π 8 a) Convert radians to degrees b) Convert radians to degrees 9 8 a) Convert to radians b) Convert π radians to degrees
Right Triangle Trigonometr Equations 8 Find the eact value of : 9 o 8 For the right triangle shown here, find: a) sin ( < A) b) cos ( < A) c) tan ( < B) C B 7 8 A 8 For the right triangle shown here, find: A a) tan ( < A) b) sin ( < A) 8 Find: a) tan ( < A) C B b) cos ( < B) B C A 87 In the right triangle below, determine an eact value for : 7 o 88 In the right triangle shown here, find: A a) cos(< A) 9 b) tan(< B) C B
Rational Equation Stor Problems 89 A runner competes in a -mile race The ear before her speed was mph slower and it took her one hour longer What was her speed this ear? 90 John s boat travels 7 km/hour in still water He travels km upstream and km downstream in a total time of hours What is the speed of the river? 9 Ernest covers 0 miles on the epresswa, going at a constant rate of speed Steven can cover 0 miles on the epresswa in the same amount of time, going at a speed that is 7 mph faster than Ernest s speed Find the speed of each driver 9 Chris rode his dog sled at a constant speed to Alaska Universit and back home to his igloo The trip was 0 miles each wa and took him a total of hours He drove miles per hour faster coming home than he did going to Alaska Universit Find his speed for each part of the trip 9 A barge moves miles downstream and 8 miles upstream in a total time of hours The current in the river is mph How fast does the barge move in still water? 9 A mile boat race takes place in Detroit ever summer The current in the river is mph What is the speed of the boat in still water, if the total time upstream and downstream is hour? 9 Brandon covers 0 miles on the epresswa in the same amount of time as Shardae can cover 0 miles If Shardae s speed is 7 mph faster than Brandan s speed, find the speed of each driver Polnomial Long Division 9 Divide, clearl stating the quotient and remainder: ( + ) ( + ) 97 Divide, clearl stating the quotient and remainder: ( 8) ( )