Worksheet #1 Fractions

Transcription

1 Worksheet # Fractions " Evaluate each expression and leave your answer in simplest form. ] 7 ] = ] + 8 ] + ] 7 ] ] 7 8] 8 9] 8 0] 9 0 ] ] 9 ] 0 #"

2 Worksheet # Simplifying/Evaluating Expressions Evaluate each expression for the given value of x and/or y. ] x y, =, y= ], x=, y= ( x+ y) x y x ] y y, x =, y = x ] ( x) y, x=, y= Simplify each expression and leave your answer in simplest form. Also, be sure your answer is in standard form. ] ( ) y y + y ] 0x + 0x 0 7] x (x ) ( x) 8] ( 9 x) (0 0 x) 9] ( 8 x) + ( x 9) Let p represent a positive number and n represent a negative number. Determine if the given expressions will be always positive, always negative or sometime positive and sometimes negative. Be prepared to support your decision. 0] np ] ( n) ] ( p) $"

3 Worksheet # Solving Linear Equations Solve the following equations for x. You must show all algebraic steps. Please also include a CHECK of your solution. ] 0 x x = + ] x (x+ ) = x+ ( x ) + ].x+.8=.8( x+ ) ] ( x ) ( x ) = + ] ( ) x = 0 + x ] x = 7 x 7] x x + = 8] ( x ) ( 0 x) = + 9] ( p p+ p ) = ( p ) 0] t = t + %"

4 Worksheet # Solving Literal Equations For each equation below, a) Solve each equation for y in terms of x, showing your work. b) Then evaluate when x =. ] x+ y= ] y+ x = y+ Solve each equation for the indicated variable. ] p=! + w for! ] LA= πrh for h ] V = (!" wh " ) for w ] C = ( F ) for F 7] A= hb ( ) + b for b 9 8] PV = nrt for t 9] " " d = + + I = P + r for P! w h for! 0] ( ) t &"

5 Worksheet # Linear Functions and Inequalities Please DO use a straightedge when graphing. Find the slope of the line passing through the given points. Include your work. ] (, ), ( 8,) ] (,8 ), (,) Find the equation of the line in slope-intercept form (y = mx+ b) using the given information. ] slope =, y int = ] m=, b= 9 ] m=, goes through(, ) ] goesthrough (,7)&(8,) Graph the functions. 7] y = x 8] y = x 9] y= '"

6 Graph the functions. 0] x= ] x+ y= 8 Graph the inequalities. ] y x ] x y> ("

7 Worksheet # Systems of Equations Please DO use a straightedge when graphing. Solve each system of equations by graphing. ] y = x+ y = x + ] x+ y = y = x + ] x y = y = x + Solve the following systems of equations using the substitution method or the elimination method. Remember to write your solution as an ordered pair. CHECK your solution in both original equations. ] y= x+ x+ y= ] 8x y= x y= ] x y= x y= 7] x+ y= x y= )"

8 Worksheet #7 Multiplying Expressions and Factoring Find each product. All answers should be in standard form. ] + ] ( x 8)( x+ 7) ] (x )(x+ ) x( ) ] (d + )(d + 7) ] (7x+ )(7x ) ] ( w ) 7] a+ 8] ( x+ )( x 9) ( ) Factor each quadratic expression. Remember to check for common factors. If the expression cannot be factored, so state. 9] ] x 8 ] + ] x x + ] x + ] 0x 0x+ 00 ] x 0x + + ] x *"

9 Worksheet #8 Factoring and Solving Quadratic Equations Factor each expression. Remember to check for common factors. If the expression cannot be factored, so state. ] x 0x ] x 9 ] ] ] x x ] x + x + x 7] x + 9x x Solve the equation by factoring. Include your algebra and be sure your solutions include statements x =. Checking your solutions is advised. 8] + 70= 0 9] x 0 = x 0] + 8 = 0!+"

10 Solve the equation by factoring. Include your algebra and be sure your solutions include statements x =. Checking your solutions is advised. ] x 7x = ] x 9x = ] 8x + x= ] + 00= 0 ] x = 0 ] + + = 0 7] x x = 0 Use the quadratic formula or completing the square to solve the following equations. 8] + = 0 9] 7= 0 0] + + 7= 0!!"

11 Worksheet #9 Exponents and Simplifying Expressions Simplify each expression. Your answers cannot include negative exponents. If an expression cannot be simplified, state simplified now. ] ] ( n ) ] ( x ) c c 7x ] 9x ] x y ] a a 7] 0 m 8] ( 7a )( a ) 9] n 0] 9 a x x x ] x x ] a ] a b ] b a a+ 7a x ] x x!#"

12 Simplify each expression. Your answers cannot include negative exponents. If an expression cannot be simplified, state simplified now. ] 7] x x 7 8] x ym x y m 8 9] ( x ) 0] x y ] yx y x ] x m ] ( a+ b) ( a+ b) 7 0 ] ( ) ] 7x y x y 0 ] a a!$"

13 Worksheet #0 Simplifying Radical Expressions Simplify each expression, that is, write it in simple radical form. If an expression cannot be simplified, state simplified now. Answers should be rationalized with no radicals in the denominator. ] 08 ] 80 ] ] 00 ] 0 ] 0 7] 8] 9] 0] + ] + 0 ] 8 ] + 0 ] ]!%"

14 Simplify each expression, that is, write it in simple radical form. If an expression cannot be simplified, state simplified now. Answers should be rationalized with no radicals in the denominator. ] 7 7] 8] 9] 7 0] ] + ] 8 ] 0!&"

15 Worksheet # Pythagorean Theorem and Right Triangle Trig Solve for x in each of the following right triangles. Find exact answers. Show work whenever possible. ] ] ] "," &","!+" " %"," " ]," ]," ] &" #+"!$" ##" " "," 7] 8] 9] " $+"!+"," $+"!#"," '+"," 0] ] ] " " " " " " """"""" %&"!#" %&" %&" 0"!'"

16 Using the given right triangle and without a calculator find the following trig ratios. ] Solve for sinθ. ] Solve for tanθ. ] Solve for cosθ. $" (" θ " $" θ " %" """"%"%" &" θ " Using the given right triangle and a calculator find the measure of θ to the nearest hundredth of a degree. ] 7] 8] $ (" θ " $" θ " " %" &" θ "!("

17 WORKSHEET ANSWERS Worksheet # Answers: ] ] 9] 0 0] ] 9 8 ] 0 ] 7 ] ] ] 7 8 ] 8 7] 8] 9 Worksheet # Answers: ] ] ] 0 ] 98 ] y + y ] x x+ 7] x 7 9] 0] always negative ] always negative ] always positive + 8] x 0 Worksheet # Answers: ] 00 0 ] R (all real numbers) ] ] ] ] 7 7] 8] 8 9] (no solution) 0] 7 Worksheet # Answers: p w LA V ] y= ( + x), y= ] y= x, y= 8 ]! = ] h= ] w= πr!"h 9 A PV I ] F = C+ 7] b = b 8] t = 9]! = d w h 0] P= h nr ( + r) t Worksheet # Answers: ] m= ] m= undefined ] y = x+ ] y = x 9 ] y = x ] y= x+ 7 7] y = x 8] y = x!)"

18 Worksheet # Answers (con t): 9] y= 0] x= ] x+ y= 8 ] y x ] x y> Worksheet # Answers: ] (,) ] infinitely many solutions ] (no solution) ] (,7) ] (no solution) ] infinitely many solutions 7], Worksheet #7 Answers: ] x x + 9x ] x x ] x 9 ] 0d + 7d + ] 9x ] w 0w+ 7] a + a+ 9 8] 0x + x 9] ( x )( x ) 0] ( x 9)( x+ 9) ] ( x 9)( x ) ] (x )(x ) ] cannot be factored ] 0( x )( x ) ] ( ) x+ ] (x )(x+ )!*"

19 Worksheet #8 Answers: ] x( x+ ) ] ( x+ )( x ) ] ( x+ )( x+ ) ] ( x 7)( x+ ) ] ( x+ )( x 7) ] x( x+ )( x+ ) 7] x ( x )( x ) ] x= ; x= ] ] x= 7] + 8] x = 7; x = 0 9] x = 0; x = 0 0] x = ; x = 0 x= ; x= ] x=, 8] x= ± 9] x= ; x= ] x= 0, ] x=± ± 0] (no solution) Worksheet #9 Answers: ] c ] n ] 9 8 8x ] x ] x y 0 ] 7] 8] a 9 7a 9] n 0] x 9 x ] ] a ] ] a ] ] 8 x 7] x 8] y x 7 x m 9] 0] x 9y 8 ] x y ] m x ] ( a+ b) ].7 0 ] ] a Worksheet #0 Answers: ] ] ] ] 0 ] ] 0 7] 8] 9] "0] ] simplified now ] ] ] ] 0 ] 80 7] 8] 9] 0] ] + ] 8+ ] + Worksheet # Answers: ] ] ] 7 ] ] ] 7] 8] 9] 0 0] ] ] ] 8 8 ] ] ].0 7] 8]. #+"