Algebra Intermediate Benchmark 1
Algebra Intermediate Benchmark 1
Algebra Intermediate Benchmark 1
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OUESD <strong>Algebra</strong> <strong>Intermediate</strong><strong>Benchmark</strong> 1 Study Guide9Find each root.9Find each root.a.36100b. − 144a.425b. − 49a. b.====361003610061025=− 144=−1210The sum of the measures of two angles is180 o . One angle measures 3a , and the otherangle measures 3a − 25 . Find a . Then findthe measure of each angle.3a+ 2a− 25 = 1805a− 25 = 1805a− 25 + 25 = 180 + 255a205=5 5a = 4110The Drama club sold 120 child tickets and 80adult tickets to a play. A child ticket cost $3less than an adult ticket. The club collected atotal of $640 from ticket sales. What is thecost of and an adult ticket? a child ticket?1 st Angle: 2 nd Angle:3a = 3( 41)2a − 25 = 2( 41)−25= 82 −25o= 123o= 57∴ a= 41, 3a= 123 o , 2a− 25 = 57oPage 4 of 9 MDC@ACOE (NEBMC) 09/07/11
OUESD <strong>Algebra</strong> <strong>Intermediate</strong><strong>Benchmark</strong> 1 Study Guide11Solve the proportion.w 5 =6 211Solve the proportion.3x 3 =25 5Method 1: Cross Productsw 5=6 22⋅ w = 5⋅62w30=2 2w = 15Method 2: LCDMethod 1: Cross ProductsMethod 2: LCDw 5=6 2w 5⎛3⎞= ⎜ ⎟6 2⎝3⎠w 15=6 6∴ w = 1512a What percent of 90 is 36?Method 1:x • 90 = 3690x = 3690x90 = 3690x =2 i2i 3i 32 i5i 3i 312aWhat percent of 40 is 24?Method 1:x = 2 5x = 40%∴ 40% of 90 is 36.Page 5 of 9 MDC@ACOE (NEBMC) 09/07/11
OUESD <strong>Algebra</strong> <strong>Intermediate</strong>12b What percent of 90 is 36?Method 2:percent!100!x100 = 369090x = 36 10090x9090x90! part!whole( )( )36 100=90=4i 9 i10 i109 i10x = 40∴ 40% of 90 is 36.12b<strong>Benchmark</strong> 1 Study GuideWhat percent of 40 is 24?Method 2:12c What percent of 90 is 36?Method 3:10 20 30 40 50 60 70 80 90 100 %9 9 9 9 9 9 9 9 9 9 =9012cWhat percent of 40 is 24?Method 3:3640%∴ 40% of 90 is 36.Page 6 of 9 MDC@ACOE (NEBMC) 09/07/11
OUESD <strong>Algebra</strong> <strong>Intermediate</strong>ANSWER KEY1. Simplify:( )25 − 10 + 17 ÷ 3=1225 − 27 ÷ 3=125 − 27 ÷ 9=125−3=122=121=6110 −x 5 − y for x= 2 and y=22. Evaluate: ( )⎛ 1 ⎞= 10 −( 2)⎜5 − ⎟⎝ 2 ⎠⎛10 1 ⎞= 10 −( 2)⎜ − ⎟⎝ 2 2⎠⎛2⎞⎛9⎞= 10 − ⎜ ⎟⎜ ⎟⎝1⎠⎝2⎠18= 10 −2= 10 −9= 13. Simplify: − 4( x + 9)Method 1 Method 2( x )=− 4 + 9=−4⋅ x +−4⋅9=−4x−36( x )( x ) ( x ) ( x ) ( x )=− 4 + 9=− 1 + 9 − 1 + 9 − 1 + 9 − 1 + 9=−x−9−x−9−x−9−x−9=−4x−36<strong>Benchmark</strong> 1 Study Guide4. Find the absolute value.a. 6.4 =6.4b. −− 12 = − 12Solvec.5. Solve:x − 3=5x − 3+ 3= 5+3x = 812 =−4 −62 x − 3 = 101 1⋅2 x − 3 = ⋅102 2x − 3 = 5( x )x ( )( )12 =−4⋅ − −4 612 =− 4x+ 2412 − 24 =− 4x+ 24 −24−12 −4x=−4 −43 = x∴ x = 36. Solve for r C = 2πrC 2πr=2π2πC= r2πC∴ r =2πx − 3=−5x − 3+ 3=− 5+3x =−2Page 7 of 9 MDC@ACOE (NEBMC) 09/07/11
OUESD <strong>Algebra</strong> <strong>Intermediate</strong>7. The quotient of n and − 8 is − 4. What is thevalue of n ?n=−4−8n−8⋅=−4⋅−8−8n = 32−3 and − 348. Simplify ( ) 4( )− =− ⋅ ⋅ ⋅43 1 3 3 3 3=−814( − 3) = ( −3)( −3)( −3)( −3)= 9 ⋅ 9= 819. Find each root.10.a = adult ticketa − 3 = child ticket( a )<strong>Benchmark</strong> 1 Study Guide120 − 3 + 80a=640120a− 360 + 80a=640200a− 360 = 640200a− 360 + 360 = 640 + 360200a1000=200 200a = 5∴ adult ticket a = $5( )( a )child ticket − 3 = $211. Solve the proportion.3x 3 =25 5Method 1: Cross Productsa. b.===42542525=− 49=−73x3=25 53x5 3 25( ) = ( )15x75=15 15x = 5Method 2: LCD3x3=25 53x3⎛5⎞= ⎜ ⎟25 5 ⎝5⎠3x15=25 25Therefore3x15=3 3x = 5Page 8 of 9 MDC@ACOE (NEBMC) 09/07/11
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