Review Math for Students Entering Geometry

Transcription

1 Review Math for Students Entering Geometry Solving Equations Write answers in Simplified Radical Form. ( 5) ( ) ( )() = Simplifying Epressions Perform the Indicated Operation ( 4) ( 4) ( y)( 4 y ) y y y 5y ( ) 5. ()( ) Solving Inequalities

2 Simplifying Radicals ( 4) Coordinate Geometry Find the slope of: a. y = +5 b. line passing through (,) and (-,4) c. line parallel to y + = ( + 5) d. line perpendicular to + y = Solving Systems. Find the slope intercept form of each line: a. m, b bm., (,) 4. Find the slope Intercept, Point- Slope and Standard form of: a. line going through (, ) and (-4, ) b. line that is parallel to y = 4( 4) and passes through ( -, ) 5. Solve this system by graphing: + y = 4 y = + 7. By Elimination/Linear Combinations + y = y = 7. By Substitution y 5 y 5 Factoring Factor each problem completely

3 Word Problems Define necessary variables, write equation(s), and solve 4. The length of a rectangle is more than its width. Find its dimensions if its area equals Bill is years older than Ben. In 9 years, Bill will be twice as old as Ben. How old is Ben? 4. The sum of three odd consecutive integers is less than 00. Find the greatest of the three integers. 44. Peter bought ice cream sodas and cakes. Ice cream sodas cost $5 each, while cakes are only $0 each. If Peter spent $5 and only ended up with 0 items, how many ice cream sodas and cakes did he buy? 45. On a table there are 0 coins, some quarters and some dimes. Their value is $.05. How many of each coin are there? EXAMPLES ~ Graph Using a Table of Values Using Intercepts 4. y 47. 4y 8 Using Slope Intercept Form 48. y Tim scored 88, 9, 7, and 80 on 4 of his Algebra tests. He wants his end of the year average to be a 85. What is the lowest score he can receive on his 5 th test? Use the quadratic formula to solve the equation. Simplify radical answers =

4 Solutions a, b 8, c b b 4ac a

5 9. - = = 0 ( - 5)( +) = 0-5 = 0, += 0 = -,.5 = = 5 æ ( 5) ö ç - 5 è 5 ø - 5 = 5 = 5 = 5 ( ) 5 æ ç ö è æ ö = ( 5) ç ø è5ø y y 5y y y y4y y ( ) = (+9)( ) y y 8 7 y

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7 a. m = b. m = 5 c. m = d. y = + y = + m =. a. y = + - b. y = + b - = ( ) + b - = - + b - = b y = +

8 4. A. = = 4 y = + b = + b b = 5 y = y = 5 y = ( ) B. y = 4 + b = -8 + b 9 = b y = y = 9 y = 4( + ) 5. 4 y y 4 y y 4 y 4 m b m, b 4 (, ). y 5 y5 5 y ( 5) (4) 5 y 85 y y (4,)

9 7. 8. y 8 y 7 y 5 y 5 58 (,5) (9 ) ( 4) 4( )( ) ( )( ) 4. w = width w + = length Area = length width ww ( ) 88 w w 88 0 ( w)( w8) 0 w 0 w 8 0 w w 8 Answer: width cannot be negative, so width is 8 and length is 4. Now = Ben s age now y = Bill s age now + = y In 9 years + 9 = Ben s age in 9 years y + 9 = Bill s age in 9 years y + 9 = ( + 9) y 9 8 y 9 (continued on net page)

10 4 (continued). By substitution y (4) 9 y 89 y 7 Answer: Ben is 4 years old now and Bill is 7 years old now 4. = first consecutive odd integer + = nd consecutive odd integer + 4 = rd consecutive odd integer is the greatest integer that is less than so the three integers are,, and 5. (The sum of these three is 99 which is just less than 00) Answer: 5 is the greatest of these three integers 44. Ice cream sodas = ; cakes = y X + y = y = y = y = 5 5y = 85 Y = 7 7 cakes and ice cream sodas

11 45. q = number of quarters d = number of dimes 5q = number of cents in q quarters 0d = number of cents in d dimes qd 0 5q0d 05 (0) q(0) d (0)0 ( )5 q ( )0 d ( )05 0q0d 00 5q0d 05 5q 05 q 7 7 d 0 d Answer: There are 7 quarters and dimes on the table. 4. y = 85 + = = 45 = 94% = 0 b b 4ac a y y 8