Algebra Work Sheets. Contents

Transcription

1 The work sheets are grouped accordig to math skill. Each skill is the arraged i a sequece of work sheets that build from simple to complex. Choose the work sheets that best fit the studet s eed ad will brig him up to the desired level. Cotets Work Sheet Title Itroduced Page Simplifyig Equatios 1 Simplifyig Expressios Math 407, Lesso Simplifyig Expressios i the Right Order Math 408, Lesso Simplifyig Expressios With Paretheses Math 408, Lesso Substitutig Numbers for Variables Math 603, Lesso Order of Operatios With Expoets Math 705, Lesso Order of Operatios With Groupig Symbols: Paretheses, Brackets, ad Braces Math 804, Lesso Simplifyig Expressios With Divisio Bars Math 806, Lesso Addig ad Subtractig 8 Combiig Like Itegers Math 503, Lesso Combiig Ulike Itegers Math 503, Lesso Rules for Combiig Itegers Math 606, L.14 & Math 607 L Subtractig Negative Itegers Math 702, Lesso The Subtractio/Negative Sig Math 802, Lesso Multiplicatio ad Divisio Algebra Work Sheets 13 Multiplyig Positive ad Negative Itegers Math 706, Lesso Simplifyig Negative Numbers Math 808, Lesso Dividig With Negative Itegers Math 706, Lesso Additio ad Subtractio Terms Math 609, Lesso Multiplicatio ad Divisio Symbols Math 603, Lesso Multiplicatio ad Divisio Terms Math 610, Lesso Divisibility Rules Math 502, Lesso

2 Cotets, cotiued Work Sheet Title Itroduced Page Writig Equatios 20 Expressios ad Variables Math 407, Lesso Traslatig Words Ito Equatios Math 707, Lesso Choosig Equatios for Problems Math 707, Lesso Equatios Must Balace Math 505, Lesso Solvig Equatios 24 Solvig Equatios Math 506, Lesso Variables o Either Side of a Equatio Math 509, Lesso Multiplyig to Solve Equatios Math 702, Lesso Solvig Two-Step Equatios With Multiplicatio Math 704, Lesso Dividig to Solve Equatios Math 606, Lesso Solvig Two-Step Equatios With Divisio Math 607, Lesso Fractioal Aswers i Two-Step Equatios Math 703, Lesso Simplifyig Before Solvig Equatios Math 704, Lesso Multiplyig Expressios That Iclude Variables Math 703, Lesso Usig the Distributive Property to Solve Equatios Math 707, Lesso Combiig Like Terms Math 606, Lesso Combiig Like Terms to Solve Equatios Math 707, Lesso Simplifyig Expressios With Differig Variables Math 803, Lesso Solvig Equatios With Squared Variables Math 804, Lesso Solvig Equatios With Fractioal Coefficiets Math 807, Lesso Solvig Equatios with Negative Numerical Coefficiets.... Math 807, Lesso Variables o Both Sides of a Simple Equatio Math 808, Lesso Variables o Both Sides of a Complex Equatio Math 809, Lesso Reducig Algebraic Fractios Math 805, Lesso Usig Fractioal Coefficiets to Fid Missig Dimesios of Triagles ad Trapezoids Math 807, Lesso

3 Cotets, cotiued Work Sheet Title Itroduced Page Squares ad Square Roots 44 Squares ad Square Roots Math 409, Lesso Perfect Squares ad Irratioal Square Roots Math 803, Lesso Multiplyig Square Roots Math 808, Lesso Combiig Square Roots Math 809, Lesso Iequalities 48 Graphig Iequalities Math 705, Lesso 2, Solvig Iequalities ad Graphig Solutios Math 705, Lesso Solvig Iequalities: Multiplyig or Dividig by a Negative Number Math 809, Lesso Coordiate Plaes 51 Coordiates o a Grid Math 605, Lesso Poits o a Coordiate Plae Math 708, Lesso Liear Relatios Math 709, Lesso Graphig Liear Equatios Math 710, Lesso Expoets 55 Numbers With Expoets Math 606, Lesso The Expoets 1 ad 0 ad Negative Expoets as Fractios. Math 706, Lesso Negative Expoets as Decimals Math 707, Lesso Multiplyig Variables With Expoets Math 708, Lesso Dividig Variables With Expoets Math 805, Lesso Scietific Notatio 60 Scietific Notatio Math 709, Lesso 12 & Math 710 Lesso Multiplyig Numbers i Scietific Notatio Math 805, Lesso Dividig Numbers i Scietific Notatio Math 806, Lesso Simplifyig After Multiplyig or Dividig i Scietific Notatio Math 807, Lesso

4 Work Sheet 2 Math 408, Lesso 1 Simplifyig Expressios i the Right Order Follow these order of operatio rules whe simplifyig expressios: 1. First, do all the multiplicatio ad divisio from left to right. 2. The, do all the additio ad subtractio from left to right. Simplify each expressio. The first oe is doe for you. 1. a b c a b c a b c a b c

5 10 Work Sheet 10 Math 606, Lesso 14; & Math 607, Lesso 6 Rules for Combiig Itegers Hills ad holes help us to visualize what is happeig whe we combie itegers, but they would be difficult to use for large itegers. Istead, we use rules to help us add positive ad egative itegers. 1. Positive + Positive Add the umbers = 12 Make the aswer positive Negative + Negative Igore the sigs. 4 + ( 3) =? Add the umbers = 7 Make the aswer egative Negative + Positive or Positive + Negative Igore the sigs =? 10 + ( 6) =? Subtract the umbers. 8 5 = = 4 Use the sig of the larger 3 4 umber i the problem. Combie itegers. 1. a. 3 + ( 8) = b = c = 2. a = b. 2 + ( 20) = c. 5 + ( 3) = 3. a = b. 2 + ( 2) = c. 1 + ( 1) = 4. a. 4 + ( 1) = b = c. 5 + ( 2) = 5. a = b. 5 + ( 2) = c. 4 + (8) = 6. a ( 7) = b. 4 + ( 4) = c. 9 + ( 8) = 7. a. 6 + ( 8) = b. 6 + ( 1) = c = 8. a = b. 6 + ( 8) = c. 3 + ( 5) = 9. a = b = c. 4 + ( 8) = 10. a ( 18) = b ( 6) = c ( 6) = 11. a ( 7) = b = c ( 8) =

6 Work Sheet 22, cotiued o ext page Math 707, Lesso 13 Choosig Equatios for Problems To solve the problem of how old is Steve if twice Steve s age decreased by thirtee is fiftee, we must write a equatio. Twice decreased Steve s by 13 is 15 Write equatio age 2a 13 = 15 Solve the equatio a = Steve is 14 years old. a = 14 Traslate ito equatios. The solve ad check. The first oe is doe for you. The quotiet of a umber ad twelve is four. Six more tha a umber is fiftee. Check 1. a. 48 = 4 12 b. 12 = 4 c. d = = 4 Check = 48 For each problem, choose the equatio which ca be used to fid the solutio. Solve it. 2. Twice Carol s height decreased by 4 is 90 iches. How tall is Carol? 90 4 = 2c 2c 4 = c = 90 a. Equatio: b.aswer: 3. The umber of people divided by 3 the icreased by 5 is 13. How may people are there? + 5 = = = a. Equatio: b. Aswer: 22

7 Work Sheet Jesse is 26 years old. The rate he ca ru is 21 mph less tha his age. How fast ca he ru? = r r = = 26 r a. Equatio b. Aswer 4. Six times George s shoe size is 72. What is George s shoe size? = 72 6 = = a. Equatio: b. Aswer: 5. Kara rode her bike 9 km. This was 5 km more tha her fried Ashley rode. How far did Ashley ride? 9 = 5 5 = = + 5 a. Equatio: b. Aswer: 6. Jesse ca ru 5 mph. How may hours will it take him to ru 15 miles? 15 t = 5 5t = t = 5 a. Equatio b. Aswer 7. Jesse hiked 30 miles i 2 days. He hiked twice as far the first day as he did the secod day. How may miles did he hike the secod day? 30 x + 2x = 30 x + x = 30 x = 2 a. Equatio b. Aswer 8. Three times Jeifer s age less 40 is 23. How old is Jeifer? 3j 40 = j = = 3 40 j a. Equatio: b. Aswer: 23

8 Work Sheet 37 Math 804, Lesso 6 Solvig Equatios With Squared Variables To solve a equatio like x 2 = 9, we fid the *square root of both sides of the equatio. Example 1: x 2 = 9 Example 2: x 2 = 19 Not a perfect x 2 square. = 9 x 2 = 19 x = 3 x = 19 Sice 9 i Example 1 is a perfect square, its square root is a whole umber. But 19 i Example 2 is ot a perfect square; therefore, we leave it uder the radical sig. This is as far as we eed to go to solve the equatio uless we are solvig a story problem ad eed a approximate value for the square root. To solve more complicated equatios with a squared variable, follow the usual steps to isolate the variable term o oe side of the equatio, the fid the square roots of both sides. 2x 2 4 = x 2 = x 2 = 100 x 2 = 100 x = 10 Add 4 to both sides. Divide both sides by 2. Simplified. Fid the square root of both sides. Solutio. Solve ad fid the square root. If it is ot a perfect square, leave your aswer uder the radical sig. 1. a. x 2 = 144 b. a 2 = 25 c. y 2 = a. 3x 2 = 75 b. x = 32 c. x 2 15 = *If studet does ot uderstad square root assig worksheet 44.

9 Work Sheet 58 Math 708, Lesso 1 Multiplyig Variables With Expoets A expoet shows how may times the base is used as a factor. 2 meas 3 meas 4 meas Notice what happes whe we multiply the followig: 2 3 is ( ) ( ) which is also 5 To multiply like variables with expoets, you simply add the expoets. Remember that a umber or variable with o expoet is the same thig as a umber or variable with a expoet of 1 ad therefore 2 = 3. Also Remember that multiplyig variables ( = 3 ) is ot the same as addig variables ( + + = 3) Simplify the expressios. Watch the sigs! 1. a. s 3 s 2 b. b 2 b 7 c. m m 4 m 2 d. c c c 2 Sometimes you must multiply a combiatio of variables, costats, ad expoets. Cosider the followig expressios ad the steps used to simplify them. 4a 3 7a (4 7) (a 3 a) 28 a 4 28a 4 Usig the associative property of multiplicatio, metally group the like terms. Fid the product i each group. Write the products together. 2a 2 7b 3 (2 7) (a 2 ) (b 3 ) 14 a 2 b 3 14a 2 b 3 Simplify. The first oe is doe for you. 1. a. 2c 3 c b. 3x y 2 z c. 4s s 2 d. 3a 2 5a 2 2c 4 2. a. 4a b b. 5b 2b c. 3b 2 2 d. 3x 2 9x y 2 3. a. 9x 2x 3 b. 4y 3y y c. 4a 3 3a d. 2x 2 4y 3 4. a b. a 2b 4a 2 c. 5y 2y 3 d. 4x 2 2x 2 61