Study Guide and Intervention - New Lexington City School ...

1 Study Guide and InterventionVariables and ExpressionsNAME _____ DATE _____ PERIOD _____1-11-1 Glencoe/McGraw-Hill1 Glencoe Algebra 1 Lesson 1-1 Write Mathematical ExpressionsIn the algebraic expression, w, the letters and ware called variables. In algebra, a variable is used to represent unspecified numbersor values. Any letter can be used as a variable. The letters and ware used above becausethey are the first letters of the words lengthand width. In the expression w, and warecalled factors, and the result is called the an algebraic expression for each verbal four more than a number nThe words more thanimply more than a number n4 nThe algebraic expression is 4 each the difference of a number squared and 8 The expression difference ofimplies difference of a number squared and 8n2 8 The algebraic expression is n2 an algebraic expression for each verbal number decreased by number divided by number times a number divided by number multiplied by sum of 9 and a

2 Less than 5 times a the sum of 15 and a the square of more than the product of 6 and a increased by 3 times the square of a numberEvaluate each 3434 3 3 3 3 Use 3 as a factor 4 times. five cubedCubedmeans raised to the third 5 5 5 Use 5 as a factor 3 times. Glencoe/McGraw-Hill2 Glencoe Algebra 1 Write Verbal ExpressionsTranslating algebraic expressions into verbal expressionsis important in a verbal expression for each algebraic 6n2the product of 6 and 12mthe difference of ncubed and twelve times mWrite a verbal expression for each algebraic (n2 1) 32 31 46k3 51 3 Study Guide and Intervention (continued)

3 Variables and ExpressionsNAME _____ DATE _____ PERIOD _____1-11-1 ExercisesExercisesExampleExampleStudy Guide and InterventionOrder of OperationsNAME _____ DATE _____ PERIOD _____1-21-2 Glencoe/McGraw-Hill7 Glencoe Algebra 1 Lesson 1-2 Evaluate Rational ExpressionsNumerical expressions often contain more than oneoperation. To evaluate them, use the rules for order of operations shown 1 Evaluate expressions inside grouping ofStep 2 Evaluate all 3Do all multiplication and/or division from left to 4Do all addition and/or subtraction from left to each 7 2 4 47 2 4 4 7 8 4 Multiply 2 and 4.

4 15 4 Add 7 and 8. 11 Subtract 4 from 3(2) 4(2 6)3(2) 4(2 6) 3(2) 4(8)Add 2 and 6. 6 32 Multiply left toright. 38 Add 6 and each 3[2 (12 3)2]3[2 (12 3)2] 3(2 42)Divide 12 by 3. 3(2 16)Find 4 squared. 3(18)Add 2 and 16. 54 Multiply 3 and Evaluate power in numerator. Add 3 and 8 in the numerator. Evaluate power in denominator. 4811 16 311 42 33 8 42 33 23 42 33 23 42 3 Example1 Example1 Example2 Example2 ExercisesExercisesEvaluate each (8 4) 22.(12 4) 2 8 12 (20 17) 3 3 2 (2 8) 3 22 7 20 [5(3 7 4)] 22 (2 8) 452 3 20(3) 2(3)4(52) 4 3 4(4 5 2)4 32 3 2 3 52 42 8 2 (5 2) 28(2) 4 8 44 32 12 115 60 30 5 Glencoe/McGraw-Hill8 Glencoe Algebra 1 Evaluate Algebraic ExpressionsAlgebraic expressions may contain more than oneoperation.

5 Algebraic expressions can be evaluated if the values of the variables are , replace the variables by their values. Then use the order of operations to calculate thevalue of the resulting numerical x3 5(y 3) if x 2 and y 5(y 3) 23 5(12 3)Replace xwith 2 and ywith 12. 8 5(12 3)Evaluate 23. 8 5(9)Subtract 3 from 12. 8 45 Multiply 5 and 9. 53 Add 8 and solution is each expression if x 2,y 3,z 4,a , and b . y (a b) (2y 3z)10.(10x)2 (z x)2 ax19. 2 y x zz x yx z y 2zy zx z5a2b y25ab y xz(z y)2 xz2 y2 x23xy 4 7xy2 x23 54 5 Study Guide and Intervention (continued)Order of OperationsNAME _____ DATE _____ PERIOD _____1-21-2 ExampleExampleExercisesExercisesStudy Guide and InterventionOpen SentencesNAME _____ DATE _____ PERIOD _____1-31-3 Glencoe/McGraw-Hill13 Glencoe Algebra 1 Lesson 1-3 Solve EquationsA mathematical sentence with one or more variables is called anopen sentence.

6 Open sentences are solvedby finding replacements for the variables thatresult in true sentences. The set of numbers from which replacements for a variable may bechosen is called the replacement set. The set of all replacements for the variable thatresult in true statements is called the solution setfor the variable. A sentence thatcontains an equal sign, , is called an the solutionset of 3a 12 39 if thereplacement set is {6, 7, 8, 9, 10}.Replace ain 3a 12 39 with eachvalue in the replacement (6) 12 39 30 39false3(7) 12 39 33 39false3(8) 12 39 36 39false3(9) 12 39 39 39true3(10) 12 39 42 39falseSince a 9 makes the equation 3a 12 39 true, the solution is solution set is {9}.

7 Solve b. bOriginal equation bAdd in the numerator; subtract in the denominator. solution is .8 98 92(4) 3(3)2(3 1) 3(7 4)2(3 1) 3(7 4)Example1 Example1 Example2 Example2 ExercisesExercisesFind the solution of each equation if the replacement sets are X ,, 1, 2, 3 and Y {2, 4, 6, 8}. 8 2 1 2 5 (x 3) 78.(y 1)2 y 20 Solve each 23 62 62 3213. k14. 3 21 41 215 6 27 2418 3 2 35 81 49 41 41 165 21 21 21 4 Glencoe/McGraw-Hill14 Glencoe Algebra 1 Solve InequalitiesAn open sentence that contains the symbol , , , or is calledan inequality.

8 Inequalities can be solved the same way that equations are the solution set for 3a 8 10 if the replacement set is {4, 5, 6, 7, 8}.Replace ain 3a 8 10 with each value in the replacement (4) 8 ?10 4 10false3(5) 8 ?10 7 10false3(6) 8 ?10 10 10false3(7) 8 ?10 13 10true3(8) 8 ?10 16 10trueSince replacing awith 7 or 8 makes the inequality 3a 8 10 true, the solution set is {7, 8}.Find the solution set for each inequality if the replacement set is X {0, 1, 2, 3, 4, 5, 6, 7}. 2 3 184.

9 15. 26. 4 (8 x) 1 (x 3) 20 Find the solution set for each inequality if the replacement sets are X , , 1, 2, 3, 5, 8 and Y {2, 4, 6, 8, 10} 3 3 3 5113. 414. 215. 1 3 (y 1) 2 821.(6 2x) 2 31 21 42y 5y 4x 21 21 43x 8x 5x 3 Study Guide and Intervention (continued)Open SentencesNAME _____ DATE _____ PERIOD _____1-31-3 ExampleExampleExercisesExercisesStudy Guide and InterventionIdentity and Equality PropertiesNAME _____ DATE _____ PERIOD _____1-41-4 Glencoe/McGraw-Hill19 Glencoe Algebra 1 Lesson 1-4 Identity and Equality PropertiesThe identity and equality properties in the chartbelow can help you solve algebraic equations and evaluate mathematical IdentityFor any number a, a 0 IdentityFor any number a, a 1 Property of 0 For any number a.

10 A 0 Inverse PropertyFor every number , a, b 0, there is exactly one number such that PropertyFor any number a, a PropertyFor any numbers aand b, if a b, then b PropertyFor any numbers a, b, and c, if a band b c, then a PropertyIf a b, then amay be replaced by bin any aa bb aa bName the property used ineach equation. Then find the value of 8n 8 Multiplicative Identity Propertyn 1, since 8 1 3 1 Multiplicative Inverse Propertyn , since 3 11 31 3 Name the propertyused to justify each 4 5 4 Reflexive Propertyb.