FOR ALL STUDENTS TAKING ALGEBRA I SUMMER REVIEW PACKET

Transcription

1 FOR ALL STUDENTS TAKING ALGEBRA I - SUMMER REVIEW PACKET

2 Dear Student and Parent/Guardian, The math department at Central Dauphin School District wants ou to be successful in Algebra I. We also want ou to be prepared for PSSA and Kestone Eams. This summer packet is designed to help ou reach these goals b reviewing necessar skills. Be sure to follow the ke information below when completing this packet: The packet is due when ou return to school in August. Ever problem must be completed. None left blank. The packet is worth times a regular homework grade. Work must be shown to receive credit no work, no points. Show the work on the packet pages. Do NOT add additional pages. Final answers must be shown on the answer pages at the back of the packet. A possible Quiz covering the material from the packet ma be given at the end of the first week of school. These topics also tie in with the first few units of Algebra. All topics covered in the packet should be completed without the aid of a calculator. If it is decided to give a Quiz on the summer packet topics, no calculator will be allowed on the Quiz. When ou return in August, ou will have the opportunit to ask questions. Math Help will also be available during the first week. We hope that ou have an enjoable summer and return to school read to be successful in Algebra I! Helpful Websites (a website where ou can subscribe for individual math lessons)

3 ORDER OF OPERATIONS USING INTEGERS A Review on Operations on Integers Addition Problems: Subtraction Problems: negative + negative negative + positive Subtraction is the same as adding the opposite. + ( ) + ( ) ( ) ( ) ( ) + + Multiplication & Division Problems: negative & positive negative & negative ( ) 5 ( ) Remember PEMDAS 5 5 Find the value of the epression ( 7 + 8) 7 + ( 8 ) ( ) parentheses eponents (of the nd number) multiplication/division (left to right) addition/subtraction (left to right). ( ) 5. ( 7). [ ( ) ] + 7. ( ) ( ) [( ) ( 5) ]. 8 ( 5 + ). Let =, =, and z = Evaluate ( ) z +

4 OPERATIONS ON FRACTIONS & MIXED NUMBERS Addition & Subtraction Problems: You must have common denominators before adding or subtracting. Making them improper fractions first is optional (our choice) side work or make them improper fractions 57 5 or Multiplication & Division Problems: You must make mied numbers become improper fractions before multipling or dividing. There s no need to get common denominators or ou can reduce an numerator with an denominator before multipling 8 7 Find the value of each epression. Final answers must be in simplest form (including improper fractions to mied numbers).. 8 or 7 8 or Division = Multipling b the Reciprocal or (of the nd number) 5

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6 VERBAL EXPRESSIONS ADDITION SUBTRACTION MULTIPLICATION DIVISION EXPONENTS Plus Minus Multiplied b Divided b Square of ( nd power) Increased b Decreased b Times Quotient of Cube of ( rd power) More than Fewer than Product Into Power of Sum of Less Twice, One-half, etc. Less than Of (usuall with fractions) Difference of Write an algebraic epression for each verbal epression. The sum of two-fifths a number and eight: n Seven more than twice the difference a number and five: 7 + ( n 5) or ( n 5) + 7. The sum of and a number. The difference of a number cubed and twelve. A number decreased b 8. Three less than 5 times a number 5. One-third the square of b. The product of four and increased b 7. The quotient of a number and negative 5 8. A number to the power of five less seven. Twice the sum of 5 and a number. The quotient of three and the sum of a number and

7 SOLVING EQUATIONS USING INVERSE OPERATIONS Eamples on Solving Equations Using Inverse Operations: h.) + 7 =.) = r 5.) 8w = 8.) 5 = ( 8) ( 8) 5 5 = 58 = r w = h = n 5.) h + = 75.) + = think: ( ) n h = 8 = ( ) ( ) ( ) ( ) h = n = 8 S A D M E P When using inverse operations, go in the inverse order of PEMDAS. (SADMEP) Solve each equation using inverse operations. Final answers must be in simplest form (including improper fractions to mied numbers). No decimals.. =. ( 8 ) =. =. = =. 7 = = 7 8. =. = 8. + = 7 5

8 GRAPHING POINTS ON A COORDINATE PLANE For each equation, use the given -coordinates to complete the table. Then, graph the line. Eample: = + sample work: - - = + = + = + = = + = ( ) + = + = = + = + = + = For each equation, use the given -coordinates to complete the table. Show our work in the spaces provided. Then, graph the ordered pairs and line on the coordinate plane provided on the answer page.. =. = +. = = + 5. =

9 ANSWER PAGES ORDER OF OPERATIONS OPERATIONS ON FRACTIONS USING INTEGERS AND MIXED NUMBERS VERBAL EXPRESSIONS SOLVING EQUATIONS USING INVERSE OPERATIONS GRAPHING POINTS ON A COORDINATE PLANE Continue

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