Northwest High School s Algebra /Honors Algebra Summer Review Packet 0 DUE Frida, September, 0 Student Name
This packet has been designed to help ou review various mathematical topics that will be necessar for our success in Algebra /Honors Algebra. Instructions: DO ALL PROBLEMS WITHOUT USING A CALCULATOR. Show all work that leads ou to the correct solution. Additional copies of this packet ma be obtained from the Northwest High School website: http://northwesths.net ALL work should be completed and read to be turned in. This packet will count as part of our first quarter grade. Due Date: Frida, September, 0 Deadline: Frida, September 9, 0 If ou have an questions regarding the summer math packet, please call Aimee Conwa at (0) 60-6. ENJOY YOUR SUMMER! WE ARE LOOKING FORWARD TO SEEING YOU IN THE FALL.
Table of Contents. Fractions page. Order of Operations page. Solving Equations page. Table of Powers page. Eponents page 6. Radicals page 6 7. Add, Subtract & Multipl Polnomials page 7 8. Factoring Polnomials page 8 9. Solving Sstems b Substitution page 9 0. Solving Sstems b Elimination page 0. Quadratic Formula page. Graphing Functions page. Honors Algebra page
Fractions To simplif a fraction, divide numerator and denominator b a common factor. 8 6 E.- = 6 To add or subtract fractions, rewrite the fractions using a common denominator, then add or subtract the numerators. 8 E.- = = To multipl fractions, multipl numerator times numerator and denominator times denominator. To divide fractions, multipl b the reciprocal. Simplif answers as needed. 6 6 E.- = = E.- = = = 0 0 6 Simplif the following fractions: 8. =. =. = 0 Perform the following operations and simplif if necessar:. 7 6 =. = 6. = 8 7 7. 9 7 = 8. = 9. = 8 7 0. 8 =. =. = 8 7. 7 =. =. = 9 8 6 6. 6 = 7. = 8. = 8 7
Order of Operations Hints/Guide: The rules for multipling integers are: positive positive = positive negative negative = positive positive negative = negative negative positive = negative The rules for dividing integers are the same as for multipling integers. REMEMBER: Order of Operations (PEMDAS) P parentheses E eponents M/D multipl/divide which comes first A/S add/subtract which comes first Eercises: Solve the following problems. Show all work.. 00 9 8. [ ( 6 ) ]. ( ) 7. 6 8 Use grouping smbols to make the equation true.. 6 8 = 7
Hints/Guide: Solving Equations Equation Solving Procedure:. Multipl on both sides to clear the equation of fractions or decimals.. Distribute.. Collect like terms on each side, if necessar.. Get all terms with variables on one side and all constant terms on the other side.. Multipl or divide to solve for the variable. 6. Check all possible solutions in the original equation. Eample: ( ) 7 = ( ) Distribute. 0 7 = Combine like terms. Simplif. = Move all terms with variables to one side. = Divide to isolate the variable. = Eercises: Solve each equation. Show all work.. ( 6) = t 9 = r. ( ) 6. ( ) 0 = ( 6). a ( a ) = a ( a )
Table of Powers Please complete the following table of powers ecept for the shaded areas. 6 7 8 9 0 0
Eponents Hints/Guide: Rules of Eponents Negative Eponents: Product Rule: a m a m mn Power Rule: ( ) a 0 = a = a n a = n a n m n = a Quotient Rule: a a m n = a mn n a a = a Quotient to a Power: b n n ab = a b Product to a Power: ( ) n n = a b n n Eercises: Simplif using the Rules of Eponents.. 6 6 6.. ( a ) ( a ) 8.. 8 6. ( ) ( ) 7. ( ) 8. ( ) 9. ( a b) 0. ( ) ( ). ( ). ( ) ( ) Epress using a positive eponent... 8
Hints/Guide: Radicals Roots or radicals are the opposite operation of appling eponents; ou can "undo" a power with a radical, and a radical can "undo" a power. For instance, if ou square, ou get, and if ou "take the square root of ", ou get. To simplif a square root, ou "take out" anthing that is a "perfect square"; that is, ou take out front anthing that has two copies of the same factor. E.- = = To simplifing multiplied radicals,we use the fact that the product of two radicals is the same as the radical of the product, and vice versa. ab = a b E.- 6 = = Just as with regular numbers, square roots can be added together. But ou might not be able to simplif the addition all the wa down to one number. Just as "ou can't add apples and oranges", so also ou cannot combine "unlike" radicals. To add radical terms together, the have to have the same radical part. E.- = Eercises: Simplif the radicals.. 9.. 96. 9. 6. 7 7. 7 6 6 8. z Multipl the radicals. 9. 8 0. 6. 6 0... 6 Add or subtract the radicals.. 6. 9 7. 8. 9. 9 0. 8
Addition, Subtraction and Multiplication of Polnomials Hints/Guide: Onl like terms can be added or subtracted. Like terms have the same variables with the same eponents. Onl the coefficients (numbers) are added or subtracted. A subtraction sign in front of the parentheses changes each term in the parentheses to the opposite. Multipl the coefficients and use the rules of eponents for the variables. Remember: FOIL F first O outers I inners L last OR Bo Method Eamples: ) Add the polnomials. ) Subtract the polnomials. ( ) ( ) ( ) ( ) 9 = ( ) 9 = = 7 = ) Multipl the polnomials. ( )( ) ( ) ( ) = 8 = 8 = Eercises: Add, subtract, or multipl the polnomials. Show all work.. ( ) ( ). ( ) ( ) 6. ( ) ( ) 7 6. ( ) ( ) 9 8. ( ) 6. ( ) 6 7. ( )( ) 8. ( )( ) 9. ( )( ) 0. ( )
Factoring Polnomials Hints/Guide: Alwas look for the greatest common factor first. Don t forget to include the variable in the common factor. Factor into two parentheses, if possible. Check our answer b multipling. Eamples: Factor 7 Question: What factor is common to the coefficients of,, 7, and? Answer: Question: What eponent is common to variables of,,, and Answer: 9 = ( ) Factor t t Think: What multiplies to - and adds to? = ( t )( t 8)? Pairs of Factors Sums of Factors -, -, 0 -, 8 -, 6 Eercises: Find the GCF from the lists of factors for each pair of numbers.. :,,,, 6,. 6:,,,, 6, 9,, 8, 6. 8:,,,8 8:,,,, 6, 9, 8 :,,, 6, 9, 8, 7, :,,,, 6, Factor the polnomials. Show all work.... 0. 6. 8 6. 8 7. 8. 8 6 9. 7
Solving Sstems of Equations b Substitution Hints/Guide: Solve one equation for one of the variables with a coefficient of. Substitute what the variable equals into the other equation of the original pair. (The new equation should now have onl one variable.) Solve for that variable. Use that answer to solve for the other variable. Answers are ordered pairs: (, ). Eample: Solve = 6 =. Solve the first equation for : = 6 Substitute our answer above into the second equation: (6 ) = Distribute: 8 6 = Combine like terms: 8 8 = Collect like terms to one side (subtract 8 from both sides): 8 = - Isolate the variable (divide b 8 on both sides): = 7 or 8 7 = = 6 0 = or Substitute the value into an original equation to solve for : 6 The solution to the sstem of equations: 7, Eercises: Solve the sstem of equations using the substitution method. Show all work.. s t = -. = 6 s t = = -. = -6. = = = 7
Solving Sstems of Equations b Elimination Hints/Guide: Answers are ordered pairs (, ). Eliminate one variable b adding the two equations together. Sometimes, one equation must be multiplied b a number to have a variable with the same coefficient and opposite sign. Eamples:. Solve = 8 = 7 = 8 Multipl the equation b - to make the coefficients opposite: - = -7 Add the equations together and solve for : 0 = = Substitute the value of into the original equation: () = 8 Solve the equation for : = 6 = The solution for this sstem: (,). Solve 6 = -6 = 6 = -6 Multipl the second equation b to make the coefficients opposites: 6 = Add the equations together and solve for : 8 0 = 6 = Substitute the value of into the original equation: () 6 = -6 Solve the equation for : 6 = - = - The solution for this sstem: (,-) Eercises: Solve the sstems of equations b elimination. Show all work.. = 0. = 7. = 8. = = 8 = = =
Hints/Guide: Quadratic Formula Assume that the radical etends over the whole epression b ac. Equation must be in the form a b c = 0 (standard form) to begin. Tr to factor first. If ou cannot find factors, then use the quadratic formula. Quadratic Formula b ± = b ac a Eample: Solve = 7 Write the equation in standard form: 7 = 0 Identif a, b, and c for the formula: a =, b = -, c = -7 Substitute into the formula: Simplif: = ( ) ± ( ) ( )( 7) ( ) ± 6 8 = Separate into two solutions: Solutions: =. and =. = and = Eercises: Solve using the quadratic formula. Show all work.. =. = 6 9. 7 = 0
Graphing Functions Use slope (m) and -intercept (b) to graph the following linear equations = m b.. = =. =.. =. = 6. =
7. = 7 6 X - - 0 Y 7 6 6 7 6 7 8. = X - - 0 Y 7 6 7 6 6 7 6 7 9. = 7 6 X - 0 9 Y 7 6 6 7 8 0. = X - 0 Y 7 6 7 6 6 7 6 7
***** Questions through 9 are for Honors Algebra ONLY *****. Line k passes through the point (8, -) and is parallel to the line =. Write an equation for line k.. Line m is perpendicular to = and passes through the origin. What is the equation of line m? 7. Use A = a. A B and B = 6 0 to perform the indicated operations. b. B A c. -A. Simplif the epressions. a. ( ) ( 8) (9 ) b. ( )( ) c. ( )( ) 6 d. e. ( ) f. ( 6) ( ). Factor completel. a. 9 b. 0 c. 0 d. 8 e. f.
6. A car salesman s weekl salar is base amount plus an additional amount for each car sold. The table below shows a person s weekl salar earned for the last three weeks. Cars Sold (C) Weekl Salar (S) $00 9 $000 $00 What is the person s weekl salar when cars are sold? Justif our answer. 7. Sketch a graph of f ( ) =. Then complete the characteristics below. Domain: Range: Ais of Smmetr: Increasing Interval: Decreasing Interval -intercepts: -intercept: Minimum Value: Maimum Value: Verte: Continuous? 8. What can ou sa about the -coordinates of two distinct points on a vertical line? 9. Simplif each of the following using eact answers no decimals. (Leave our answers in radical form.) a. b. 9 c. d. 8 8 e.