01 Algebra I Summer Math Packet DHondtT Grosse Pointe Public Schools 5/0/01
Evaluate the power. 1.. 4. when = Write algebraic epressions and algebraic equations. Use as the variable. 4. 5. 6. the quotient of a number and 10 less a number twice a number m plus is 1 41 Use the order of operations to evaluate the following. 7. 8. 55 10 + 4 9 + 15 ( + ) 9. 7(14 )+15 Evaluate each epression. 10. 4t(n + v ) if v = 4, n = 6, and t = 8 11. ab 8b if a 4 and b 1 Use the formula d=rt to solve the following word problems. 1. 1. Kateln drove 6 mph for ½ hrs. And drove 10 miles at 50 mph. How far did she drive? How man hours did he drive?
Graph the function using a table given the domain. 14. 15. = + 5 Domain: 0, 1,, = Domain: 0,, 4, 6 Domain Range Domain Range Find the sum or difference without using a calculator! 16. 17. 18. 1 + 7 7 + ( 9) 5 ( 6) 19. 1 7 10 Find the product or quotient without using a calculator! 0. 1.. 61 4 5 9 4. 4 9 Use the distributive propert to write an equivalent epression. 4. 5. 6. ( + 5) ( + )6 ( 1) Simplif the epression. 7. 8 + ( 1) 8. + 6 + 1 9. ( + 4) + 7
Solve the following equations. Show our steps! 0. 1. 6 10 14. 8 10. 10 4. 1 15 5. 8 6. 6 5 4 7. 14 (4 5) 8. 1 Solve each of the following proportions. No decimal answers. 9. 40. 41. 4 6 1 a 5 7 w 8 4 5 4. Solve using a proportion. A map has a scale of 1 in.: 8 ft. Use the given map distance to find the actual distance: 5.5 in.
Give the coordinates of the points labeled A, B, C, and D. 4. A = B = C = D = 44. A = B = C = D = Graph the function with the given domain. Then identif the range of the function. 45. = + 4; domain:, 1, 0, 1, Plot the points and draw a line through them. Without calculating, tell whether the slope of the line is positive, negative, zero, or undefined (no slope). 46. (, ) and (7, 1) 47. ( 4, 5) and (, ) 48. ( 7, 1) and ( 7, 8)
Write the inequalit that is represented b each graph. 49. 50. Write the verbal sentence as an inequalit. Then graph the inequalit. 51. 5. A number is greater than or equal to 8. An infant car seat is designed for babies and toddlers weighing less than 40 pounds Solve the inequalit b adding or subtracting. Graph our solution. 5. 54. a + > 8 4 < 8 55. m > 0 (Remember what happens here?) 56. 1 4c <
Here are some other important topics from Algebra I that ou need for Geometr: SOLVING A SYSTEM OF EQUATIONS Here is an EXAMPLE to help ou remember: 6 1 5 Now that ou know, ou can just plug into either equation to find the value of. 5 SOLUTION: (, ) Solve using the ELIMINATION method. Solutions must be written as an ordered pair, no solution Ø, or infinite solutions! 57. 14 1 58. 19 9 5 ***MULTIPLYING BINOMIALS FOIL*** FOIL- Multipl the FIRST terms, then the OUTER terms, then INNER, and finish with the LAST terms of each grouping. Combine all like terms for our final answer. Here is an EXAMPLE: 6 1 6
Find each product using FOIL. 60. 59. 1 61. 4 5 7 ***FACTORING*** FACTORING- For factoring, ou break up a polnomial into factors or parts, which is the opposite of multipling like FOIL. There are man tpes of factoring so let s separate them into tpes. GCF-Greatest Common Factor Pulling out (dividing b) a GCF is the opposite of distributing. Take out the GCF and then write what is left in parentheses. Here is an EXAMPLE: 1 4 Factor using the GCF. 6. 6 a a 6. a 8a 64. 8 6 Here is an EXAMPLE: Difference of Two Squares 6 6 6 Factor the following. 65. 16 66. 4 5 67. 16 5
Trinomials When ou factor a trinomial, make sure ou find numbers that multipl to the last term and add to the middle term. Watch our signs! FOIL our answer to check! Here are two EXAMPLES: c 8c 1 c 6c 4 7 7 1 Factor the following trinomials. 68. 69. 10 1 18 81 70. 5 ***SOLVING QUADRATICS*** Solving Quadratic Equations b Factoring STEPS for solving a quadratic equation, a b c 0, b factoring: 1. Get the equation equal to zero. Factor. Set each factor or part equal to zero 4. Solve each equation algebraicall to get the two solutions. Here is an EXAMPLE: 5 0 5 15 0 5 0 0 Solve b factoring. 71. (This one is alread factored!) 0 7. 6 0 7. 1 0
Here some formulas ou need to know for Geometr. Distance Formula: Use the distance formula when ou want to find the length of a line segment or the distance between ordered pairs. D 1 1 Use the Distance formula to find the distance between the two points. Round to tenths place. 74. 75. (9, 7) and (1, 1) (5, ) and (8, ) Midpoint Formula: Use the midpoint formula when ou want to find the midpoint of a line segment with the specified endpoints. Write our answer as an ordered pair. Midpoint 1 1 Use the Midpoint formula to find the midpoint between the two points. Write answer as (, ) 76. 77. (, 4) and (6, 8) (, 6) and (8, 6), Pthagorean Theorem: Use the Pthagorean Theorem to find a missing side of a right triangle a b c c a b
Find the length of the missing side of each right triangle. Round to tenths place. 78. 79. 80. 15 8 60 61 11 6 Last but not least. Here are some of the terms that ou will learn in Geometr. See which ones ou alread know! Write the correct term net to its definition. 1. Like a dot:. Straight and goes forever in two directions:. Starts at a point and goes forever in one direction: 4. Straight with two endpoints a piece of a line: 5. Flat and goes forever in all directions: 6. Two lines intersect in a 7. Two planes intersect in a 8. An angle that measures 90is a angle 9. An angle that measures 180is a angle 10. Angle that measures less than 90 11. Angle that measures more than 90 Have a fun and safe summer and be prepared and read when school starts!