3 when n = x Summer Math Packet Moving from Algebra 1 Academic to Advanced Geometry. Name:

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1 01 Summer Math Packet Moving from Algebra 1 Academic to Advanced Geometry Name: This packet provides insight to the topics that were either not covered in Algebra 1, but were covered in Algebra 1 Advanced, or were not covered in as great a depth as the Algebra 1 Advanced. It is your responsibility to complete this packet before the first day of class. Your success in making the move to the Advanced level will be enhanced by achieving an understanding of these topics. These topics may be reviewed in your advanced level course, but they will not be retaught. You are allowed to receive help on the completion of this packet. DO NOT WAIT UNTIL THE LAST MINUTE TO COMPLETE THIS PACKET Evaluate q when q = 6.. 3a 7 when a = 4 3. n 3 when n = when = a when a = 7 6. (a b) 3 when a = 10 and b = 6 Simplify (-1.7) b 4 b Check whether the given number is a solution = 9 3; ; 5

2 Are the following relations functions? Eplain. Then, name the domain and range of each relation. 15. {(,3), (4,-1), (9,0), (,17)} D: R: Solve. 16. You randomly choose an integer from 0 to 9. What are the odds that the integer is 3 or more? 17. You toss three coins. What is the probability P that all are heads? 18. If you are driving at a constant speed of 65 miles per hour, how long will it take you to travel 60 miles? 19. If you save $5 a month, how many months must you save to buy a stereo that costs $5? 0. You invest $500 at a rate of 3%. How long will it take you to earn $60? Solve for the indicated variable. 1. Volume of a cone.. Perimeter of a rectangle. Solve for h: V r h 3 Solve for w: P l w Rewrite the equation so that y is a function of. 3. y y Solve. Be sure to define a variable, set up an equation, and then solve. 5. A store sells 8 ounces of peanut butter for $.4. The store also sells 3 ounces of the same peanut butter for $.40. Which is the better buy?

3 6. A local gym charges nonmembers $8 per day to use the volleyball courts. Members pay a yearly fee of $150 and $ per day to use the volleyball courts. Write and solve an equation to find how many days you must use the volleyball courts to justify becoming a member. Eponential Functions: Use a t-chart! For the following problems. Write each number in standard notation: 7. 8.

4 Simplify and write your answers in scientific notation Evaluate the epressions b 4ac when a 4, b 3, c 1 Solve the equation by finding the square roots Simplify the epression Write the quadratic formula. Solve, if possible, the following quadratic equations using the quadratic formula = Decide how many solutions the equation has. Show how you determined how many solutions there are

5 Find the -intercepts of the following equations. 6. y y 5 Add or Subtract the following: 8. ( 4 3) (3 3 5) 9. ( 3 8) ( 8 4) (4 9) ( 7 5 ) 31. (5 1) ( 3 6 ) Find the Product (41)( 8) 3 3 t (7t t 3) 34. (4)(4 ) 35. (3 5) 36. ( 4 5)( 3) (s 3s 6)(3s 5s 1) Solve the Following. 38. ( 4)( 3) ( 5)( 4)(3 7) ( 9) (416)(3 ) 0 Factor the Following t 10t 1

6 n 7n z 19z v t 18t c c c y y 1y 7 Solve the following by Factoring

7 Find the -intercepts and verte. Sketch the graph. 61. y 1 5 -intercepts: y intercepts: verte: 6. y -intercepts: y intercepts: verte: Solve the following equations if possible (14 8 a ) 9 a 64. 7( b1) 5( b ) ( 8) (3 6) Graph the following equations 66. y y 3

8 Write an equation of the line that passes through the given point and has the given slope. Write the equation in slope-intercept form, point-slope form, and standard form. 68. (4, ), m = 3 Point-Slope Form: Slope-Intercept Form: Standard Form: Write the equation of the line that passes through the given points in point-slope form, slope-intercept form, and standard form. 69. (-5, 3), (3, -5) Point-Slope Form: Slope-Intercept Form: Standard Form: Write an equation of the line for the following lines. Give the equation in slope-intercept form. 70. A line parallel to the line y 3 5, and passes through the point (3, 1). 71. A line perpendicular to y 1 and passes through the point (6, -) 3 7. The variables and y vary directly. Use the given values to write an equation that relates and y. a. 6, y 4 b. 4, y The variables and y vary directly. a. If = 8 when y =, find when y = -3. b. If = 6 when y = -3, find y when = 4.

9 Evaluate the functions. 74. f 1 f ( 1) f () f (6) Determine whether the relation is a function. Eplain your answer Write an inequality that describes the graph shown Solve the inequality and graph its solution or and 9-5 4

10 Solve the absolute value equations Solve and graph the following inequalities: Is each ordered pair a solution to the inequality? y 6 ( 3,1) (,7) Graph the following linear inequality. 90. y y 7

11 Solve the following linear systems by graphing. y y 0 Solve the following linear system using the SUBSTITUTION method. 4y y 17 Use the method of your choice to solve the linear system and tell how many solutions the system has and graph the system. y 10 3y y 5 4 y y 6 6 4y y 3 1 4y 10 Graph the following systems of linear inequalities. y y 4

12 99. Write a system of linear inequalities that defines the shaded region You are buying flowers for your favorite Algebra teacher. You buy a total of 30 flowers that are a miture of roses and daisies for $66. Roses cost $4 and daisies cost $1. How many of each type did you buy? Define Variables: Equation #1: Equation #: Solution to the linear system: Solve. Check for etraneous solutions Solve the percent problem. (You may use your calculator on these.) 103. What number is 95% of 150? is what percent of 30? Solve the proportion. State and etraneous solutions

13 n 1 n n Simplify the epression, if possible. For what values is the epression undefined, if any Simplify the epression (8 16) 35