Honors Algebra 2 Summer Packet

Transcription

1 Honors Algebra 2 Summer Packet This summer packet is for students entering Honors Algebra 2 for the Fall of The material contained in this packet represents Algebra 1 skills, procedures and concepts that we expect students to know as they enter Honors Algebra 2. Students are expected to complete this packet by the first day of school. We strongly suggest that students not wait until the last minute to do the packet. Completed packets will be collected and graded. The packet is worth 5% of the student s first marking period grade. No credit will be given unless all work is shown. Whereas in past years we have been able to review Algebra 1 content during the first month to month and a half of the school calendar year changes in the New Jersey Common Core Content Standards require us to significantly reduce the time spent reviewing Algebra 1 content in order to adequately cover the required Algebra 2 content as specified by the New Jersey Common Core Standards. Completion of this packet will therefore ensure a smooth transition into new Algebra 2 topics that we need to cover right away. Teachers teaching Honors Algebra 2 will use this summer packet to conduct an abbreviated review of prerequisite Algebra 1 content, followed by an exam on the majority of the prerequisite material within the first two weeks of the school year. That exam will be worth 10% of the first marking period grade. This summer packet is specifically designed to review the following topics: Working with fractions and ratios when performing algebraic operations Solving linear equations and linear inequalities Solving absolute value equations and inequalities Evaluating functions and identifying the key characteristics of functions (e.g. domain and range) Computing slope or rate of change Graphing linear equations given an equation either in slope intercept form or standard form Writing linear equations Graphing linear inequalities in two variables. Solving systems of linear equations Factoring polynomials Operations with Polynomials

2 Part I: Number Sense 1) of Without using a calculator to evaluate Justify your answer., use the information from above to circle the correct value ) John thinks that. Without calculating, explain why John must be wrong. Part II: Evaluating and Simplifying Expressions Directions: Evaluate each expression. Be sure to follow order of operations (PEMDAS). Leave answers as reduced fractions, no decimals! 1) ( ) ( ) ( ) 2) (( ) ) ( ) 3) when x = 3, y = 5 and z = - 4) Only one-third of the student body has failed a class during their high school career. Of those students, twofifths failed more than one class. What fractional part of the entire student body failed more than one class during high school? 5) The equation y = - x 2 +9x + 10 models the flight of a projectile where y is the height of the projectile in meters x seconds after launch. Determine the height after: a) 1 second b) 3 seconds c) 10 seconds

3 6) Simplify the following expressions a) ( ) b) Part III: Solving Linear Equations Solve each equation. 1) 4x + 2(3x-1) = 16x 10(x+5) 2) 2n + 6 = ( ) 3) Create a linear equation which has infinitely many solutions 4) a. The perimeter of a rectangle is 64. The length of the rectangle is 8x +2 units. The width of the rectangle is 2x units. Write an equation, in terms of x, for the perimeter of the rectangle. Then find the value of x. b. Mr. Ring started with 95 updates on Facebook. Every day he gets 43 more. Write an equation that models the number of updates, U, Mr. Ring will have t days from the start of his updates. Then find out how many updates Mr. Ring will have after 23 days. 5) Solve the following equation for the specific variable ( ) = c, for b

4 6) A spherical satellite is placed in orbit around the Earth. Its volume is 270 cubic feet. Determine the radius of the satellite. (HINT: Volume of a sphere ) Part IV: Functions 1) Determine whether each relation below is a function. State your reasoning. 2) Create a relation that is a function that has four coordinate points and all x- coordinates are negative. 3) Determine whether each graph is a function. State your reasoning. a) b) 4) Write a function rule for each table of values

5 5) State the domain and range of the function that is graphed below Domain: Range: 6) Your cap size is based on your head circumference (in inches). For head circumferences from inches cap sizes can be modeled as a function of head circumference, c, by this equation: size with the given head circumference.. Where s is the cap a) Identify the domain and range of the function. b) If you wear a size 7 cap, what is your head circumference?

6 Miles Traveled Part V: Slopes and Linear Equations ) The following graph depicts a race car driver s road trip to Washington DC from home on Sunday (solid line) and his drive from Washington DC back home the following Friday (dashed line). Use the graphs to answer the following questions Distance Traveled On Vacation to and From Washington DC a) Which ride was faster, the one to Washington DC or the ride back home? How did you come to this conclusion? b) Estimate the average speed during the first two hours of his drive to Washington DC c) Estimate the average speed during the last two hours of his drive back home (Make answer positive) d) He took one break on each trip. Which break lasted longer, and by how much? 2) Circle all equations below that have the same slope ) ) ) ) ( ) ( )

7 3) A scuba diver is 30 feet below the surface of the water 10 seconds after he entered the water and 100 feet below the surface after 40 seconds. What is the scuba divers rate of change? 4) Write an equation in slope-intercept form that (Slope Intercept Form y = mx + b) a) passes through the point ( - 1, 8 ) and has a slope of 5 b) passes through the point ( 2, 3 ) and is perpendicular to the line y = 2x 3 (HINT: slopes of perpendicular lines are opposite reciprocals) c) is parallel to the line 4x +8y = 32 5) You have two suitcases to bring on an airplane. The weight of the large suitcase is L pounds, while the weight of the small suitcase is S pounds. The airline will only allow the two pieces of baggage if their combined weight is equal to 128 pounds. a) Write an equation to model this situation b) If you do not bring a small suitcase, what is the maximum weight of your large suitcase? c) If your large suitcase weighs 75 lbs, what is the maximum weight of your small suitcase?

8 6) Graph each linear equation below (You must show at least two points on the line). Then, write an equation that is parallel to each line and graph them with their respective parallel line. a) 4x + 2y = 12 b) y = 7) Write and Graph a vertical line and a horizontal line. Are these lines perpendicular? Explain your reasoning 8) Solve each linear system. Choose your method to solve. a) 3x + 3y = 6 b) y 3x = 10 2x - 8y = 14 4x +2y = - 30

9 c) A woman owns 21 pets. Each of her pets is either a cat or a bird. If the pets have a total of 76 legs, and assuming that none of the bird's legs are protruding from any of the cats' jaws, how many cats and how many birds does the woman own? Part VI: Inequalities 1) Graph the following linear inequality. Shade the solution set. Will the boundary line (line that separates the solution set from the non-solutions) be part of the solution for the inequality above? Explain your reasoning. Describe two different ways you can determine whether (- 4, 3) is a solution to the inequality above. 2) Solve each inequality and graph on a number line a) ( )

10 B and C are compound inequalities For help, look to the guided solutions b) 15 c) 3x + 5 < - 4 or 2x 1 > 3 d) The velocity of an object fired directly upward is given by V = 80 32t, where t is in seconds. When will the velocity be between 32 and 64 feet per second? Sketch your solution on a number line. Part VII: Absolute Value 1) Solve each equation: a) b) 2) A thermometer comes with a guarantee that the stated temperature differs from the actual temperature by no more than 1.5 degrees Fahrenheit. Write and solve an equation to find the minimum and maximum actual temperatures when the thermometer states the temperature is 87.4 degrees Fahrenheit.

11 Solve each inequality. Graph your solution on a number line. 3) 4) Part VIII: Factoring Expressions Factor each expression completely 1) 2) 3) 4) 5) 6) Part IX: Operations with Polynomials Simplify each expression completely. The simplified expression should be written in standard form. 1) 2) ( ) ( ) ( ) 3) ( )( ) 4) ( )( )