South Brunswick Schools

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1 South Brunswick Schools Summer Packet For Rising Honors Algebra students Directions: All students entering Honors Algebra are expected to be proficient in all their previously-learned algebra and geometry skills. The following exercises are intended to provide a review of the Algebra skills needed to be successful in Algebra Honors. Show all work even for multiple choice problems! If you need assistance with any topics, please refer to the following websites: In addition, summer math help will be provided by honor society students during the summer. Please see the summer assignment description for dates and times. Answers to the exercises are provided on the last page however, you must show all work to receive full credit. We highly recommend that students use a graphing calculator for success in mathematics. While our math classrooms are equipped with graphing calculators for students to use during class, students are encouraged to purchase their own graphing calculator for use at home. If you choose to purchase one, we recommend the TI-8+ or TI-8 for Advanced Algebra and the TI-89 for Honors Algebra. Because these calculators are costly, students should permanently mark the calculator with their name and keep them in a safe place if they bring them to school. These calculators can be used for all four years of high school mathematics as well as for other standardized tests such as the SAT so they are a worthwhile investment. *** Note: THIS PACKET SHOULD BE COMPLETED FOR TURN-IN ON THE FIRST DAY OF CLASS. YOU WILL TAKE A SKILLS QUIZ, BASED ON THIS PACKET, ON YOUR rd DAY OF CLASS

2 6 ) What is the value of 8 ( b) 7)? c) 8 d) e) ) Halie s bedroom is a square measuring 0 feet along the base of each wall and 0 feet high. Which expression is used to calculate the square footage needed to wallpaper her room? 0 b) 0 c) (0 ) d) 0 e) (*0) ) The volume of a cylinder is given by V r h, where r is the radius, h is the height, and is approximately.. What is the volume of the cylinder in terms of x? d) 9.x b) 8.6x e) 8.6x c) 887.x 9.x ) Evaluate ( )( )( ). 0 b) c) d) 0 e) ( x y) ) Simplify xy 9x 8y x y xy b). 0 x y c) 9 xy d) 9 xy e) 9xy 6) You want to fence in a pool and deck area. Find the expression which correctly determines the amount of fencing required to complete the job.

3 c) e) x x b) 0x x 0 d) 0x 8x 0 0x 6 x x 6x 0 7) The area of a rectangle is given by x x. One side has length x. Find the length of the other side. 8) The length of a box is inches less than twice the width. The height is inches more than three times the width. The box has a volume of 0 cubic inches. Which of the following equations can be used to find the height of the box? w(l-)(h+)=0 b) w(w-)(w+)=0 c) w(w+)(w-)=0 d) w(w-)(hw-)=0 e) w(-w)(h+)=0 9) Factor completely, if possible, the following expressions: a. m 7m 0 b. 0y 9y 6 c. d. 0k w w w 0) Which one of the following is the simplified form of b) 0 8? c) 6 d) 6 e)

4 ) Simplify the expression b) 8 c) 0 d) 8 e) 0 ) The area of a rectangle is. If the length of one side is, what is the length of the other side? 7 b) 7 7 c) d) 7 e) 7 ) Find the area of the triangle. Give the answer as a simplified radical. ) You are at an altitude of 00 feet in a hot-air balloon. You turn on the burner and rise at a rate of feet per minute for 6 minutes. Write an equation for your altitude as a function of time (define all variables). Input Output b) Make an input-output table for the function. ) Which equation would best fit the given graph?

5 9 9 y x b) y x c) 6 y x d) y x e) y x i. 6) Use the graph to determine the zeros of the equation of the graph. and b) and c) and d) and e) and 7) Adding and Subtracting Polynomials Simplify each expression. (x + x ) + (x 8x 9) i. b) (x 7x ) (x + x ) c) (x + ) + (x ) d) (x ) 7(x ) 8) Lake Braddock High School Band is selling sub sandwiches for a fundraiser. It costs $. to make each sandwich. They sell them for $.0 each. Write a function that determines the profit from the sale (identify all variables). b) The band must pay a $7 fee to use the cafeteria to assemble the sandwiches. Write a function that includes this cost. c) The band wants a $000 profit. How many sandwiches must they sell? d) If they sell 80 sandwiches, what was the profit earned?

6 9) Solve the equation 0 x ( x) (x 8). b) c) d) e) 0) Rewrite the equation y ( x ) y ( x 6) so that y is a function of x. y x 0 b) y x 0 c) x y d) y x 0 e) x y ) The relationship between the sale price S, the list price L, and the discount rate r is given by S L rl. Solve for r in the above formula. b) Solve for L in the above formula. ) Describe the solution to the inequality x 6. All real numbers greater than or equal to -0. b) All real numbers greater than or equal to 0. c) All real numbers less than or equal to -0. d) All real numbers less than or equal to -. e) All real numbers greater than or equal to -. ) Solve the equation or inequality. When appropriate, round answers to the nearest thousandth. ( 8 b ) ( b ) b).x.9.07(.0.7 x )

7 ) Your cell phone company charges $9.9 per month and gives you 0 free minutes per month. Additional minutes cost $. per minute. Your last bill came to $6.8. Let x represent the number of minutes you talked last month. Write an equation that models this situation. b) Approximately how many minutes did you use the phone? Round to the nearest thousandth. c) How many minutes did you have to pay extra money for? ) What is the equation of the horizontal line that passes through point (, -8)? y b) x c) y 8 d) x 8 e) y 0 6) Choose the inequality whose solution is shown in the graph. y x b) y x c) y x d) y x e) y x 7) What is the x-intercept of the line x y? 0 0 b) c) 00 d) 0 e) 0 8) What is the equation, in slope-intercept form, of the line shown?. x y 0 b) y x c) y x d) x y 0 e) y x

8 9) Find the value of y so that the line passing through (, 6) and (, y) has a slope of. b) 9 c) 7 9 d) e) 0) What is the slope of the graph of x y? b) c) d) e) ) What is an equation of the line that passes through points (, ) and (-, )? y x b) y x c) y x d) y x e) y x ) What is an equation of the line that is parallel to y x and has an x-intercept of -? y x b) y x c) y x d) y x e) y x ) A line passes through the points (-, ) and (-7, -). Write an equation of the line in standard form. b) Write an equation of the line in slope-intercept form. c) Write an equation of the line in point-slope form. ) What is the standard form of an equation of the vertical line in the graph? y b) x c) y d) x e) y

9 ) Which point represents the solution of the system of equations? y y x x (0, -) b) (0, -) c) (/, -/) d) (, ) e) (/, -7/) 6) If x y 8 and x y, then x y? 6 b) 8 c) 7 d) e) 7) Two hunters start from different points in the woods and hike towards their campsite. The first hunter travels a trail along the line y x. The second hunter s trail follows the line y x 8. They meet at the campsite. What are the coordinates of the site? (-08/7, 0/7) b) (-0/7, 08,/7) c) (-, ) d) (-, ) e) (-0/7, 8/7) 8) You are selling tickets for a high school play. Student tickets cost $ and general admission tickets cost $6. You sell tickets and collect $876. Write a system of equations that models this situation (identify all variables). b) How many of each type of ticket did you sell? 9) Which of the following quadratic equations is represented by the graph? y x x b) y x x c) y x x d) y x x e) y x x

10 0) Which of the following is a solution of 7 b) c) 7 d) 7 e) 7 7x x 8 0? ) Multiplying Polynomials Simplify. x(x x + 7) b) (x )(x +7) c) (x )(x + ) d) (7x )(x + x - )

11 Algebra Advanced/Honors Summer Packet Answers ) b ) c ) d ) c ) e 6) b 7) x 8) b 9) (m - 0)(m + ) b) (y +)(y +) c) (k-)(k+) d) 7w (w )(w + ) 0) a ) d ) e ) 6 7 ) y x 00 where y represents altitude (in feet) and x represents time (in minutes) b) Input Output ) a 6) d 7) 8x 6x 0 b) x 8x c) x d) 8x 8) y.x b) y.x 7 c) 860 sandwiches d) $90 9) b 0) d L S ) r L S b) L r ) a ) b b) 0.08 ) y = (x 0) b) 8.79 minutes c).79 minutes ) c 6) b 7) e 8) c 9) e 0) c ) d ) e ) x y b) y x c) y = /(X + ) or Y + = /(x + 7) ) b ) e 6) e 7) a 8) x represents the number of student tickets, y represents the number of general tickets x 6y 876 x y b) 7 student tickets and 88 general tickets 9) d 0) a ) 0x 6x x b) x 6x 7 c) x d) 7x 9x x 0