Honors Algebra

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1 Honors Algebra Honors Algebra is a rigorous course that requires the use of Algebra skills. The summer work is designed to maintain and reinforce these prerequisite skills so as to prepare ou for the upcoming school ear. If ou need help with a topic, use the online Algebra tetbook as a resource (the link is on our Google Classroom). Complete the summer packet in pencil onl Show all necessar work Due on the first da of class A test on the summer packet will be given on the first da of class Please join Google Classroom using the code skgnr5 Google Classroom will be used for future postings and information throughout the summer. For the school ear, ou will be required to bring the following supplies to class ever da TI-84 Plus or TI-84 CE graphing calculator inch -ring binder with 8 dividers Red pen Mechanical pencils Loose leaf paper Colored pencils

2 Honors Algebra Summer Packet Name Pencil onl! Show all necessar work to receive credit. Due: First da of class. Chapter : Solving Linear Equations ) 6a 0 a 7 ) a ) 5w 4 7w ) w 4 c ) c ) 4 5c 5 p 4) p 4) 4 4 4p 47 p 7 e 5) e 5 5 5) 6 e 0 7 ) Solve: 4 9 Solving Proportions ) = ) Solve: 4 ) =

3 Determine if each equation has no solution or an infinite number of solutions. ) 4 ) m ) ) 6 4 4m m 9 Rewriting Equations and Formulas t M P. 0 ) The formula above gives the amount of mone M earned after P dollars is invested for t ears. Which of the following gives P in terms of M and t? P M. 0 B) A) t P M C) P M. 0 t D) P M. 0 t. 0 t a, t ) The speed of a sound wave in air depends on the air temperature. The formula above shows the relationship between a, the speed of a sound wave, in feet per second, and t, the air temperature, in degrees Fahrenheit. Which of the following epresses the air temperature in terms of the speed of a sound wave? A) a 05, t B). 08 a 05, t C) , a t D). 08 t. 08 a 05, A B C ) The equation above represent the standard form of a line. Which of the following epresses in terms of A, B, C, and? A) C A B B) C A C) B C B D) A C A B

4 Write an inequalit that represents the graph. Chapter : Solving and Graphing Inequalities ) ) Solve each inequalit. ) 4 ) 4) ) What is the solution to the inequalit 5? A) 7 B) 7 C) 8 D) 8 Determine if each inequalit has no solution or an infinite number of solutions. ) ) ) )

5 Compound Inequalities Graph the compound inequalit. ) or 4 ) Choose the compound inequalit represented b the graph. ) 4) A) 0 A) or B) 0 B) or C) 0 C) D) 0 or D) Solve the compound inequalit and graph the solution. 5) or 6) 6 5

6 Chapter : Graphing Linear Equations Give the slope of each line. ) m = ) m = ) m = 4) m = 5a) What is the -intercept of the graph of the equation 6 6? A) B) C) D) 6 5b) What is the -intercept of the graph of the equation 6 6? A) B) C) D) 6 6) What is the -intercept of the line with equation 6? 6) 7) Find the slope of the line passing through the given points. a) 4, and 6 b), 4 and 4,4 c), 4 and 7 d) 6, and 8, a) b), c) 6, d) 8) Which of the following is the slope-intercept form of 4 8? A) 4 4 B) C) D) 4 4

7 Graph each line using the slope and -intercept. 9) 4 0) 5 slope -int slope -int Graph each horizontal or vertical line. ) ) ) The total amount of water, w, in gallons, left in a tank can be modeled b the equation w 00 5t, where t is the number of hours since the tank started leaking. Which of the following is the best interpretation of the number 5 in the equation? A) The tank is empt after 5 hours B) The tank loses 5 gallons of water each hour C) The tank continues to lose water until 5 gallons are left D) Each hour, the tank loses 5 less gallons of water than it did in the previous hour a 8t 5 4) A bank customer made an initial deposit into a savings account, and then deposited a fied amount each week into the account. The equation above models the amount, a, in dollars after t weeks. What was the dollar amount of the initial deposit? $

8 Chapter 4: Writing Linear Equations Write the equation of each line in slope-intercept form. ) ) Write the equation of each line. ) 4) Write the slope-intercept form of the equation with the given characteristics. 5) slope = 4 ; passes through (0, ) 5) 6) What is the equation of the line that has a slope of 4 and passes through the point (, -0)? A) 4 B) 4 C) 4 4 D) 4 4 Write the slope-intercept form of the equation with the given characteristics. 7) passes through (, ) and (, -5) 7) 8) parallel to 5 ; passes through (-4, 6) 8)

9 9) perpendicular to 8 ; passes through (0, 6) 9) 0) a horizontal line that passes through (, -5) 0) ) The table below shows the distance covered b a spaceship in ) outer space. Write an equation in slope-intercept form that represents the distance traveled as a function of time. ) Which point-slope equation represents a line that passes through (5, -) with slope 6? A) 5 6 B) 5 6 C) 6 5 D) 6 5 ) Rewrite the equation below in standard form A B C ) 4 (A, B, and C are integers and A > 0)

10 Chapter 5: Solving Sstems of Equations ) Give the (, ) solution to the sstem graphed below. ) ) Find the (, ) solution to the sstem of equations b graphing. ) 4 ) Which of the following ordered pairs (, ) is a solution of the sstem below? 5 0 A), 0 B) 0, C), 4 D) 4, 6 4) Write a sstem of equations for the sstem graphed below. Find the (, ) solution to the sstem of equations. 5) 4 5)

11 4 0 6) 6) 7) An online movie club has an initiation fee of $0 plus $4 per movie rented. Another club has an initiation fee of $0 plus $ per movie rented. The equations below model the memberships for the two clubs. c 4m 0 c m 0 a) After how man movies will the memberships cost the same amount? a) b) What is that cost? b) 8) Solve the sstem ) 9) What is the solution to the sstem solved below? = 6 A) (0, 6) B) (6, 0) C) No solution D) Infinitel man solutions 0) Find the (, ) solution to the sstem of equations )

12 Graphing Linear Inequalities ) Graph the linear inequalit. Use a color pencil to shade the solution. 4 ) Is 5 4, a solution of the inequalit? Show our work! ) Which one of the following points is not a solution of the inequalit graphed below? A), B), C), D),4 4) Which of the following linear inequalities is graphed below? A) B) C) D)

13 Sstems of Linear Inequalities ) Is, a solution of the sstem of linear inequalities below? Show our work! 8 4 ) Graph the sstem of linear inequalities. Use different color pencils to shade. Clearl label the solution region. ) Choose the sstem of inequalites graphed below. A ) B ) C ) D )

14 ) The product of A) B) 6 8 and 5 4 C) is Chapter 6.: Eponents. 5 4 D) 6 ) 4 A) 6 B) 6 C) 8 D) 8 ) 4 A) B) C) D) 4 4) For an nonzero value of, A) 8 B) 8 C) D) 8 5) Epressed in simplest form, A) 8a B) a C) a c D) a c a c is equivalent to 4ac 6 8 6) Which epression is equivalent to A) 9 B) C) 9? D) ) A) 8 B) 7 8 C) 7 6 D) 6 8) 5 A) 5 5 B) C) 5 D) 5 0 9) A) 0 B) C) D)

15 Chapter 7: Polnomials ) Write 4 in descending order for the variable. ) ) What is the sum of the two polnomials above? A) B) C) D) ) Which of the following is equivalent to the epression above? A) B) C) D) ) Find each product. a) 5 4 a) 4 b) 7 b) 5) Find each product. a) 4 a) b) 7 b) c) 6 6 c) d) d) e) 4 e)

16 6) Which trinomial is equivalent to 4? A) 4 B) 4 C) 4 D) 4 Factoring a Polnomial ) ) ) 5 50 ) The polnomial factors to a b. What are the values of a and b? a = b = Factor the polnomial. 4) 0 4) 5) 8 5 5) 6) 6) 7) 64 7) 8) 8) 9) ) Factor as the square of a binomial. 0) 8 6 0) ) )

17 Factor using the GCF. ) 4 0 ) ) 6 ) 5 4 4) 4) Factor completel. 5) 50 5) 6) 0 6) 7) Which represents the complete factorization of? A) B) 6 C) 6 D) 8) Which represents the complete factorization of 5 4? A) 7 B) 7 C) 4 D) 4 9) Which binomial is a factor of 5 6? A) 6 B) C) D)

18 Chapter..: Functions ) Determine whether each relation represents a function. If it is not, circle elements that fail Use the Vertical Line Test (VLT) to determine if each graph represents a function. ) ) 4) 5) 6) 7) 8) What number(s) can be placed in the empt cell so that the table of values satisfies the definition of a function? Select all that appl. A. -5 B. - C. 0 D. E. F. 7

19 Function f is graphed at the right. 9) Find f 5. 0) For what value of does f 6? The table represents a function f. ) f ) For what value of does f? a) What is the -intercept of the function? b) What is the -intercept of the function? f() c) Write an equation in slope-intercept form to represent the function. 4) If f is a function defined b 5, does f? f for what value of 4) 5) Let f and g 4. Find the following: a) f a) b) g b) c) f c) d) g f d) e) g f e) f) g f f)

20 6) The function f is defined b f a, where a is a constant. If f 7, A) 5 B) 7 C) 8 D) 9 what is the value of a? 7) Graph the function 4 f using the slope and the -intercept. 8) Give the domain and range of the function. Domain Range 9) Give the domain and range of each function. Domain Domain Domain Domain Range Range f Range Range

21 0) What is the domain of the function graphed below? A) B) C) D) all real numbers ) What is the range of the function graphed below? A) B) C) D) all real numbers ) What is the range of the function graphed below? A) B) 0 C) 0 D) all real numbers

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