ALGEBRA SUMMER MATH PACKET

Transcription

1 Algebra Summer Packet 0 NAME DATE ALGEBRA SUMMER MATH PACKET Write an algebraic epression to represent the following verbal epressions. ) Double the sum of a number and. Solve each equation. ) + y = ) 8 y = 6 7 ) bh In the formula A =, solve for b. ) Evaluate y if = - and y =. 6) Graph on the number line. In questions #7 and #8, solve each equation or inequality. 7) c + 6= 0 8) > a + 7 9) Write the inequality 0 using set builder notation and interval notation. Set builder notation: Interval notation: 0) (Multiple Choice) This graph show Men s World Records in the 00, 00, 00, and 800 meter distance runs. Which equation could be a prediction equation for the scatter plot?

2 Algebra Summer Packet 0 For questions #, write an equation, in slope-intercept form, for the line that satisfies each set of conditions: ) slope =, passes through (-, ). ) passes through (-, -), parallel to the line whose equation is y = +. ) Write an equation in slope-intercept form for this graph. ) Find the domain and range of the relation {(, ), (-, 0), (, )} AND determine whether it is a function. Domain: Range: Is it a function? (Yes/No) ) Evaluate f ( ) = + for f. 6 6) Solve the system of equations graphically and write the solution as an ordered pair. 7) Use substitution to solve the system of equations. Write the solution as an ordered pair. 7 y = 0 + y = 8) Use elimination to solve the system of equations. Write the solution as an ordered pair. y = 9 + y =

3 Algebra Summer Packet 0 Simplify each sum or difference. 9) ( + 9) + ( + 8) 0) ( + 6y ) ( 8 + y ) In questions # -, multiply the following polynomials and write the answers in the simplest standard form. ) (6 ) ) (+ )( ) ) ( + 9)( 0) Simplify. Assume no variable equals zero. Write answers using positive eponents only! ) 0 ) ( )( 7 ) 6) Divide and simplify using only positive eponents. 7 8y y y 7) Use long division to find the quotient. 8) Use synthetic division to find the quotient. 6 + ( ) (6 ) ( + + ) ( + 7) Factor each polynomial completely. 9) ) + ) Simplify the following epressions. ) 6 9 ) ( + ) ( ) (Write as a fraction, not a decimal.) ) 6 y ) ) Evaluate and write in simplest form: 7) Simplify: 6 8) Solve the equation and CHECK YOUR ANSWER to determine whether the solution is a real number. + 9 =

4 Algebra Summer Packet 0 9) Solve the equation and write your solution using imaginary notation. 0) Simplify: ( i) ( i) 0 + = ) Solve 9 = 0 using the Zero Product Property. ) Solve 0 = 0 by completing the square and then using the Square Root Property. ) Solve = using the Quadratic Formula. ) Solve + + = 0 by graphing. Absolute value Algebraic epression Ais of symmetry Binomial Coefficient Constant Discriminant Domain Inde Parallel Perpendicular Range Substitution Variable ) A(n) is a polynomial that has two unlike terms. 6) The is a number s distance from zero on the number line. 7) The set of all -coordinates of the ordered pairs of a relation is the. 8) A(n) contains at least one variable. n 9) In the epression, n is the. 0) is a method of solving equations in which one equation is solved for one variable in terms of the other variable. ) The line passing through the verte of a parabola and dividing the parabola into two mirror images is the. ) A(n) is a symbol, usually a letter, used to represent an unknown quantity. ) The epression b ac is the. ) A(n) is a monomial that contains no variables. ) Two lines in the same plane having the same slope are.

5 Algebra Summer Packet 0 For questions #6-8, y = ( ) 6) Describe the horizontal AND vertical shift (magnitude and direction) when compared to y=. 7) Does the graph have a maimum or minimum? 8) Identify the verte. 9) Write y = + + in verte form. 60) For f () = ( + ), graph the verte and at least two other points. Then graph the parabola. 6) (Multiple Choice) Solve A. { 6} B. { 6 } C. { or 6} D. { 6 or } 6) (Multiple Choice) Which quadratic inequality is graphed below? A. B. C. D 6) (Fill in the blank) For f () = + 9, use the leading coefficient and the function s degree to describe the function s end behavior. y as. y as +. 6) Find g( + ) if g() = 9.

6 Algebra Summer Packet 0 6) Solve + = 0. 66) Use synthetic substitution to find f () for f () = +. 67) One factor of + 90 is +. Find the remaining factors. For the functions f( ) = 8 7 and g() = +, find: 68) ( f g)() 69) ( f g)() For the functions f ( ) = + and g() = +, find 70) f! g () 7) g! f () For g() = : 7) Find g (). 7) Graph g(), g (), and the line of reflection. 7) Graph y = +. 7) Graph the circle with the equation + y 6 + y =. 76) Write the equation in standard form for the ellipse with the major ais 6 units long and parallel to the -ais, minor ais units long, and, center at (-, ). 77) Graph the hyperbola and its asymptotes with the equation ( ) 6 y 9 =. 78) Write the equation 0 + y = 0 in standard form. For questions #79-8, without writing the equation in standard form, state whether the graph of each equation is a parabola, circle, ellipse, or hyperbola. 79) ( + ) ( y ) = 80) ( ) + ( + 6) = 8) ( 7) + ( y ) = 8) ( y +) + = 6

7 Algebra Summer Packet 0 8) Find the eact solution(s) of the system of equations. 8) Solve the system of inequalities by graphing. + y = + y 8 = y y + 8) A concrete supplier sells premied concrete in 00-ft truckloads. The area A that the concrete will cover is inversely proportional to the depth d of the concrete. Write a formula for the relationship between the area and the depth of the truckload of poured concrete. 86) The weight of an object on Earth is directly proportional to the weight of that same object on the moon. A 00-lb astronaut would weigh lb on the moon. How much would a 0-lb dog weigh on the moon? Asymptote Circle Conjugates Depressed Polynomial Direct Variation Ellipse Inverse Variation Parabola Quadratic Form Relative Maimum Relative Minimum 87) A point on the graph of a polynomial function that has no other nearby points with greater y-coordinates is a(n) 88) When a binomial is divided by one of its binomial factors, the quotient is called a(n) 89) A(n) is the set of all points in a plane that are equidistant from a given point in the plane. 90) The equation y = k is a(n) equation. 9) Writing the polynomial + 9 as u + 9u by substituting u for uses the idea of. 9) A line that the branches of a hyperbola approach but do not intersect is called a(n). 7