Ocean Township High School Mathematics Department

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1 Algebra Summer Assignment Name Period Date Ocean Township High School Mathematics Department These are important topics from Algebra 1 that you must be comfortable doing before you can be successful in Algebra. This packet is to be completed in full and turned in on the first day of class. It will be graded and counted as your first quiz grade. If you find that you need some assistance, please feel free to Google or YouTube the concepts. Within the directions of each problem, you will see key words that you should be using in your research. Show all work that is required to be performed in order to solve the problem! Partial credit will be awarded for every correct step given even though the final answer might be incorrect. Points will be deducted if your work is messy and illegible. All answers must be exact and simplified unless the problem asks for an approximation! 1) Evaluate the expression. 5xy 6y if x 3 & y 4 ) Evaluate the expression. 3x xy if x 3 & y 4 3) Evaluate the expression. x 3 y y x if x 6 & y 4) Evaluate the expression. xy x x y if x 6 & y 5) Combine the like terms. 11x 5y 7y 4x 6) Combine the like terms. 13 x 7x 8x x Ocean Township HS Mathematics Department (Algebra Summer Assignment) 1

2 7) Combine the like terms. 7xy x y 9x y 4xy 8) Combine the like terms. 3 8x 1x 3x 5x 3 9) Solve the linear equation. x ) Solve the linear equation x 11) Solve the linear equation. x ) Solve the linear equation. x 6x 4 13) Solve the linear equation. x 4x ) Solve the linear equation. x ) Solve the linear equation x 16) Solve the linear equation. 4 0 x 3 x Ocean Township HS Mathematics Department (Algebra Summer Assignment)

3 17) Solve the linear equation. x 33x ) Solve the linear equation. x 1 8x 45 5x ) Solve the linear equation. 6x 4x 0 0) Solve the linear equation. 11x 9x 14 1) Solve the linear equation. 7 4x 10x 19 ) Solve the linear equation. x x 3) Solve the linear equation. x 5x ) Solve the linear equation. 3 x 5x 8 1 5) Solve the linear equation. 3x 14 5x 5x Ocean Township HS Mathematics Department (Algebra Summer Assignment) 3

4 6) Solve the linear equation. 8 x 5 x 11 7x x 7) Solve the linear equation. x 4 3x 1 4x 3 8) Solve the linear equation. x 8 6x 3x x 8 4 9) Solve the inequality & graph the solution set. 3x 10 30) Solve the inequality & graph the solution set. 6x ) Solve the inequality & graph the solution set. 3 x 8 3) Solve the inequality & graph the solution set. x ) Solve the inequality & graph the solution set. x 9 5 Ocean Township HS Mathematics Department (Algebra Summer Assignment) 4

5 34) Solve the inequality & graph the solution set x 35) Solve the inequality & graph the solution set. 3x 7 6x 0 36) Solve the absolute value equation. x ) Solve the absolute value equation. x ) Solve the absolute value equation. x ) Solve the absolute value equation. 3 x ) Solve the absolute value equation. x ) Solve the absolute value inequality & graph the solution set. x 7 11 Ocean Township HS Mathematics Department (Algebra Summer Assignment) 5

6 4) Solve the absolute value inequality & graph the solution set. x ) Solve the absolute value inequality & graph the solution set. x ) Solve the absolute value inequality & graph the solution set. x ) Solve the absolute value inequality & graph the solution set. x ) Solve the absolute value inequality & graph the solution set. 3 x ) Graph the linear equation (slope-intercept form). y 3x 4 Ocean Township HS Mathematics Department (Algebra Summer Assignment) 6

7 48) Graph the linear equation (slope-intercept form). 3 y x 1 49) Graph the linear equation (slope-intercept form). y x 50) Graph the linear inequality (slope-intercept form). 1 y x 3 51) Graph the linear inequality (slope-intercept form). y x 3 5) Graph the linear equation. y 4 Ocean Township HS Mathematics Department (Algebra Summer Assignment) 7

8 53) Graph the linear equation. x 54) Graph the linear equation (standard form). 6x y 8 55) Graph the linear equation (standard form). 3x 6y 1 56) Write the equation in slope-intercept form and standard form for the line that is graphed. Slope-intercept form Standard form Ocean Township HS Mathematics Department (Algebra Summer Assignment) 8

9 57) Write the equation in slope-intercept form and standard form for the line that is graphed. Slope-intercept form Standard form 58) Write the equation in slope-intercept form and standard form for the line that is graphed. Slope-intercept form Standard form 59) Determine the slope of the line that goes through the points. 5,6 &, 15 60) Determine the slope of the line that goes through the points. 11, 7 & 4,3 61) Determine the slope of the line that goes through the points. 5,6 &,6 6) Determine the slope of the line that goes through the points. 11, 7 & 11,3 63) Find the equation for a line with the given properties. 0 5,6 Slope & containing the point Ocean Township HS Mathematics Department (Algebra Summer Assignment) 9

10 64) Find the slope-intercept equation for a line with the given properties. 3 4 Slope & containing the point 8, 16 65) Find the slope-intercept equation for a line with the given properties. Containing the points 4, 4 & 6,1 66) Find the slope-intercept equation for a line with the given properties. y int x int 3 & 8 67) Find the slope & y-intercept of the line. y 4 Slope = Y-intercept = 68) Find the slope & y-intercept of the line. x 5 Slope = Y-intercept = 69) Find the slope-intercept equation for a line with the given properties. Parallel to x 7 7,6 y & containing the point 70) Find the slope of the line perpendicular to the line containing the points., 5 & 6, 9 71) Find the slope-intercept equation for a line with the given properties. Perpendicular to y 4x 8,9 & containing the point Ocean Township HS Mathematics Department (Algebra Summer Assignment) 10

11 7) Find the equation for a line with the given properties. Perpendicular to 4 y & containing the point 11, 9 73) Simplify using properties of exponents xy 3x y 74) Simplify using properties of exponents x 1xy y 10 75) Simplify using properties of exponents x y 4 76) Simplify using properties of exponents xy 3x y 77) Simplify using properties of exponents x 1x 1 y y 10 z z 6 78) Subtract the polynomials x 6x x 9x 16 3 x 5x 7x x 1 79) Multiply the polynomials x 5x 7x x 1 80) Multiply the polynomials. 5 3 x 4x 6x x 9x 16 Ocean Township HS Mathematics Department (Algebra Summer Assignment) 11

12 81) Multiply the polynomials. x 4 x 3 8) Multiply the polynomials. 3x 4 x 1 83) Factor the polynomial (greatest common factor). 30x 18y 1 84) Factor the polynomial (greatest common factor) x 16x 4x 85) Factor the polynomial (greatest common factor). 4 1x 16xy 4x 86) Factor the polynomial. x 10x 16 87) Factor the polynomial. x 10x 4 88) Factor the polynomial. x 1x 7 89) Factor the polynomial. x 5x 1 90) Factor the polynomial. 3x 37x 1 91) Factor the polynomial. 4x 0x 5 Ocean Township HS Mathematics Department (Algebra Summer Assignment) 1

13 9) Factor the polynomial. x 49 93) Factor the polynomial. 9x ) Factor the polynomial. x 14x 4 95) Factor the polynomial. 3x 3 1x 96) Solve the system of equations by graphing. y 3x 4 1 y x 3 97) Solve the system of equations by graphing. x y x 3y 6 98) Solve the system of equations by using substitution or elimination. y 5x 1 x y 99) Solve the system of equations by using substitution or elimination. x y 5 x y 3 Ocean Township HS Mathematics Department (Algebra Summer Assignment) 13

14 100) Solve the system of equations by using substitution or elimination. x 1 7y 3x 5y ) Solve the system of equations by using substitution or elimination. x y 5 x y 11 10) Solve the system of equations by using substitution or elimination. x 6y 10 3x y 9 103) Solve the system of equations by using substitution or elimination. 4x 3y 3x y 3 104) Simplify the radical ) Simplify the radical ) Multiply the radicals and simplify ) Multiply the radicals and simplify ) Multiply the radicals and simplify ) Multiply the radicals and simplify Ocean Township HS Mathematics Department (Algebra Summer Assignment) 14

15 110) Add the radicals ) Add the radicals ) Add the radicals ) Add the radicals ) Evaluate the function notation. f x x 7 Find f 5 115) Evaluate the function notation. g x 3 x 4 5 Find g ) Evaluate the function notation. h x 4 x 3x 11 Find h 3 117) Find the value of x in the function notation equation. f x x 7 Find x so that f x 5 Ocean Township HS Mathematics Department (Algebra Summer Assignment) 15

16 118) Find the value of x in the function notation equation. g x 3 x 4 5 Find m so that g m ) Use the graph of p x to answer the following questions. Find p 9 10) Find p4 11) Find p8 1) Find x so that p( x) 5 13) Find x so that p( x) 4 14) Find x so that p( x) 1 15) Solve the problem using a system of equations. A farmer has only chicken and pigs on his farm with a total of 48 heads and 130 legs. How many chicken and pigs does he have? 16) Solve the problem using a system of equations. At the Strikes to Spare bowling lanes, the management is trying to decide on a plan to attract large groups on Sundays. Plan A is a $5 charge for the group, then $1.50 per game per each member. Plan B is to lower the charge to $0 but raise the price per game to $1.60. How many games would need to be bowled to result in the same price? What is that price? 17) Solve the system of equations by using substitution or elimination. x y z 3 x y z 5 x y z 8 Ocean Township HS Mathematics Department (Algebra Summer Assignment) 16

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