PreCalculus. Ocean Township High School Mathematics Department

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1 PreCalculus Summer Assignment Name Period Date Ocean Township High School Mathematics Department These are important topics from previous courses that ou must be comfortable doing before ou can be successful in PreCalculus. This packet is to be completed in full and turned in on the first da of class. It will be graded and counted as our first quiz grade. If ou find that ou need some assistance, please feel free to Google or YouTube the concepts. Within the directions of each problem, ou will see ke words that ou should be using in our research. Show all work that is required to be performed in order to solve the problem! Partial credit will be awarded for ever correct step given even though the final answer might be incorrect. Points will be deducted if our work is mess and illegible. All answers must be eact and simplified unless the problem asks for an approimation! 1) Solve the linear equation ) Solve the linear equation ) Solve the linear equation ) Solve the linear equation ) Solve the linear equation ) Solve the linear equation Ocean Township HS Mathematics Department (PreCalculus Summer Assignment) 1

2 7) Solve the linear equation ) Solve the linear equation ) Solve the linear equation ) Solve the linear equation ) Solve the equation algebraicall ) Solve the equation algebraicall ) Solve the inequalit & graph the solution set ) Solve the inequalit & graph the solution set ) Solve the inequalit & graph the solution set. 8 Ocean Township HS Mathematics Department (PreCalculus Summer Assignment)

3 16) Solve the inequalit & graph the solution set ) Solve the inequalit & graph the solution set ) Solve the inequalit & graph the solution set ) Solve the absolute value equation ) Solve the absolute value equation ) Solve the absolute value equation. 4 0 ) Solve the absolute value equation ) Solve the absolute value inequalit & graph the solution set. 9 Ocean Township HS Mathematics Department (PreCalculus Summer Assignment)

4 4) Solve the absolute value inequalit & graph the solution set. 1 5) Solve the absolute value inequalit & graph the solution set ) Solve the absolute value inequalit & graph the solution set ) Solve the absolute value inequalit & graph the solution set ) Graph the linear function (slope-intercept form). 4 9) Graph the linear function (slope-intercept form). 1 Ocean Township HS Mathematics Department (PreCalculus Summer Assignment) 4

5 0) Graph the linear function (slope-intercept form). 1) Graph the linear function (slope-intercept form). 1 ) Graph the linear function (slope-intercept form). ) Graph the linear function. 4 4) Graph the linear function. Ocean Township HS Mathematics Department (PreCalculus Summer Assignment) 5

6 5) Graph the linear function (standard form) ) Graph the linear function (standard form) ) Write the equation in slope-intercept form and standard form for the line that is graphed. Slope-intercept form Standard form 8) Write the equation in slope-intercept form and standard form for the line that is graphed. Slope-intercept form Standard form 9) Determine the slope of the line that goes through the points. 5,6 &, 15 Ocean Township HS Mathematics Department (PreCalculus Summer Assignment) 6

7 40) Determine the slope of the line that goes through the points. 11, 7 & 4, 41) Determine the slope of the line that goes through the points. 5,6 &,6 4) Determine the slope of the line that goes through the points. 11, 7 & 11, 4) Find the equation for a line with the given properties. Slope 0 & containing the point 5,6 44) Find the slope-intercept equation for a line with the given properties. 4 Slope & containing the point 8, 16 45) Find the slope-intercept equation for a line with the given properties. Containing the points 4, 4 & 6,1 46) Find the slope-intercept equation for a line with the given properties. int & int 8 47) Find the slope & -intercept of the line. 4 Slope 48) Find the slope & -intercept of the line. 5 Y-intercept Slope Y-intercept 49) Find the slope-intercept equation for a line with the given properties. Parallel to 7 & containing the point 7,6 Ocean Township HS Mathematics Department (PreCalculus Summer Assignment) 7

8 50) Find the slope of the line perpendicular to the line containing the points., 5 & 6, 9 51) Find the slope-intercept equation for a line with the given properties. Perpendicular to & containing the point 8,9 4 5) Find the equation for a line with the given properties. Perpendicular to 4 & containing the point 11, 9 5) Find the zero of the linear function. f ) A tai compan charges $.0 plus $1.15 per mile. Write a linear function that relates the cost C, in dollars, of riding the tai for miles. What is the cost of riding the tai if the ride is miles? 55) Population of Ocean Township YEAR Population,89 4,00 6,74 11,6 18,64,570 5,058 6,959 Find the equation of the line of best fit then use the linear function to estimate what will be the population of Ocean Township in the ear ) Simplif using properties of eponents ) Simplif using properties of eponents ) Simplif using properties of eponents. 5 4 Ocean Township HS Mathematics Department (PreCalculus Summer Assignment) 8

9 59) Simplif using properties of eponents ) Simplif using properties of eponents z z 6 61) Rewrite the epression using rational eponent notation ) Rewrite the epression using radical notation ) Evaluate the epression. 4 64) Evaluate the epression ) Evaluate the epression. 6 66) Subtract the polnomials ) Multipl the polnomials ) Multipl the polnomials ) Multipl the polnomials Ocean Township HS Mathematics Department (PreCalculus Summer Assignment) 9

10 70) Multipl the polnomials ) Factor the polnomial (greatest common factor) ) Factor the polnomial (greatest common factor) ) Factor the polnomial (greatest common factor) ) Factor the polnomial ) Factor the polnomial ) Factor the polnomial ) Factor the polnomial ) Factor the polnomial ) Factor the polnomial ) Factor the polnomial ) Factor the polnomial ) Factor the polnomial Ocean Township HS Mathematics Department (PreCalculus Summer Assignment) 10

11 8) Factor the polnomial. 1 84) Graph the quadratic function (standard form). Identif the following: 4 Direction of Opening Y-intercept Ais of Smmetr Verte X-intercept(s) 85) Graph the quadratic function (standard form). Identif the following: 6 1 Direction of Opening Y-intercept Ais of Smmetr Verte X-intercept(s) 86) Write the equation of the quadratic function in standard form ) Write the equation of the quadratic function in verte form ) Find the value of c that makes the epression a perfect square trinomial then write the epression as the square of a binomial (completing the square). 7 c 89) Find the value of c that makes the epression a perfect square trinomial then write the epression as the square of a binomial (completing the square). 10 c Ocean Township HS Mathematics Department (PreCalculus Summer Assignment) 11

12 90) Solve the quadratic equation (factor or quadratic formula) ) Solve the quadratic equation (factor or quadratic formula) ) Solve the quadratic equation (factor or quadratic formula). 5 9) Solve the quadratic equation (factor or quadratic formula) ) Solve the quadratic equation (square root method) ) Solve the square root equation. 6 96) Solve the square root equation ) Solve the square root equation ) Write the epression as a comple number in standard form. 5 7i 8 9i 99) Write the epression as a comple number in standard form. 5 7i 8 9i 100) Write the epression as a comple number in standard form. 5 7i 8 9i Ocean Township HS Mathematics Department (PreCalculus Summer Assignment) 1

13 Ocean Township HS Mathematics Department (PreCalculus Summer Assignment) 1 101) Solve the sstem of equations b graphing ) Solve the sstem of equations b graphing. 6 10) Solve the sstem of equations b using substitution or elimination ) Solve the sstem of equations b using substitution or elimination ) Solve the sstem of equations b using substitution or elimination ) Solve the sstem of equations b using substitution or elimination. 4

14 107) Simplif the radical ) Simplif the radical ) Multipl the radicals and simplif. 110) Multipl the radicals and simplif ) Multipl the radicals and simplif ) Multipl the radicals and simplif ) Add the radicals ) Add the radicals ) Add the radicals ) Add the radicals. 117) Rationalize ) Rationalize ) Evaluate the function notation. g 4 5 Find g10 Ocean Township HS Mathematics Department (PreCalculus Summer Assignment) 14

15 10) Evaluate the function notation. h 4 Find 11 h 11) Evaluate the function notation. 7 f 11 Find f 7 1) Find the value of in the function notation equation. f 7 Find m so that f m 5 1) Find the value of in the function notation equation. g 4 5 Find so that 14) Find the value of c. f g & f 7 c Use the graph of 15) Find p 9 16) Find p4 17) Find p8 18) Find so that p( ) 5 19) Find so that p( ) 4 10) Find so that p( ) 1 p to answer the following questions. 11) Determine whether the relation represents a function, then find the domain & range. 4, 5,,7, 1,, 5, &, 8 Function Domain Range Ocean Township HS Mathematics Department (PreCalculus Summer Assignment) 15

16 1) Find the distance between the points & the midpoint of the line segment joining the points., 5 & 6, 9 Distance 1) Find the domain of the function. 4 1 f 9 14) Find the domain of the function. g 5 15) Find the domain of the function. h g Midpoint 16) Let f 5, and 1 h. Perform the indicated operation (parts A through F composition of functions & parts G through H inverse of functions). A) h f 11 B) g h10 C) f g 4 D) f g E) g f F) h f 1 G) f H) h 1 Ocean Township HS Mathematics Department (PreCalculus Summer Assignment) 16

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