Name Vetter Midterm REVIEW January 2019 1. Name the property that justifies each step in the following equation: 3x + 1+ 2x 7 = x + 22 ( 3x + 2x + 1 7 = x + 22 ( (2) x(3 + 2) 6 = x+ 22 5x 6 = x+ 22 (3) 5x 6 + 6 = x+ 22 + 6 5x= x+ 28 (2) (3) ( 5x x = x + 28 x ( (5) x(5 = 28 4x = 28 (5) (6) 4 = 4 (6) x = 7 2. Which of the following is the correct interval notation for the given number line? ( (-4,2) (2) [-4, 2) (3) (-4, 2] ( [-4, 2] 3. Name the set of numbers represented by ( -2, 3] 4. A company that manufactures air purifiers first pays a start-up cost and then spends a certain amount of money to manufacture each. If the cost of manufacturing p purifiers is given by the functionc(p) = 101.25p + 625, then the value 101.25 best represents the start-up cost 2) the profit earned from the sale of one purifier 3) the amount spent to manufacture each purifier the average number of purifiers manufactured 5. AND the value of the 625 best represents the start-up cost 2) the profit earned from the sale of one purifier 3) the amount spent to manufacture each purifier the average number of purifiers manufactured 6. The function h(x) is given in the table below. Find the average rate of change over the interval 1 x 5? x h(x) -1 16 1 13 3 5 5 3
7. A function is graphed on the set of axes below. Which function is related to the graph? ( f(x) = 2x 1 x > 2 (2) f(x) = 1 x 1 x > 2 2 (3) f(x) = 1 x + 1 x < 2 2 ( f(x) = 1 x 1 x > 2 2 8. The formula for the Area of a Triangle is A = 1 bh. Solve for h. 2 9. The formula for the volume of a cylinder is V = πr 2. Solve for r. 10. Let g be a function such that g(x) = 3x + 1 is defined over the domain 3 x 6. The range of this function is ( 0 y < (2) 5 y 10 (3) < y < 100 ( 10 y 19 11. Let h be a function such that h(x) = x 2 is defined over the domain 2 x 6. The range of this function is (2) 6 y < 10 (2) 4 y 36 (3) 0 < y < ( 10 y 6 12. Which of the following represents a vertical line? ( x = 5 (2) x = 3y (3) y = 2x ( y = 1 13. Solve for x: 20 100 = x x+8 14. Which is the smallest solution to 2k < 16? ( -8 (2) -9 (3) 8 ( 9 15. Which of the following relations is a function? ( {(-1, 9), (-1, -, (6, 23)} (3) {(-4, 8), (-3, 10), (4, 3)} (2) {(4, 9), (2,, (4, 16)} ( {(5, 6), (4, -, (5, 1} 16. Which of the following inequality notation and interval notation represents the given graph : ( 2 > x < 3, ( 2,3) (2) 2 < x 3, [-2,3) (3) 2 < x 3, (-2,3] ( 2 < x 3, (3,-2]
17. Which system of equations has the same solutions as this system? 3x + 3y = 30 2x y = 3 ( x + y = 10 (2) x + y = 10 (3) x + y = 30 ( 3x + 3y = 30 4x 2y = 6 4x 2y = 3 4x 2y = 6 4x 2y = 3 18. Given the following recursive formula, determine the 4 th term of the sequence: a1 = 3 an = an-1 + 10 ( 10 (2) 13 (3) 33 ( 53 19. Given: y + x < 2 y 3x 2 Which graph shows the solution of the given set of inequalities? ( (2) (3) ( 20. Which operation should be done first to simplify the expression 10 3 + 6 (10 + 4 2)? ( 10 3 (2) 4 2 (3) 10 + 4 ( 3 + 6 21. Which equation is equivalent to 3(2x 4(3x 2) = 10? ( 18x + 20 = 10 (2) 18x 4 = 10 (3) 18x + 4 = 10 ( 6x + 4 = 10 22. Which equation can be used to generate the table to the right? ( y = x 8 (2) y = x + 8 (3) y =4x - 2 ( y = 2x 2 23. The sum of two consecutive integers is 101. Which equation can be used to find the first integer n? ( n + 1 = 101 (2) n + n + 1 = 101 (3) n + 2 = 101 ( n + n + 2 = 101 24. The sum of two consecutive even integers is 101. Which equation can be used to find the first integer n? ( n + 1 = 101 (2) n + n + 1 = 101 (3) n + 2 = 101 ( n + n + 2 = 101 25. Given the equation of a line 2y + 4x = 2, find the slope and y-intercept of the line. x y -2-10 0-2 2 6 4 14 26. Olivia went to a State Park one day this summer. All of the people at the park were either hiking or bike riding. There were 178 more hikers than bike riders. There were a total of 676 people at the park. Set up a system of equations to be used to solve this. Do not solve.
27. Write an equation in the form y = mx + b for the equation in the graph. 28. Write the equation of the line that passes through (2, and has a slope of ½? 29. Find the solution to the system of equations graphed at the right 30. Which of the following is a function? W S N X A M V 31. Which point is not on the graph represented by y = 3x 2 10x + 6 ( (-2, 19) (2) (0, 6) (3) (3, 3) ( (6, 5 32. Which coordinate point is in the solution set for the system of inequalities shown in the accompanying graph? ( (0, 2) (2) (1, 0) (3) (2, 2) ( (0, 33. Byron has 72 coins in his piggy bank. The piggy bank contains only dimes and quarters. If he has $14.70 in his piggy bank, which equation can be used to determine q, the number of quarters he has? 2) 3) 34. Tanina has $2.80 in quarters and dimes. The number of dimes is seven less than the number of quarters (x). Which of the following equations could be used to find the number of each coin? (. 25x +.10(x 7) = 2.80 (2). 10x +.25(7 x) = 2.80 (3). 25(x 7) +.10x = 2.80 (. 25x +.10(7 x) = 2.80
35. The function f is defined by the formula f(x) = x2 8. What is f(? 4 ( -18 (2) 14 (3) 2 ( 8 36. Graph the following linear inequality. Then state one point in the solution set and one point NOT in the solution set 3y 9x > 6 37. Your monthly cable bill costs $100 plus $5 for every movie ordered. You have at most $148 to spend on your next cable bill. Write and solve an inequality to determine the maximum number of movies you can rent next month? 38. Samantha went to a concession stand and bought three pretzels and four sodas and paid a total of $11.25 for them. Raza went to the same stand and bought five pretzels and two sodas and paid a total of $8.25. Write a system of equations that models the information given and solve the system of equations. 39. Express the product of 3x 2 + 2x 5 and x + 6 in standard form. 40. Express the product of 4x 2 2x + 1 and x 4 in standard form. 41. Graph the following equation: y = x 3 + 2
42. Which of the following choices is a solution to the system of equations: 4x + 3y = 37 y = x 4 ( (7, 1 (2) (-7, 1 (3) (7, 3) ( (8, 43. Given the functions g(x) = 5 x 2 and f(x) = x 6 which value of x makes g(x) = f(x)? 3 ( 1 (2) -4 (3) 3 ( 10 44. Find the 5 th term given the recursive formula: a( = 6 a(n) = a(n + 2 45. Graph the solution set for the inequality on the set of axes below. 46. At the local video rental store, José rents two movies and three games for a total of $15.50. At the same time, Meg rents three movies and one game for a total of $12.05. How much money is needed to rent a combination of one game and one movie? 47. John starts a company selling sneakers. He must first pay a start up cost and then spend a certain amount to ship each pair of sneakers. The cost is given by the function c(s) = 7.50s + 250. a) In the function, the value of the 7.50 represents b) In the function, the value of 250 represents 48. Graph the absolute value function y = 3 x + 1
53. 54. 55. 56. 57. 49. A gym membership costs $ 35 join plus an additional $ 20 month. Write and solve an inequality to represent the maximum number of months someone can go to the gym if they have $100 to spend. 50. Express the product of 3x 2 + 2x 5 and x 4 in standard form. 51. Which segment has the greatest rate of change? 52. Which graph represents a function? 53. What property is illustrated by each statement? 7 + (4 + = (7 + + 4 a. Inverse Property of Addition b. Associative Property of Addition c. Commutative Property of Multiplication d. Commutative Property of Addition
54. What is the solution of the proportion? 55. What is the graph of the function rule? 56.. Identify the mapping diagram that represents the relation and determine whether the relation is a function. a. c. b. The relation is a function. d. The relation is not a function The relation is a function. The relation is not a function.
57. Find the slope of the line. y 5 4 3 2 1 5 4 3 2 1 1 2 3 4 5 x 1 2 3 4 5 58. What is the graph of the equation?. y = 2 59. Which is a solution of the inequality? 6(k 1 > 12 a. 13 b. 12 c. 13 d. 15 60. What are the solutions of the inequality? a. c. all real numbers b. d. no solution 61. How do you write and in interval notation? a. [ 6, 3] c. [ 6, 3) b. ( 6, 3) d. ( 6, 3] 62. Use your calculator to determine the intersection point between the linear functions y = x -2 and 4x - 3y = 7
63. What is the graph of the system? a. y c. y 4 4 4 O 4 x 4 O 4 x 4 4 b. y d. 4 4 y 4 O 4 x 4 O 4 x 4 4
6 Which equation is equivalent to 4(5x + 5(7x 8) = 6? ( 15x 4 = 6 (3) -55x 7 = 6 (2) -15x 36 = 6 ( -15x + 44 = 6 66) Which verbal expression can be represented by 2x - 5? 5 less than 2 times x 2) 2 multiplied by x less than 5 3) twice the difference of x and 5 5 decreased by the product of 2 and x 68) What is the slope of the line represented by the equation? 65) Which interval notation represents the set of all real numbers greater than 2 and less than or equal to 20? 2) 3) 67) Which value of x is in the solution set of the inequality? 2) 2 3) 3 69) What is the slope of line shown in the accompanying diagram? 2) 3) 70) Which inequality is represented in the graph below? 3) 2) 72) Which point is not on the graph represented by y = x 2 + 2x + 1 ( ( -4,9 ) (3) ( 1, 4 ) (2) ( 0, 1 ) ( (-2, -1 ) 7 What is an equation of the line that passes through the point and has a slope of 2? ( y + 1 = 2(x - 3) (3) y - 3 = 2(x + (2) y + 3 = 2(x - ( y - 1 = 2(x + 3) 73) If h(x) = -3x 2 1, what is the value of f(-3)? ( -28 (3) 28 (2) 19 ( -19 7 Given the following recursive formula, determine the 8 th term of the sequence. A1 = 2 An = an-1 + 5 75) If two consecutive even integers have a sum of 182, find the larger of the two integers.
76) Solve for x : 4 8 = x x 3 177) Let g be a function such that g(x) = 4x + 1 is defined on the domain -1 x 3. Find the range of the function 78) Which relation represents a function? 2) 3) 79) Given the following recursive formula, determine the 4th term of the sequence: a1 = 6 an = an-1 + 4 ( 10 (3) 18 (2) 4 ( 24 80) Which equation could represent the relationship between the x and y values shown in the accompanying table? 8 A system of equations is graphed on the set of axes below. The solution of this system is 2) 3) 2) 3)