Algebra EOC Review

39. Use factoring to write an equation that is equivalent to 25b^16 - 64c^2. (EX: (b^2-4a)(44b^27-9a) )

(5b^8+8c)(5b^8-8c)

56. What is the vertex of 3x^2+12x+7?

(-2,-5)

35. The area of a rectangular field is represented by 2x^2 + 13x + 21. What are the length and width of the field? (Use binomial form, EX: (x-3)(4x+17).)

(x+3)(2x+7)

41. Sonja has decided to try out for the track and field team at her high school and would like to be able to jump the hurdles. She did some research to find that if her jump models the expression -2x^2 + 24x - 2, she can clear a 68cm hurdle without any problem. Write an equivalent expression to easily show the maximum height Sonja must be able to jump.

-2(x-6)^2+70

58. What are the zeros of 3x^2+12x+7? (For any decimals do 0.X)

-3.3,-0.7

44. Mrs. Rice asked his class to find the value of the function h(x) = f(x) - g(x). What is the value of h(x) = f(x) - g(x), if f(x) = 2x + 3 and g(x) = 4x^2 - 5x?

-4x^2+7x+3

25. Select all the solutions to the equation 2x^2 + 3x - 5 = 0 A. -5/2 B. -1 C. 2/5 D. 1 E. 5/2

-5/2,1

48. Tori has a cell phone plan that charges $0.09 for each text message sent. Tori plants to send no more than $40 per month on her texting bill. If c(t) = 0.09t represents the total phone bill based on the number of texts (t) that Tori sends each month, what is the domain of the function?

0 <= t <= 444

32. Complete the table of successive approximations to find the x-value of the solution of f(x)=g(x) to the nearest hundredth. x | f(x) = x^2 - 2 | g(x) = x - 1 0 | - 2 | -1 1 | -1 | 0 2 | 2 | 1 1.5 | 0.25 | 0.5

1.62

50. Mr. Downey used the function f(x) = -3x^2 + 12x to model the fight of a glider. In Mr. Downey's function, x is the amount of tiem that passes in minutes and f(x) is the glider's distance from the ground in feet. After how many seconds will the glider reach its maximum distance from the ground?

120

10. Dr. Siddiqui monitored the decay of a new type of recyclable material his developer for hiss gamma radiation study. He noted that the decay of the material could be modeled by the function f(x)=100(0.98)^x. What is the rate of decay of Dr. Siddiqui material? (Write answer in x% form)

2%

1. Find the difference between (2g^2+3g-8)-(5g+1)

2g^2-2g-9

27. Find the solution(s) of the equation 5(x-2)^2-20=0

4,0

46. Gavin needs to fill the fish tank below with water. The directions state that the water level should be 2 inches below the top of the tank. Write an expression to show the volume of water Gavin needs to fill the tank according to the directions. The fish tank is 2x by x by (2x-6)

4x^3-16x^2

29. Julio wants to make a small scale soccer field in his backyard for his daughter to practice, He has painted off lines to create a perimeter of 270 feet. He has also measured the length of the field to be 35 feet longer than the width of the field. Write a system to help you find the width of the field. (Just write the width)

50

61. The Senior Class sponsor created the two-way frequency table shown below indicating student's choice for homecoming theme. (fig. 4) Calculate the conditional relative frequency of juniors selecting a Masquerade Ball as the theme to homecoming to the nearest hundredth.

58.56

30. Three times a number is subtracted from another number and the difference is 3. The sum of the two numbers is 31. What is the smaller of the two numbers.

7

17. Tina scored 94, 68, and 88 on her first 3 Algebra 1 tests. Her next test is her final which counts double. Write and solve an equation that Tina could use to determine the minimum grade she must score on her final to have a mean score to 80.

75

40. Write the expression 7x^3 - 28xy^2 as the product of 3 factors. (EX: 2x(y+2x)(y-2x), put the negative binomial first)

7x(x-2y)(x+2y)

14. Is the product of √2 and √8 rational? A: Yes B: No C: Baby Yoda D: Dancing Crab

A

15. Does either item below contradict the statement: "The sum of two rational numbers is a rational number" Item 1: 2/5 + 1/3 = 11/15 Item 2: 1/5 + 4/5 = 1 A: Neither Item 1 nor Item 2 contradicts the given statement B: Both Item 1 and Item 2 contradict the given statement C: Item 1 contradicts the statement. Item 2 is an example when the statement is true. D: Item 2 contradicts the statement. Item 1 is an example when the statement is true.

A

33. Does y >= -x + 4 and y >= 3x - 2 have a solution of (-3,2). A: Yes B: No

A

45. The function f(x) = (3x)^2 is used to determine the area of a sandbox, where x is the number of children the sandbox is designed to hold. The function g(x) = (2x+3)^2 is used to determine the area a park needs to hold a merry go round, where x is the maximum number of children the merry go round can hold. Which expression could be used to determine A(x), the area needed for a park to have both a sandbox and a merry go round. A: A(x) = 13x^2 + 12x + 9 B: A(x) = 9x^2 + 21x + 9 C: A(x) = 13x^2 + 9 D: A(x) = (5x+3)^2

A

55. Identify the graph that matches the function given. f(x)= 2^x+3* (fig. 2)

A

8. Ken solved the linear equation 2(5y-1)=18 using the following steps. Step 1: 2(5y-1)=18 Step 2: 10y-1=18 Step 3: 10y=19 Step 4: y=1.9 Which statement is true about Ken's method? A: Ken made a mistake between Steps 1 and 2. B: Ken made a mistake between Steps 2 and 3. C: Ken made a mistake between Steps 3 and 4. D: Ken solved the equation correctly.

A

37. Select all of the factors of the expression 5x^2 - 405. A: 5 B: 9 C: x + 9 D: x - 9 E: 5x - 9

A,C,D

42. Ana received a gift of $5,000 from he grandmother and decided to invest it. The expression 5000(1.0005)^12t represents the amount of money Ana is earning on her own investment. Select all of the following that are equivalent expressions so that Ana can better understand how her money is invested A: 5000(1.0005^12)^t B: (5000 + 2.5)^12t C: 5000(1 + .0005)^12t D: 5000(1 + .06/12)^12t E: 5000(1.0005^t)^12 F: 5025^12t

A,C,E

49. Aron wrote the function f(x) = 25x - 15 find the amount of money he would make after washing x cars. Select all of the values below that are in the domain of Aron's function? A: 2 B: 2.3 C: 5 D: 7.1 E: 10

A,C,E

28. Ms. Holly is solving the system of equations 4x - 3y = 9 and 2x + 6y = 5. Which system(s) of equations has the same solution as the system that Ms. Holly is solving? A: 4x- 3y = 9 and -15y = -1 B: 4x - 3y = 9 and 9y = 19 C: 2x + 6y = 5 and 6x = 23 D: 2x + 6y = 5 and 10x = 23

A,D

4. What is the perimeter of a triangle whose side lengths are x^2+4, 2x-1, and 5x? A: 8x^2+3 B: x^2+7x+3 C: x^2+11x-1 D: 10x^4-5x^3+40x^2-20x

B

36. Niara is writing a computer program for three-dimensional graphics. Part of her program applies the expression 27x^3 + 8y^3. Which expression 27x^3 + 8y^3. A: (3x+2y)(3x-2y)(3x+2y) B: (3x+2y)(9x^2-6xy+4y^2) C: (3x+2y)(3x-2y)^2 D: (3x-2y)^3

B

60. At the Central Summer Camp, 150 children registered for the first session and 105 for the second session. The activities they chose in each session are shown in the two-way frequency table below. Which of the following represents the joint frequency of children registered in Session 2 who chose swimming? (fig. 3) A: 0.2874 B: 0.3255 C: 0.4733 D: 0.7905

B

12. Select all the expressions that are equivalent to the expression (64)^2/3. (List answers like the following: Y,P,X,L) A: √16 B: 16 C: 4^2 D: √64^2 E: 3√64^2 F: (3√64)^2

B,C,E,F

11. Ned shows that √16 = 16^1/2. Part of his work is shown below. Which expression or equation can be placed in the blank to correctly complete Ned's work? √16 = 4 = 4^1 = 4^1/2+1/2 = __________ = 16^1/2 A: (4^2)^1 B: 4^1/2 + 4^1/2 C: 4^1/2 + 4^1/2 = (4x4)^1/2 D: 4^1/2 x 4^1/2 = (4x4)^1/2+1/2

C

3. Which polynomial represents 5y(y^4+6y^2-11) A: 5y^5+30y^3-11 B: 5y^4+30y^2-55y C: 5y^5+30y^3-55y D: y^4+6y^2+5y-11

C

38. Which of the following expressions is equal to x^2 + 6x + 9. A: (x-3)(x+3) B: (x-3)(x-3) C: (x+3)(x+3) D: Cheeeeeeeeeeese

C

47. Given the function f(x), what is the transformation f(x-r), if r is a real number and r > 0? A: The graph shifts r units down. B: The graph shifts r units up. C: The graph shifts r units right. D: The graph shifts r units left.

C

53. Russell made a graph for a project which shows the relationship between the time in seconds, x, that a football is in the air after it is thrown and the number of feet, f(x), the football travels. Which of the following is the most appropriate domain for Russel's graph? A: x <= ∞ B: x >= 0 C: 0 <= x <= 10 D: 0 <= x <= 100

C

34. Select all the ordered pairs that are in the solution set of the system of inequalities given. 6x + 2y > 1 and y < 5x + 3 A: (-3, 1) B: (0, -3) C: (3, 3) D: (-7, 4) E: (1, 1) F: (4, -2)

C,E,F

54. Maya keeps her bolts in a large box in her garage. The total number of bolts in the box, f(x), is determined by the number of models (x) that she builds. The graph below shows that this relationship is a linear function. Which of the following would be the largest possible value in the domain of Maya's function? A: 4 B: 10 C: 11 D: 12

D

9. Rene graphed the functions f(x)=2^x and g(x)=x^2. Which statement best compares the values of f(x)and g(x) in Rene's graphs. A: f(x) will always be greater than g(x) B: g(x) will always be greater than f(x) C: f(x) will never equal g(x) D: f(x) increases faster than g(x)

D

16. What are the end behaviors if the function is y = (x+2)(x+3)(x-1) A: As x --> +∞, y --> +∞ As x --> -∞. y --> +∞ B: As x --> +∞, y --> -∞ As x --> -∞. y --> +∞ C:As x --> +∞, y --> -∞ As x --> -∞. y --> -∞ D:As x --> +∞, y --> +∞ As x --> -∞. y --> -∞

D

31. Nico created 2 systems of equations which are shown down below. Chose which statement correctly compares the systems. [1]: x+y=21 and 2x=33+y [2]: -5x-8y=17 and 2x-7y=-17 A: In system 1 the x value is greater B: In system 2 the y value is greater C: In both systems the coordinates are the same D: Both coordinates in system 1 are greater than system 2

D

43. A function for a popular amusement park ride in Ohio is defined by the expression -16s^2 + 64s - 60, where s is the time in seconds. Which of the following is an equivalent expression that reveals the zeros of the function. A: -16(s-2)^2 B: (2s-5)(2s-3) C: -4(s-6)(s-10) D: -4(2s-5)(2s-3)

D

51. Darius started his baseball card collection with 7 cards that he got from his dad. He bought 1 pack of cards each month for 20 years. After 1 year he had 79 cards in his collection. Darius gave his entire collection to his son 20 years after he got it from his dad. Which of the following is the domain of the function representing the number of baseball cards in Darius's collection? A: 7 <= x <= 1580 B: 7 <= x <= 1447 C: 0 <= x <= 21 D: 0 <= x <= 20

D

52. Eva graphed the results of her study below. What of the following is the domain of Eva's graph? A: 0 <= x <= 11 B: 0 <= x <= 10 C: {1,2,3,5,7,8,11} D: {1,2,3,5,6,7,9,10}

D

26. Select all the following values that are solutions of the equation 5x^2 - 2x - 8 = 1 A: -1 B: 1/5 C: 7/5 D: 1+√46 / 5 E: 1-√46 / 5

D,E

13. Larry and Jen are working together to simplify the expression 3√125^2. Larry's work shows: 125^1/3=5 Jen's work shows: 125^2/3=25 Who is correct?

Jen

6. Using the table below explain the process used for each step in solving the equation 4c+12-2c=5c-3 (List the process from Step 2 to 5, EX: Subtraction Property Of Equality,Multiplication Property Of Equality,etc.) | Steps | Solution Steps | Process | 1 4c+12-2c=5c-3 Given 2 ? ________________ 3 ? ________________ 4 ? ________________ 5 ? ________________

Simplify,Subtraction Property Of Equality,Subtraction Property Of Equality,Division Property Of Equality

7. Erica solved the equation 3(a+5)=2a+35 Step 1: 3a+15=2a+35 Step 2: 5a+15=35 Step 3: 5a=20 Step 4: a=4 Which step is the first incorrect step in Erica's solution shown above?

Step 2

5. Below is Tania's work for subtracting two polynomials, but she made a mistake. Identify the step where Tania made her error and write out the remainder of the problem correctly. (EX: Step X;3x^3+17x^2+2x+18) (x^3+8x-17)-(14x^2-11x+6) Step 1: x^3+8x-17-14x^2+11x-6 Step 2: x^3+14x^2+8x-11x-17-6 Step 3: x^3+14x^2-3x-23

Step 2;x^3-14x^2+19x-23

22. Solve the equation y-b=m(x-a) for a.

a=-(y-b)/m+x

59. Write f(x)=x^2-6x+8 in vertex form.

f(x)=(x-3)^2-1

23. Solve the equation below for f. 3-(2f-5/6)=3-f/4

f=37

18. Alyssa emptied out her change jar to buy a new binder for school. She found 147 coins consisting of dimes and nickels that totaled $11.65. Write a system of equations that could be used to determine how many dimes, d, and how many nickels, n, Alyssa had in her change jar. (Format: p+r=20.75 6p-42r=908)

n+d=147 .05n+0.1d=11.65

19. Mr. Dominguez wrote the formula below to calculate a, the acceleration of his motor. a=v-s/t-b Solve Mr. Dominguez's formula for t, the final time.

t=v-s/a+b

20. The movement of moving particles is described in the equation r=ht^2/2-2vt-2c. Solve the equation for v.

v=-r/2t+ht/4-c/t

57. What is the AOS of 3x^2+12x+7?

x=-2

21. Solve the equation below for x. a = bx+cx/2

x=2a/b+c

2. Find the product of (x+1)(x^2-3x+7)

x^3-2x^2+4x+7

24. Rewrite the quadratic equation y = 2x^2 + 12x + 1 in vertex form by completing the square.

y=2(x+3)^2-17