Math II Final Exam Review Questions

1) Simplify: x0 ∙ 643/2

2) Solve for x:

3) Solve the following equation: 12(10)3x + 2 = 120

4) Re-write the following equation in standard form: y=5(x + 2)2 – 4

5) Re-write the following equation in factored form: y = x2 + 2x – 8

6) Add: 4x2 +(−12xy) + 9y2 + 25x2 + 4xy + (−32y2)

7) Multiply: (4x – 7xy)(2y + 3x)

8) Subtract. (10a3 + 5b2 – 5c + 10) – (15 + 5c – 15b2 + 10a3)

9) Find the zeros of the following cubic function: y = (x + 3) (x – 5) (x + 2)

10) Write a quadratic function with a graph that meets the following conditions: x-intercepts at (2, 0) and (6, 0) with a minimum at (4, -8)

11) There are 60 students going on a field trip to the chocolate factory. The students are from three different classes. Mrs. Hooper's class has 24 students and Mr. Gomez's class has 18 students. Which of the equalities correctly describes the students and could be used to solve for how many students are from Mr. Anderson's class? (Let A = the number of students in Mr. Anderson's class.)

a. A + 18 = 24 b. A + A + A = 60 c. 60 – 18 = A – 24 d. 24 + 18 + A = 60

12)

There are 60 students going on a field trip to the chocolate factory. The students are from three different classes. Mrs. Hooper's class has 24 students and Mr. Gomez's class has 18 students. How many students are from Mr. Anderson's class?

(A) 16 students (B) 18 students (C) 20 students (D) 22 students

13) There are six chaperones going on a field trip. There are two buses for the trip. The chaperones divide so there is the same number of chaperones on each bus. How many chaperones are there on the first bus? (A) 2 (B) 3 (C) 6 (D) 12

14) A total of 66 people attended a field trip to a chocolate factory for a tour. A maximum of 15 people are allowed to tour at one time. Which equation correctly describes how many tour groups to organize? (Let g = the number of groups.)

(A) (B) (C) (D)

15) A total of 66 people attended a field trip to a chocolate factory for a tour. A maximum of 15 people are allowed to tour at one time. What is the minimum number of tour groups that can be formed? (A) 4 (B) 5 (C) 15 (D) 66

16) Which graph represents x = 1?

(A) (B)

C) (D)

17)

18)

19) √

20)

21)

⁄

22) Solve the following quadratic equations by factoring, taking the square root, or using the

quadratic formula and match to its solutions:

_____ 1) x2 – 3x – 28 = 0 _____ 2) 2x2 - 5 = 3x _____ 3) 6x2 - 72 = 0

_____ 4) 5x – 24 = - x2 _____ 5) 2x2 = - 9x – 7 _____ 6) x2 + 2x – 120 = 0

A. x = 2.5 and x = -1 B. x= -8 and x = 3 C. x= = -1 and x = -3.5

D. x = 3.46 and x = -3.46 E. x = 10 and x = -12 F. x = -4 and x = 7

23) Dr. Frankenstein thinks he knows more than you about what is true and false world just

because he's a doctor. (Just because he brought a corpse back to life, he thinks he's hot stuff.) He says that the equation y = 17x + 1 also includes the point (1, 8). Is Dr. Frankenstein right or wrong? (A) He's right (B) He's wrong (C) We need more information before we can say if he's right or wrong (D) None of the above

24) The Kooky Dough Company makes cookie dough, but it takes a little time for it to start reeling in the dough. The equation y = 2x – 8 models the profits y after making x pounds of cookie dough. What are the x and y coordinates of their break-even point?

(A) (4, 0) (B) (0, 4) (C) (2, 0) (D) (0, 2)

25)

26) Which pair of triangles is congruent by ASA?

a) b)

c) d)

27) By which of the following postulates could you say the triangles below are congruent.

A. SAS

B. ASA

C. SSS

D. Not congruent

28) In the figure to the right, ̅̅ ̅̅ ̅̅ ̅̅ , and D is the midpoint of segment BC. Is ΔADB ΔADC? If so, which congruence postulate states that they are congruent?

29) In the figure to the right, . Which congruence postulate states that they are congruent? Write the congruence statement (Δ??? Δ???)

30) In the figure to the right, is ΔPQR ΔKMN? If so, which congruence postulate states that they are congruent?

31) In the figure to the right, CBD and CBA are right angles, and CD CA. Is ΔCBD ΔCBA? If so, which

congruence postulate states that they are congruent?

32)

33)

36)

37) A girl 5.5 ft tall holds a string that is 50 ft. and is attached to a kite. If the string makes an angle of

elevation of 57o, how high is the kite off of the ground? Round to the nearest tenths.

38)

39)

40)

41)

42) The plastic arrow on a spinner for a child’s game stops rotating to point at a color that will

determine what happens next. Which of the following probability assignments are not possible?

Probabilities of….

Red Yellow Green Blue

a) 0.25 0.25 0.25 0.25

b) 0.10 0.20 0.30 0.40

c) 0.20 0.30 0.20 0.50

d) 0.30 0.25 0.20 0.25

43) A captain and co-captain for a soccer team are chosen from a hat with the names of all 10

members in the hat. Determine the probability that Abbie is chosen as captain Morgan as co-

captain.

A)

B)

C)

D)

44) There are 25 kids in a class and the teacher is choosing four students to help the secretary move books. If the teacher randomly chooses 4 students, what is the probability that Jason, Alexis, Michael, and Madison will be selected?

A)

B)

C)

D)

45) What is the probability that 5 books placed randomly on a shelf will be placed alphabetically?

A)

B)

C)

D)

46) Real-World Objects are listed and/or pictured below. Name the geometric 2-D or 3-D figure(s)

that best represent(s) each object. Be as specific as possible.

1. Stop sign 2. Yield sign 3. Orange (the fruit)

4. Soup can 5. Mattress for your bed 6. Tree trunk

7. Birthday Cake

8. Children’s party hat

9. Trailer part of a tractor-trailer

truck

10. The Pentagon (in DC)

11. Megaphone (ignore handle)

12. Bird house (as pictured)

47)

48)

49)

50)

51)

52)

53) f(x) = √

A) Describe in words the transformations B) Identify the Domain

C) Identify the Range D) Identify the End Behavior

54) f(x) = √

A) Describe in words the transformations B) Identify the Domain

C) Identify the Range D) Identify the End Behavior

E) Graph the function

55) f(x) = √

A) Describe in words the transformations B) Identify the Domain

C) Identify the Range D) Identify the End Behavior

E) Graph the function

56) f(x) =

√

A) Describe in words the transformations B) Identify the Domain

C) Identify the Range D) Identify the End Behavior

57)

58) What is the amplitude of the graph of the equation y = 2sin(3x)?

A. 3 B. 2 C. 0 D. 6

59) What is the midline of the graph of the equation y = 1 + 4cos(x)

A. y = 4 B. y = 1 C. x = 1 D. x = 4 .

60) What are the vertex and the axis of symmetry of the quadratic function:

a. (-1.5, -1.5); y = -1.5 b. (-1.5, -1.5); x = -1.5 c. (1.5, 1.5); y = 1.5 d. (1.5, 1.5) x = 1.5

61)

62) Label the six functions as “even”, “odd”, or “neither”. a) y = b) c)

d) y = e) f)

63)