Math Models and ApplicationsFINAL EXAM Review Sheet

Name:

Date: Period: 1ÿ3 ÿ'ÿ6 7

Complete the following:

1. y=(x+3)2+5 Zÿ

Phase shift: ÿ,, .'ÿ

Vertical shift: ÿ

how much?

how much?

,

how much?

Vertical shift: ÿ how much?l

\

Reflection Compression Stretch mession Stretch

3. y=lx2+5 4. y=-3(x-5)2+32

Phase shift: (ÿ7ÿ how much? ÿ:-ÿ) Phase shift: fÿ-.-

Vertical shift: ÿ how much? ÿ-' Vertical shift:

how much? ÿ>

how much?

Reflection Compression

Graph the following using a table - clearly label points

5. y=(x-3)2+l 6. y=2(x+1)2-3

X Y

|1

X Y

uÿ ÿ 71

: Ifll .........

; 4 ii .... i i

1 1

i I i: I1 I1 1 i

Graph the following without using a table - clearly label points.

7. y=(x+2)2+5 8. y=-(x-3)2+l

Write an equation of a quadratic using the given information -

/7

9. A shift down 3 and to the right 3.

10. A reflection and shift to the left 4.

..... t;)< -- 12.

t

Find the greatest common factor for each set of numbers:

13. IOx2, 25x4 GCF: ÿ

14. 18xZyz, 42x4y3zz, 54x3yZz3 GCF: / ÿ ÿ ÿ Iÿ

Polynomials - factor GCF out and have remaining part in parenthesis.

16. 24x3 +16xSy2 -36xy3 * ÿRdÿ

Factor completely:

19. x2 +14x+48

20. lOx2-25x

21. 81x2-25+

Radicals - simplify

"> + i ..................

+ .,. =2) ÿ'(++

Radicals - multiply

z+. l.,]iÿ+ÿ • ÿqÿ+++

Solve using the properties of exponents:

26. (++)4.(ÿ): ÿ ÿ 1.ÿ ÿ=i

28.( 4 x2y9 ) ( 3xyS ) _

lOxVy3

+

],.ÿ! /--,.+,

........ ÿJJ-+

7

, o.ÿ l .lÿj

(gx sy 2)(2x3y) _

32. Draw a bar graph using the following data, be sure to clearly label.

Enrollment in each Grade Students9th 54010th 42011th 40012th 360

Use the information from your bar graph to answer the following questions.

a. What is approximately the median enrollment?

b. What is the mean of the enrollment?

i'-? )0 flI +°--?

33. Draw a circle graph and complete the table below - be sure to clearly label.

The sales at an Ice Cream Store are as follows - there were a total of ÿ0 items sold

Types of Ice Cream Number sold Percent Sectors

Vanilla

Chocolate

Strawberry

Chocolate Chip

26

36

10lff

/oio

0

Use the information from your circle graph to answer the following question:

a. Which crops makq-up approximately half the ice cream sold?

b. What is the sector of chocolate chip?

34. Draw a double bar graph for the following data - be sure to clearly label.

Survey of Activities

Activity

Football

Dancing

Basketball

Soccer

Boys

40

12

26

30

Girls

8

36

22

16

fbÿ

0 j4s

Use your double bar graph to answer the following questions:

a. Which activity hidÿdÿhe largest difference between boys and girls?

b. What is that difference from answer to problem a? ÿ ÿ

Solve the following equations: Show work for credit

35. 5x-2=x+7 36. 2(3x-5)=-12

37. 4(2x-1)=3-(x-3) 38. 2+3(x-1)=4-2(x+5)

_;: / 0 > x; .... ,----'

Draw a circle graph for each table below: Be sure to label each section and title of circle

graph.

39. Favorite colors

Colors

Red

Blue

Yellow

Green

18

Number of people

28

20

Percent Sector

,G

b

0

40. Grade Distribution for Class

Grade

A

B

C

D

F

Students

4

8

6

4

Percent

t It

.if E "

Sector

o

©

7?ÿj

41. Given the data...fill in the table, find indicated information and draw a circle graph:

Grade on six weeks test:

GradeDistribution9O - IO0 (A)so - 89 (B)75 - z9 (c)70 - 74 (D)Below 70 (F)

TallyMarks

t

iiiii

Total number ofGrades

Percent Sector

Circle graph for #41

Probability- complete the following- be sure to reduce all fractions

Given the table of outcomes answer the questions 8 - 10:

Roll of a dice:

Roll Number

1

2

3

4

5

6

7

Outcome

2

1

3

,3

4

-1

2

Roll Number

8

9

10

11

12

13

14

Outcome

1

4

5

6-

1

2

5

42. The experimental probability of rolling a number less than 4 was iS

43. The experimental probability of rolling an even number was

44. The experimental probability of rolling a 6 and then a 3 was

Given the table - answer questions 11 - 15

Rolling a dice and flipping a coin:

Event Dice Coin Event

(1 - 6) (H or T)1 4 H 6

2 1 H 7

3 5 T 8

4 6 T 9

5 4 T 10

45. The experimental probability of rolling a 4 and a head

Dice(1 - 6)

5

6

2

5

2

Coin(H or T)

T

H

T

H

H

iÿ

¢

46. The experimental probability of rolling a number less than 3 and a tail I ÿ,J / ÿ

,t-

49. The experimental probability of rolling an even number and a tail / J /ÿ

48. The experimental probability of rolling a 3 and a head / cÿ

47. The experimental probability of rolling a 5 and a tail

Use the following information to answer questions 16 - 18

There is a container with 26 tiles with the letters of the alphabet on them andanother container with the tiles with the numbers 0 - 9 on them.

50. What is the probability that Elizabeth will draw a letter of her name and an evennumber ÿ

51. What is the probability that Jonathan will draw a letter of his name and a number that

52. What is the probability that Sally Smith will draw a letter of her name and the

number 7 ÿ ' ÿ ÿ l

Use the following information to answer questions 19 - 23

There is a container full of 32 marbles. There are 6 red marbles, 8 blue marbles,

5 yellow marbles, 7 green marbles and 6 purple marbles.

53. What is the probability that you will pull out a red marble, then without replacement

pull out another red marble? ÿ ...... .ÿ ......

54. What is the probability that you will pull out a green marble, then replace it and pull

out a blue marble?

/

55. What is the probability that you will pull out a yellow marble and not replace it, then

pull out a purple marble and not replace it, and then pull out a blu marble?

.)

56. What is the probability that you will pull out a red marble replace it then a blue marble

do not replace the blue marble, then pull out a yellow marble? jÿ

jtt

57. What is the probability that you will pull out 3 yellow marbles in a row, without

replacing after each grab. o'ÿ" , _; , .s>-