7R - Final Exam Review Packet (WITH ANSWERS).notebook€¦ · 7R Final Exam Review Packet (WITH...

7R Final Exam Review Packet (WITH ANSWERS).notebook June 08, 2016

Answer Key

> > >< <

9, 5, 3, 0, 3, 6

0.24 (any fraction or decimal)11

44

102 2100

|102 + 2||104|

|102 + 2|same as #10

104

10 212

(102 2)(100)100

|104| 104

4 4 4

((40)40

the opposite of 3 squared

(9)9

93 39

negative 3 squared


73

+

8 2520 10 + 5 012 20 21 + 14

700 78 99 105

12 31 5 6

110 + 85 = x25 = x 25 feet below sea level

22 (8) = x30 = x 30 degree difference

16 + 9 = x7 = x 7

352 33

1

37 5

17949 7

18


41

14

35

6 peaches 4 plums

15 marbles 7 blue

15 11

20 11 2 20

7 8

30 7 1 15

13 24 23 4

2 1 1

5 3 2

1 36 1 14


4 7

2 11

10 27 27

10 9

32 32 9

5 4 7

4 2 8 3

2 1 1 7

4 315 2

6.07; 6.6; 6.7; 6.75

5958.7

58.6958.686

44.14.104.100

>< 03.30

>

0.125 5.6 3.25

100 75

10 6 4

4 3

5 3 4

10 8

5 4


3.17 2.74 6.76 11.83

+3.54

5.52 0.64 0.528 0.9462

0.6 6.6 2.18 48

314 2 +

318

312 3 3

7 31 2 2 3 + 2 3

4 32+ 4

3 31

14

1.6 ( )

2.1

3 (1.6) + 2 ( )

3.8 21.6 + ( )

0.3

25 1.6 6( )

26.421

21

21 2

1


n + 12n + 7

15x2y 20 + 72

x

(2n 3)3 (12 + x)(

(

((

5x x2y 3y 75x x 2y 3y5 1 2 3

7

1

4a 10b 8 2a 74a 2a 8 74 10 28 7


10x + 30 10x 30 10x 30 10x + 30

xy + xz xy + xz xy + xz xy + xz

7x + 2 2y + 5z 2y + 9z 7

5x + 8y 6 a 13b + 7 20 + 10y 27 3y7y 7

GCF: 5 GCF: 3x GCF: 4 GCF: 4y

GCF: x GCF: 5 GCF: 5

x (1 y) 5 (3m + 10) 5 (3a 4b + 2c)

9x + 27y9(x + 3y)

8x 6x + 8 + 2

2x + 102(x + 5)

6x + 186(x + 3)


4c - 6 = 2

44c = 8

+ 6

4

+ 6

c = 2

-4 = 2x - 2

2-2 = 2x + 2

2

+ 2

-1 = x

-5 = 3m - 14

39 = 3m

+ 14

3

+ 14

3 = m

0 = 8z + 8

-8-8 = 8z

- 8

-8

- 8

-1 = z

** Checks for #'s 1 4 on Next Slide **


4c - 6 = 212

3?

2 = 2√

4 2 -6 = 28 - 6 = 2

?

check #1

-4 = 2x - 212

3?

-4 = -4√

-4 = 2 -1 - 2?

check #2

-4 = -2 - 2

-5 = 3m - 1412

3?

-5 = -5√

-5 = 3 3 - 14

-5 = 9 - 14

?

check #30 = 8z + 81

2

3?

0 = 0√

0 = 8 -1 + 8

0 = -8 + 8

?

check #4


9

-1 = 4 - 5x

-5-5

- 4

1 = x

- 4-5 = -5x

12 - 3x = 6

-3

- 12

-3x = 2

- 12-3x = -6

31

- 2.5

x = 3.6

x + 2.5 = 3.713

x = 1.2- 2.5

13

31

-

m =

12 m + = 3

514

35 - 35

12 m = 7

2021

710-

-21

-6x - 21 = 3

-6-6x = 24

+ 21

-6

+21

x = -4

6x + 6 = 10x + 30- 10x- 10x

-4-4x = 24-4

- 6-4x + 6 = 30

- 6

x = -6

2x + 5 = 20

22x = 15

- 5

2

- 5

x = 7 or 7.5 12

5y - 17 = 13

55y = 30

+ 17

5

+ 17

y = 6

--6 - 11 = 2x + 1

- 17 = 2x + 1 - 1- 1

- 18 = 2x 22

-9 = x


No NoYes Yes

50 20 -2 0

x > -2

- 12 - 12x ≤ -3

x + 12 ≤ 9

-3 0

+ 15x > 34

-15 + x > 19+ 15

340

-0.9x > 0.54-0.9 -0.9

x < -0.6

-0.6 0

12- 1

2-

x < 14

0 14

-7-7

n ≤ -5

-2x ≥ 10-2 -2

-5 0

-2x + 7 ≥ 17

+ 7

- 5x

x ≤ -4

8x - 7 ≤ 5x - 19

3 3

- 5x3x - 7 ≤ - 19

+ 73x ≤ -12

-4 0

10

+ 10x ≥ 3

+ 1010x - 10 ≥ 20

10x ≥ 3010

30


n + 4 ≤ 13

4n + 9 ≥ 303 ≤ 54

x

(n 6) < 9( (n 11 ≥ 17

4x + 9 ≤ 30

3x + 5 ≥ 13

( ( (2n + 9) < 376(x 3) > 24( (

3x 4 ≤ 5

5 x > 8


16x = 9

16x = 14416 8

x = 35

8x = 2808

3x = 6

3 (x+4) = 30

3

3x + 12 = 30- 12 - 12

3x = 18

3.5 0.3 = 0.7 1.5?

1.05 = 1.05

Yes3 2

5 2

4 3

7 3 =?

7 2

10 3 =?

No

60x = 555

60n = 33,3006060 900 =37 n

555 red blood cells would be expected.

10 n =1 3.5 1x = 35

1n = 351 The actual distance to

the food court is 35 m.

6 n =1 4Length:

1n = 24

1n = 241

6 n =1 3Width:

1n = 18

1n = 181

Length = 24ftWidth = 18 ft


3 shortcakes10 quarts2 1

= 2 1 3 quarts/ shortcake

3 weeks6 inches = 2 inches/ week

5

4 hours$25 = $6.25/ hour

20 pounds$14.99 = 0.7495 $0.75/ pound

50 pounds$37.99 = 0.7598 $0.76/ pound

The 20 pound bag is a better buy because it costs less per pound.

2 CD's$26.50 = 13.25 $13.25/ CD

3 CD's$40.00 = 13.3333... $13.33/ CD

The 2 pack of CD's is a better buy because it

costs less CD.


$8/lb $8.50/lb $9/lb**16 oz = 1 lb


5 2

yy

x x

* Remember: The C.O.P. (Constant of Proportionality) is the value of y when x = 1.


4 5

3

c = 3g$60

42 gallonsy

x

# of gallons

Cost

1 2 3 4 5

3691215

6 70 8

The Constant of Proportionality is the value of y when x = 1.

The graph repersents a proportional relationship because it is a straight line that passes through the origin.

Looking at the graph, when x = 1, y = 3. Therefore the constant of proportionality is 3.


1.2

23.5%

320 0.15

2825

325

OR 1

47 200

120%

83.3% OR 83 %13

350

112%

0.83

0.06

p 95

12 100

=

11.4 = p

1140 = 100p100100

15 b

60 100

=

25 = b

1500 = 60b6060

23115

= r 100

115115r = 20R = 20%Rate

#

115r = 2300


n 5.49

6 100

= 0.3294 = n

32.94 = 100n100100

5.49 + 0.33 = $5.82 per roll5.82 4 = 23.28

$23.28

Let n = sales tax per roll

n 192

25 100

=48 = n

4800 = 100n100100 Mary earned

$48 commission.Let n = amount of commission

n 85

15 100

=12.75 = n

1275 = 100n100100 Jenny paid $72.25 for the boots.

discount = $12.75Sale Price = 85 - 12.75 = 72.25

Let n = amount of discount

Let n = amount of tax n 99.50

7.5 100

=7.4625 = n

746.25 = 100n100100

The bicycle costs $106.96.

tax = $7.46Total = 99.50 + 7.46 = 106.96

n 350

12 100

=

42 = n

4200 = 100n100100 42 people will win a door prize.

Let n = # of people who win a door prize

Let R = % of question he got correct4260

= r 100

6060r = 70, R = 70%

60r = 4200 Robert got 70% of the

questions correct.

13.4975.99

= r 100 75.99

r = 17.7523... R ≈ 17.8%

75.99r = 1349 It was a 17.8%

decrease in price.75.99

Let R = % of decrease in price


n 22

5.25 100

=

1.155 = n

tax = $1.16

bill = 22+1.16 = 23.16

n 23.16

15 100

=

3.474 = n

tip = $3.47Total = 23.16+3.47

= $26.63

Let n = amount of tax Let n = amount of tip

Find the discount first:

n 300

= 30 100

90 = n

The discount is $90$300 - $90 = $210

Now find the sales tax on the discounted price:

n 210

= 8 100

16.8 = n

The tax is $16.80.$210 + $16.80 = $226.80

Let n = amount of discount Let n = amount of tax

I = PRTI = 4,000 (0.06) (3)I = 720Interest = $720

Evie will owe$720 interest.

T = 3 years

I = IP = $4,000R = 6% 0.06

I = PRT165 = P 0.045 165 = 0.03P

0.035500 = P

T = 8 months years

I = $165P = PR = 4.5% 0.045

You would have to invest $5500.2

3

23

0.03

0.75 11.75

= r 100

75 = 11.75r

6.3829... = r

Let R = % error

The percent error is about 6.4%.

Amount of error: 12.5 - 11.75 = 0.75

R ≈ 6.4%

Actual: 11.75 11.75 11.75


12

12

A = bh

A = (8) (5)

A = 20 ft2

A = bhA = (11.2) (5) A = 56 in2 1

2A = (b1 + b2)h

12

A = (2.3+1.6)1.3

A = 2.535 cm2

C = πdC = π 20C = 20πC = 20π mm

A = πr2

A = π (10)2

A = 100π

d = 20, so r = 10

A = 100π mm2

C = πdC = π 10C = 10π

C = 10π m

A = πr2

A = π (6)2

A = 36π

d = 12, so r = 6A = 36π in2

12 = r

The radius is 12mThe diameter is 24m

C = 2πr 24π = 2 π r 2π 2π

24π = 2 π r21


A B

A A = lwA = 15 8A = 120

B A = bhA = 12 6A = 36

12

12

Total Area = 120 + 36Total Area = 156 m2

2mTotal Area = A + B

AB

A A = lwA = 5 3 A = 15

BA = 4 3A = 12

Total Area = 15 + 12Total Area = 27 ft2

A = lw

5 ftTotal Area = A + B

AB

A A = lwA = 9 8 A = 72

BA = 5 2A = 10

Total Area = 72 + 10Total Area = 62 yd2

A = lw

Total Area = A - B8 yd

SA = 2lw + 2lh + 2wh = 2(15)(5) + 2(15)(10) + 2(5)(10) = 150 + 300 + 100

= 550

SA = 550 m2

l w

h

V = lwhV = (15)(5)(10)

V = 750 m3

22


V = lwh13

V = (5)(7)(12)13

V = 140 in3

V = ( bh)h12

V = ( 12 8) 1512

V = 720 ft38

1215

23


24


heads

tails

heads

tails

headstails

headstails

heads

tails

headstails

headstails

8 possible outcomes

skirtsblousesx3 4 = 12 12 outfits

5 Total = 20 pens

1

=20 4 7 20

3 + 4

0 20

= 0 (impossible) 3 20

3 + 0 20 20

1 3 20

0 20

0 (impossible)(certain)

5 + 3 + 8 + 4=

5 20

4 20

1 20

= 5 20

4 19

1 19

= 3 20

8 19

1 57

= 5 18

8 20

3 20

3 50

=

25


108

67

3

Total = 34

10 34

= n 500

5000 = 34n3434

n = 147.0588...

About 147 people would like comedies.

158 9

sum of terms # of terms

= 17.5

11, 12, 15, 17, 18, 19, 20, 21, 25

median = 18mode = none

meanmean = 17.5

medianrange 25 - 11 = 14 range = 14

41 10

sum of terms # of terms

= 4.1

2, 2, 3, 3, 3, 4, 5, 6, 6, 7median = 3.5mode = 3

mean mean = 4.1

median

range 7 - 2 = 5range = 5

2, 2, 3, 3, 3, 4, 5, 6, 6, 7mode

26


18 26 21

213 10

= 21.3

18, 18, 20, 21, 21, 21, 22, 22, 24, 26

mean

median

range 26 - 18 = 821.3 21 8

14 15 16 17 18 19 20 21 2322 24 25 26 27 2815 27

15, 21, 22, 22, 23, 24, 272221 24

24 - 213

27 - 1512

mean = 154 7

= 22 |22 - 15| = 7 |22 - 23| = 1|22 - 21| = 1 |22 - 24| = 2|22 - 22| = 0 |22 - 27| = 5|22 - 22| = 0

MAD = 16 7

= 2.2857... MAD ≈ 2.3 27


scale: 1 cm = 4 m

12 cm

9 cm

length = 12 cm; width = 9 cm

Length:

48 = x1 1

48 = 1x 1 4

12 x

=Width: 1 4

9 x

=36 = x1 1

36 = 1x

length = 48m width = 36m

Area = lwA = 48 x 36 A = 1728 m2

scale: 1 cm = 12 m

3 cm4 cm

solve for length

1 12

x 48

=

4 = xlength = 4 cm

solve for width

1 12

x 36

=

3 = x

width = 3 cm

12 1248 = 12x

12 1236 = 12x

AIt's median time is 5 minutes faster, it also has a lower range and IQR (interquartile range)

50%75%

is 5 minutes faster, it also has a lower range and IQR (interquartile range) so it's data are more clustered together.

A It's median time

28


x 6

28 8

=21 = x

168 = 8x8 8

21 ft

big little 12

28 9 x

=21 = x

252 = 12x12 12

21 ft

little big

50 125

complementary

x = 37.52

x + x + 15 = 90

- 15

2

2x + 15 = 90

2x = 75- 15

37.5 + 15= 52.5

37.5

x = 54.54

x - 38 + 3x = 180

+ 38

4

supplementary

4x - 38 = 180

4x = 218+ 38

54.5 - 38= 16.5

3 54.5= 163.5

36

2x x = 272

90 + 36 + 2x = 180

- 126

2

2x + 126 = 180

2x = 54- 126

29

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