ep math pre-algebra workbook answers...2020/05/27 · ep math pre-algebra workbook answers d[y 4...

EP Math Pre-Algebra

Workbook Answers

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EP Math Pre-Algebra Workbook Answers

D[y 1 Order of Operations

D 40 14

2 16

49 11

44 3

64 7

4 124

D[y 1 Practice

A 14 37

51 35

36 22

1000 34

57 29

3 43

29 101

26 14

B 16 5

3 9

8 54

D[y 2 Number Properties

C (27 + 23) + 15 = 50 + 15 = 65

(16 + 34) + (8 + 12) = 50 + 20 = 70

(4 x 5) x 13 = 20 x 13 = 260

(5 x 2) x (7 x 5) = 10 x 35 = 350

8 x (20 + 7) = (8 x 20) + (8 x 7) = 216

(30 + 6) x 5 = (30 x 5) + (6 x 5) = 180

9 x (50 + 5) = (9 x 50) + (9 x 5) = 495

(8 x 6) + (8 x 7) = 48 + 56 = 104

(4 x 8) + (5 x 8) = 32 + 40 = 72

(5 x 9) − (5 x 4) = 45 − 20 = 25

(8 x 6) − (3 x 6) = 48 − 18 = 30

D[y 2 Practice

A O

O O

O O

B O

O O

C (4 x 5) + (4 x 7) = 20 + 28 = 48

(8 x 5) + (3 x 5) = 40 + 15 = 55

(7 x 9) − (7 x 4) = 63 – 28 = 35

(6 x 8) − (2 x 8) = 48 – 16 = 32

D[y 2 Practice (Continued)

D (45 + 15) + 28 = 60 + 28 = 88

(56 + 14) + (9 + 11) = 70 + 20 = 90

(5 x 6) x 12 = 30 x 12 = 360

3 x (6 x 5) x 7 = (3 x 30) x 7 = 630

8 x (50 + 4) = (8 x 50) + (8 x 4) = 432

(30 + 5) x 7 = (30 x 7) + (5 x 7) = 245

E 105 420

88 630

75 960

D[y 3 Divisibility Rules

C 2, 3, 4, 6, 9 3, 5, 9

2, 3, 6, 9 2, 3, 4, 6, 9

2, 3, 4, 5, 6, 10 2, 4, 5, 10

2, 3, 4, 6, 9 2, 3, 4, 6, 9

2, 3, 4, 5, 6, 9, 10 2, 4, 5, 10

D O O O O

O O O

O O O O O O

D[y 3 Practice

A 2, 3, 5, 6, 9, 10 2, 3, 4, 6

2, 3, 4, 6, 9 2, 3, 4, 6, 9

3, 5, 9 2, 4

2, 3, 4, 6, 9 3, 5, 9

2, 3, 4, 6 2, 3, 6, 9

2, 4, 5, 10 2, 3, 4, 6, 9

B O O O O

O O O O

O O O

C 81, 375, 6288

D[y 4 Prime Factorization

D 2, 3, 5, 7, 11, 13, 17, 19, 23, 29

E Prime Prime

Composite Composite

F 22 x 32 2 x 3 x 13

2 x 32 x 5 2 x 52

22 x 3 x 7 32 x 7

33 x 11 2 x 32 x 19

5 x 7 x 17 23 x 34


D[y 4 Practice

A 7, 17, 37, 47, 67, 97

B Prime Composite

Prime Prime

Composite Composite

C 22 x 5 2 x 5 x 7

22 x 17 3 x 52

3 x 29 23 x 7

32 x 19 22 x 3 x 13

23 x 3 x 5 x 7 34 x 11

D 32, 117, 972

D[y 5 GCF and LCM

D GCF = 4 LCM = 48 GCF = 5 LCM = 150

GCF = 6 LCM = 120 GCF = 16 LCM = 96

GCF = 9 LCM = 180 GCF = 27 LCM = 162

D[y 5 Practice

A GCF = 3 LCM = 36 GCF = 5 LCM = 60

GCF = 8 LCM = 48 GCF = 14 LCM = 84

GCF = 15 LCM = 75 GCF = 4 LCM = 288

GCF = 16 LCM = 160 GCF = 8 LCM = 120

GCF = 9 LCM = 108 GCF = 24 LCM = 144

B 10 a.m.

7 baskets

12 tiles

D[y 6 Adding and Subtracting …

D 4/7 2/9 8/11 6/7

E 1 1/4 1/2

1 2/3 2/5

4 1/9 2 1/2

5 3 1/5

D[y 6 Practice

A 3/5 5/8 4/9 5/14

B 1/2 1/7

1 1/4

2 3/4 1 2/3

2 2/7 5 1/2

6 1/5 3 2/3

5 1/9 1 1/5


C 16 3/5 lbs

18 1/4 yrs

2 2/3 lbs


C 1 1/2 19/30

1 3/14 5/14

2 17/20 2 5/8

5 1/18 2 1/2

3 19/24 5/12

D[y 7 Practice

A 1 3/2 3 12/7 7/5 2 13/9

B 1 11/36 3/20

1 3/8 5/12

3 5/12 3 3/8

2 2/45 3/4

6 3/8 1 5/18

4 23/36 2 1/3

C 4 3/5 gallons

4 1/4 cups

18 1/8 rows

D[y 8 Multiplying and Dividing …

D 1/6 4/5

4 1/5 7/12

1 3/4 1 3/4

4 1/14 4/9

D[y 8 Practice

A 7/2 11/4 12/7 37/8

B 2/7 1 1/9

1/6 1/20

11 2/3 56

16 2/3 10/27

42 1 7/18

22 1/2 1 7/8

C 10 3/14 miles

Sandy

1/4 gallon


D[y 9 Estimating Sums and …

E 1/2 0 1 1/2

F 1 1/2 1/2

1/2 1

3 1/2

6 3

D[y 9 Practice

A 1/2 0 1 1/2

B 1/2 1/2

1 1/2

1 1/5 1

3 2 1/2

4 1/2 1/2

8 3

C About 6 miles

About 2 1/2 feet

About 4 1/2 gallons

D[y 10 Estimating Sums and …

C 2 1/2 1/6

3 3/5 1/7

3 1 7/8

7/10 2

2 1/10 2 7/9

20/21 1 7/8

D[y 10 Practice

A 13 1/2 1/10

7 1/8

9/10 7/15

1 1/2 1 19/35

4/9 5/28

2 2/5 1 7/8

B 1 1/44

D[y 11 Decimal Place Value and …

C Tenths Hundredths Ones

Tens Tenths Thousandths

D 0.05 15.7

0.012 0.132

E 2.09, 2.9, 2.91, 9.2 1.002, 1.02, 4.78, 4.87

D[y 11 Decimal Place … (Continued)

F 40 35 35.1 35.09

870 873 873 872.96

1,610 1,610 1,609.8 1,609.8

D[y 11 Practice

A Tens Hundredths Thousandths

Hundredths Ones Tenths

B 0.9 0.027

0.011 0.402

5.6 30.27

128.549

C 2.03, 2.3, 3.2, 3.21 0.42, 4.077, 4.2, 4.707

0.01, 0.1, 0.101, 0.11 0.97, 0.973, 7.23, 9.73

D 10 10 9.5 9.53

40 39 38.6 38.59

200 204 203.5 203.5

6,000 5,996 5,996.2 5,996.19

E 0.247 0.038 0.007


B 48.7 6.6

47.42 3.45

9.653 1.864

70.25 16.18

114.42 5.347

21.005 5.853

4.419 513.796

10.543 9.586

D[y 12 Practice

A 62.52 24.6

42.7 2.552

45.48 23.891

51.712 27.28

38.32 5.322

9.203 23.052

22.98 9.857

B $14.72

39.92 inches

11.2 °F

$29.81



C 6.23 0.45

12.28 7

9.125 8.3

27.229 96

31.314 9.25

D[y 13 Practice

A 6.72 8.3

4.152 26

16.72 37

3.848 180

0.063 8.05

112.406 126

1.6245 82.05

B 24.5 inches

$5.80

165.1 cm

$2.60

D[y 14 Absolute Value and Opposites

D 0 11 236

8 45 603

E 0 9

4 ‐15

F ‐9, ‐4, 0, |‐4|, |‐8|, 9 ‐8, ‐2, |‐1|, 7, |‐8|, 16

‐7, ‐1, 1, 2, |‐5|, |‐6| ‐10, ‐6, ‐5, 2, |‐4|, |‐11|

G ‐53

0

$512

D[y 14 Practice

A False, True, True, True, False

B 1 32 116

7 56 1027

C 1 ‐9

‐7 23

D ‐2, 0, |‐3|, |‐5|, |‐6| ‐9, ‐8, 0, |‐9|, |‐11|, 23

‐7, ‐5, 1, |‐5|, 7, |‐8| ‐13, ‐10, ‐2, |‐1|, 2, |‐5|

E ‐17, 11, 4.2


C 3 ‐11 ‐18

9 2 3

‐11 10 ‐30

‐14 3 ‐5

D ‐11 30

10 16

‐18 17

‐8 ‐4

E ‐8 °C

7th floor

11 °C

D[y 15 Practice

A False, False, False, True

B 9 ‐5 6

2 2 ‐17

12 ‐11 ‐26

‐14 ‐2 7

C 14 15

‐4 ‐6

22 22

‐18 ‐2

D $53

6 °C

$425

16 °C


B Examples will vary. Sample:

Like signs: 6 ÷ 3 = 2 ‐6 ÷ ‐3 = 2

Unlike signs: 6 ÷ ‐3 = ‐2 ‐6 ÷ 3 = ‐2

C ‐63 ‐1 4

40 ‐24 35

‐5 ‐7 7

D ‐47 1

‐31 ‐12

56 22

E $386

‐1,100 feet

29 hours


D[y 16 Practice

A False, True, False, False

B ‐42 ‐1 12

35 ‐24 28

‐28 15 ‐5

C ‐30 ‐14

‐63 ‐4

28 31

D $6,770

4 minutes

70 feet/minute

D[y 17 Operations with Negative …

C 11.25 ‐60

‐3.405 ‐12.4

‐4.085 ‐218.88

‐17.65 3.5

‐0.877 ‐8.712

0.816 2.009

‐19.03 ‐8

5.033 5.35

D[y 17 Practice

A ‐2.32 ‐3.5

‐4.58 ‐256.2

‐2.379 0.82

‐0.247 ‐0.378

‐4.004 ‐14.6

3.045 0.4368

‐6.195 0.92

B $16.60

‐1.4 °C

$75.60

D[y 18 Coordinate Plane

C (‐4, 4) Q2 (1, 3) Q1

(0, ‐2) None (1, ‐4) Q4

(3, ‐3) Q4 (4, 0) None

(‐2, 0) None (‐3, ‐3) Q3

(‐5, 2) Q2 (5, 4) Q1

D C Q2 E None

A Q1 I Q3

H Q4 D Q2

G None J Q1

B None F Q4

D[y 18 Practice

A False, True, False, False

B (3, 4) Q1 (3, ‐3) Q4

(1, 0) None (‐3, 1) Q2

(‐2, ‐4) Q3 (‐4, 3) Q2

(0, ‐2) None (5, ‐2) Q4

(‐5, ‐2) Q3 (1, 2) Q1

C E None F Q2

D Q2 C Q4

H Q1 I Q3

J None B None

A Q3 G Q4

D (‐1, ‐2)

(‐4, 1)

D[y 19 Catch up and Review!

B Yes 0.3

2 x 3 x 3 x 3 8.82

GCF = 8, LCM = 48 3.6

11/24 20

8/27 Q4

D[y 19 Practice

A True, True, False, True, True

False, True, False, False, True

B 4.47 0.283

1.28 0.5

37.6 0.419

C 7 − ‐5 = 12 ‐24 ÷ 8 = ‐3

+ × ÷ ×

‐3 − ‐9 = 6 ‐4 − ‐7 = 3

= = = =

4 45 6 ‐56

‐7 + ‐8 = ‐15

+ ×

9 × 5 = 45

= =

2 ‐40


D[y 20 Ratios and Rates

D 8/9 8:9 8 to 9

5/60 5:60 5 to 60

4/15 4:15 4 to 15

E 3 to 2 6:7 5/3

2:3 3/2 5:3

F $7.40/ticket 76 heartbeats/minute

$18/hour 54 customers/hour

D[y 20 Practice

A 29/14 29:14 29 to 14

24/3 24:3 24 to 3

10/40 10:40 10 to 40

B 3 to 4 3/7 2:5

3:5 3/4 5/3

2/7 2:3 2 to 3

C 0.75 inches/hour 18 seats/row

62 miles/hour 256 births/minute

D 24 miles

Kyle

Carter

Store M

D[y 21 Proportions

D x = 6 x = 25

x = 15 x = 18

x = 9 x = 49

x = 7 1/5 x = 22 2/5

x = 12 1/2 x = 19 1/5

D[y 21 Practice

A x = 15 x = 6

x = 6 x = 36

x = 20 x = 37 1/2

x = 57 3/5 x = 9 3/8

x = 10 x = 25

x = 3 1/2 x = 4 4/5

B 14 cups

72 miles

15 boys

2,040 m

D[y 22 Fractions, Decimals, and …

D 3/5 0.6 60%

3/4 0.75 75%

5/8 0.625 62.5%

19/40 0.475 47.5%

27/50 0.54 54%

D[y 22 Practice

A > = >

< < =

B 1/8 0.125 12.5%

4/5 0.8 80%

14/16 0.875 87.5%

7/20 0.35 35%

18/24 0.75 75%

13/25 0.52 52%

C 0.25

15%

3/5

6/15

D[y 23 Percent of a Number

D x/800 = 45/100

x = 360

24/160 = x/100

x =15%

99/x = 22/100

x = 450

x/325 = 16/100

x = 52

E 16%

$195

$1.68

$252

$23.60


D[y 23 Practice

A 60% 0.6 3/5

35% 0.35 7/20

144% 1.44 1 11/25

378% 3.78 3 39/50

B x/400 = 65/100

x = 260

153/x = 90/100

x = 170

18/75 = x/100

x = 24%

x/700 = 48/100

x = 336

126/x = 70/100

x = 180

56/350 = x/100

x = 16%

C 40%

$46.20

$116.60

$2.60

Store M

D[y 24 Percent of Change

B +80% ‐45% +240%

C 27 92 84

C $756

$29.40

Ali

D[y 24 Practice

A +70% +210% ‐30%

‐25% +150% ‐80%

B 455 36 126

806 163 2,352

C 30%

18%

$180.80

$36.72

Store M

21%

D[y 25 Converting Metric Units

C 14,000 m 0.35 g 200 mL

2.3 kg 2400 L 235 cm

1.5 kL 0.005 km 8,000 mg

D 22.4 km

6 liters

10 kg

D[y 25 Practice

A kg g

cm mL

mg km

mm kL

B 5,900 mg 4,200 cm 0.09 kL

0.035 L 11,000 g 700 mm

0.097 km 0.082 kg 430 mL

50,000 mL 1.7 m 5.13 kg

C 6 bottles

192 cm

0.03 kL

680 kg

370 g

D[y 26 Converting Customary Units

B 6 ft 28 qt

264 ft 93 yd

22.5 lb 25 gal

C 6 pounds

96 cookies

13 pieces

D[y 26 Practice

A lb gal

in mi

ft yd

oz c

B 44 oz 1,584 ft

168 in 24 c

5.25 lb 35.5 ft

70 gal 63 yd

C 6 cups

8 ounces

2.5 gallons

Mark

D[y 27 Converting Units of Measure

B 2.3 kg About 15 cm

About 60L 2,300 m

About 15 mi About 14 oz

25.6 c 0.004 kL

About 4 c 136 oz


D[y 27 Practice

A 5400 mL 0.42 m

28 yd About 1,362 g

About 750 mL 20,000 mg

About 310 in 66.4 pt

4.8 lb About 6.5 gal

B 0.6 m

0.25 kg

Carol

Alex’s

Container P


B 65 miles per hour

x = 48

3 2/5

15.3

34%

About 40 cm

D[y 28 Practice

A 210 words/page $5.99/pound

$26/hour 28 miles/gallon

B x = 14 x = 56

x = 10 x = 75

C 60, 38, 100, 92, 3/4

D[y 29 Squares and Square Roots

D 4 36 0.25

64 81 1.21

121 144 1.69

E 1 5 7

2 8 13

6 9 15

F 24 13

20 ‐8

D[y 29 Practice

A 1 9 0.04

16 25 0.36

49 64 1.44

100 169 2.25


B 0 2 0.1

3 6 0.7

5 9 1.1

12 13 1.4

C 11 9

1 27

‐73 ‐6

D 81, 25, 45

D[y 30 Rational and Irrational Numbers

D 3/1 125/100 or 5/4

7/10 13/5

E Irrational Irrational

Rational Rational

Rational Rational

Irrational Irrational

D[y 30 Practice

A The 4th statement is false.

B 0/1 106/10 or 53/5

11/10 29/7

C Rational Rational

Rational Rational


Irrational Rational

Rational Rational

Rational Rational


Rational Irrational

D Every integer can be written as the integer over

1.

D[y 31 Approximating Square Roots

B 1, 4, 9, 16, 25, 36, 49, 64, 81, 100

D 4 & 5 7 & 8

5 & 6 13 & 14

E 3 8

7 11

F √8, 4, √17, 5, √31 5, √26, √32, 6, √7

√60, 8, 9, √88, √92 √93, 11, 12, √150, 13


D[y 31 Practice

A True, True, True, False

B 1 16 49 100 169

4 25 64 121 196

9 36 81 144 225

C 4 & 5 9 & 10

7 & 8 14 & 15

D 4 9

6 12

E √3, 2, √7, √8, 3 √15, 4, √18, 5, √27

√39, 7, √50, 9, 11 √84, √93, 10, √113, 13

D[y 32 Approximating Square Roots

C 4 & 5 8 & 9

7 & 8 10 & 11

D 2.8 6.7

4.5 9.1

5.9 10.2

9.6 11.3

E 2, √5, 2.6, √8, 3 4, √19, 4.7, 5, √28

D[y 32 Practice

A 6 & 7 9 & 10

7 & 8 12 & 13

B 3 6

6 11

C 1.7 4.7

3.9 6.8

5.8 10.9

8.1 13.1

9.5 14.5

D 6, √37, 6.5, √47, √50 7, √50, 7.3, √65, 8.6

√79, 9.1, √92, 9.7, √99 9, 9.2, √89, √95, √101

D[y 33 Simplifying Square Roots

D 4√2 2√5

2√7 3√2

3√5 3√7

3√3 4√6

4√5 8√2

2√6 7√3

D[y 33 Practice

A 2√2 4√2

4√6 2√5

6√2 4√3

3√7 2√6

3√5 2√7

2√3 8√2

7√2 7√5

5√2 6√3

3√3 5√6

3√6 4√7

5√3 6√5

D[y 34 Simplifying Square Roots

C 4√6 7√3

9√5 13√7

30√3 ‐14√2

5/6 4√5

1 10√3

D[y 34 Practice

A 6√6 11√2

35√2 2√5

12√2 ‐9√3

9√7 29√7

12√5 7√6

40√3 16√3

24√6 6√5

21√5 11√2

2/3 ‐5

2 1/5 2√2

D[y 35 Simplifying Surds

C Rational numbers are marked:

4√5 2√3

6√6 18

4√7 1√6

52 0

√5 4√5

5 ‐6√2


D[y 35 Practice

A Rational numbers are marked:

6√2 10

9√3 3√14

4√13 40√21

12√5 9√3

75 2√11

15√11 0

3 ‐√7

2√3 7√13

3/5 ‐4√11

√7 22

D[y 36 Pythagorean Theorem

E Yes Yes No

F 10 3√2

3√5 2√13

5√3 13

D[y 36 Practice

A Yes No Yes

No Yes Yes

B 5 √5

5√2 16

26 6√3

C 5 + 3√5

5√5

D[y 37 Cubes and Cube Roots

E 125 ‐1 0.008

27 729 ‐0.064

‐512 216 ‐0.343

F 9 ‐21

‐6 12

15 24

D[y 37 Practice

A True, True, False, False

B ‐8 64 0.001

512 27 ‐0.125

343 ‐1000 0.216

C 5 ‐18

7 32

‐16 28

14 ‐30

D 0 9

‐3 2


B 17

π, √2

7

2√7

16√3

10

‐997

D[y 38 Practice

A False. √4 is rational because √4 = 2.

B 5.29 36,100

0.55 2600

1.7 0.003375

C 3√7 9√2

8√3 7√5

15√6 13√2

D 2750, 169, ‐3

D[y 39 Exponents

F 1 1/49 ‐81

32 1/125 ‐64

1 1/100 1/81

G 1 1/3 7 4/5

1 5/9


D[y 39 Practice

A 0 1/25 ‐32

49 1/8 ‐1/1000

81 1/1 81

16 1/216 ‐1

1 1/400 1/64

B 81 7 7/8

4/9 9

2 2

2/5 26

8 2

‐1/125 16

‐5 1/3 ‐1 1/2

D[y 40 Negative Exponents

C ‐8 1 ‐1/64

1/25 81 1

‐343 ‐729 1/10000

D 2 1/2

3 1/5 ‐1/2

‐1/2 4

2 2/3 16

‐8 ‐10,000

‐8/9 ‐96

D[y 40 Practice

A 16 ‐1/36 ‐1/125

1/64 ‐729 196

‐81 1/16 1/100

B 4 2

1/32 ‐1/9

64 2 1/2

‐16 54

‐2 2/3 36

‐1/9 ‐1/3

C x = 7 x = 3

x = 2 x = ‐1

x = ‐3 x = ‐2

D[y 41 Simplifying Exponents

E a5 a‐3

a4 a‐2

F 5x6 x2/y5

6x7 ‐20y3/x4

2/x ‐4x/y3

D[y 41 Practice

A c11 c3

c‐3 c‐9

c4 c‐5

B 4x5 x6y3

14/x3 ‐27y5/x2

3/x2 ‐3x/y2

10/x8 4x2y/z5

C 25 15

1 36

‐16 1


E a6 a‐20

9a2 (1/4)a‐2

(1/25)a2 ‐27a‐3

C 4x10 16x6/y10

‐27/x12 x12y8/16

16/x4 ‐8y12/x9

D[y 42 Practice

A c20 c‐10

125c3 (1/64)c‐2

(1/16)c2 ‐32c‐5

B 9x14 32x20/y15

x15/64 x12y6/64

25x16 27x6/y15

16/x28 ‐x15/y6

C 1/8 16

81 18

1/7 1/4


B 9x7 16x‐6

24x‐8 ‐48x11

‐10x11 2x18

3x3 (1/27)x3

10x‐8 36x‐10


D[y 43 Practice

A O O

O O O

O O O

B 4x5 36x‐6

35x‐1 (1/49)x‐18

‐14x6 32x11

6x‐7 3x4

4x‐13 9x10

(‐1/5)x5 25x4

‐3x‐2 27x‐8

D[y 44 Scientific Notation

C Yes No

Yes No

D 23,000 0.0063

527,000,000 0.0000328

7,425,000 0.0001229

E 3.2 × 107 3.2 × 10‐7

1.59 × 109 7.28 × 10‐4

2.543 × 108 9 × 10‐11

D[y 44 Practice

A No No

Yes Yes

B 1,500 0.00073

830,000,000 0.00000034

2,270,000 0.0000916

17,800,000 0.00449

656,200 0.000005103

C 7.5 × 104 5 × 10‐11

6 × 1010 2.14 × 10‐4

1.95 × 109 3.67 × 10‐8

8.2 × 106 5.04 × 10‐7

6.123 × 108 6 × 10‐10

D 3 × 105

9.3 × 107

2 × 10‐8

1 × 10‐12

2.7 × 107

3.3 × 108

D[y 45 Scientific Notation

D 1.5 × 106 7 × 10‐5

1.4 × 104 3.6 × 10‐7

7.5 × 103 5 × 10‐6

8 × 10‐6 6 × 1013

1.6 × 103 1.8 × 10‐6

D[y 45 Practice

A 6,000 45,420

0.00003 0.0000028

20,000 137,000

B 3.29 × 10‐5 1.45 × 108

2.7 × 10‐8 5 × 10‐11

8.3 × 106 2.736 × 109

C 5.4 × 1010 3.3 × 10‐2

2 × 104 1.15 × 10‐7

4 × 109 2.7 × 104

D 5 x 102

2.1 x 10

1.728 x 1011

D[y 46 Reciprocals in Algebra

D 9 ‐2 2/5 7/23 ‐6/25

E x5 x3y4 y2/x4 2/x2

F Left column:

12x8 ↔ (1/12)x‐8

(1/8)x‐12 ↔ 8x12

(‐1/3)x3 ↔ ‐3x‐3

Right column:

(1/9)x‐5 ↔ 9x5

(1/27)x3 ↔ 27x‐3

(1/36)x‐2 ↔ 36x2


D[y 46 Practice

A 3 1/2 ‐2 4/5 4/11 ‐7/38

9/13 ‐6/29 1 3/5 ‐3 5/7

B 1/2x x2 xy x2/y2

x3 1/x4 y3/x5 x3/y5

C Left column:

28x6 ↔ (1/28)x‐6

(1/64)x‐10 ↔ 64x10

(5/8)x4 ↔ (8/5)x‐4

‐5x‐4 ↔ (‐1/5)x4

Right column:

‐5x3 ↔ (‐1/5)x‐3

(1/2)x10 ↔ 2x‐10

(3/4)x‐2 ↔ (4/3)x2

81x8 ↔ (1/81)x‐8


B 1/25

x‐1

X9

1.25 x 10‐6

2 x 1011

x3

D[y 47 Practice

A 64 1/7

12 5

B a3 9v2/u6

3pq6/r2 4s5t2

C 3.2 x 10‐5 1.5 x 104

2.5 x 102 4 x 10‐7

D ‐3, 6, 15


B False, True, True, True, False

True, True, False, True, True

False, False, True, True, False

True, False, True, True, False, False

D[y 48 Practice

A 4 9

7 2

90 0.024

24 75

8 2

10 9

6 5

B

5

-5 0 5

C

-5

C 5 3√17 5√2 2√29

D[y 49 Measuring Angles

D ∠AOD =140° ∠BOA = 20° ∠COE = 130° ∠EOD = 40° ∠BOD = 120°

E Use your protractor to check the accuracy of

your construction.

D[y 49 Practice

A ∠AOE = 165° ∠DOB = 100° ∠COF = 130° ∠BOC = 15° ∠EOD = 30°

B ∠PQR = 135° ∠QRS = 100° ∠RSP = 70° ∠SPQ = 55° Sum = 360°

C Use your protractor to check the accuracy of

your construction.

B

A

C

D


D[y 50 Angle Relationships

C Right Acute Obtuse

D Suppl. Comp. Neither

Neither Suppl. Comp.

E 60° 35°

44° 73°

74° 31°

D[y 50 Practice

A Obtuse Acute Right

Acute Straight Obtuse

B 45° 16° 70°

32° 60° 49°

C 90° 145° 60°

113° 96° 25°

D The 2nd and 3rd statements are true.

E 67° 130°

131° 38°

93° 75°


D 44° 28°

124° 130°

E 45 107

D[y 51 Practice

A ∠2 ∠7 ∠2, ∠4, ∠8

B Suppl. Vertical Comp. Corresp.

C 27° 108°

138° 64°

60° 45°

D 18 13


C Alt ext. Comp. Alt int. Vertical

D 113° 88°

E 14 7

32 112

D[y 52 Practice

A Alt int. Comp. Alt ext. Vertical

Vertical Alt ext. Suppl. Corresp.

B 13 56

170 15

10 36

90 28

D[y 53 Triangles

C A/E O/I A/S R/I

A/I R/S O/S A/E

D 60° 53° 48° 35°

D[y 53 Practice

A O

O

O

B D, F, G, H B, E, I A, C, J

D, H C, E, F, I A, B, G, J

C 34 6

8 15

13 101

D[y 54 Quadrilaterals

C Rectangle, Square

Rhombus, Square

Trapezoid, Kite

Rectangle, Square

Parallelogram, Rhombus

Rhombus, Square, Kite

D Square Kite

90° 82°

Rhombus Trapezoid

123° 84°


D[y 54 Practice

A O O

O

O

B Rhombus Trapezoid

120° 107°

Kite Parallelogram

129° 105°

C e = 50° g = 80°

f = 50° h = 70°

D Rectangle

Square

Rectangle

Kite

D[y 55 Polygons

D O O O O

O O O O

E Hexagon Heptagon

720° 900°

Octagon Decagon

1,080° 1,440°

D[y 55 Practice

A O O O O

B Pentagon 5 3 540°

Hexagon 6 4 720°

Octagon 8 6 1,080°

Decagon 10 8 1,440°

C 138 122

220 155

D[y 56 Pythagorean Theorem

B Yes No Yes

Yes Yes No

C 8 10

4√3 6√2

D 3√5

4√5

2√26

D[y 56 Practice

A Yes Yes Yes

No Yes No

B 8√2 15

2√5 2√34

2√14 7√3

C 5 km

5 inches

36 cm

9.9 cm

12 feet


B C = 45°, S = 135°

72°

31°

Rhombus

Not a polygon (no straight sides)

No (52 + 62 ≠ 92)

D[y 57 Practice

A 16 109

90 22

25 49

57 115

5 13

B a = 75°, b = 30°, c = 60°, d = 45°

C 180° x (n – 2)

D[y 58 Similar Figures

D A, L

C, E

D, H

F, J

K, N

E 18 5

12 35


D[y 58 Practice

A O O

O

B 5 6

16 36

8.5 14.4

C A & B: 8 9 34 72

16 18 68 288

M & N: 30 4 68 120

45 6 102 270

P & Q: 2.1 4.8 13.8 10.08

3.5 8 23 28

X & Y: 4.8 7.2 24 34.56

3.6 5.4 18 19.44

D[y 59 Similar Figures

B x = 6, y = 10 x = 5, y = 4

x = 24, y = 8 x = 12, y = 10

C 175 feet

15 feet

9 feet

1.5 m

180 in2

64 inches

D[y 59 Practice

A x = 15, y = 24 x = 6, y = 6

x = 15, y = 12 x = 30, y = 25

x = 8, y = 2 x = 52, y = 11

B 16 feet

180 meters

9.6 meters

24 inches

90 cm

2 gallons

D[y 60 Scale Drawings

A 8 in 16 ft

30 cm 60 m

5.5 cm 220 km

6 in 600 miles

D[y 60 Scale Drawings (Continued)

B 102 km

1 in = 4 ft

1.8 x 2.4 cm

16.5 in2

D[y 60 Practice

A 7 in 28 ft

9 in 22.5 ft

3.5 cm 14 m

4.2 cm 210 km

8 in 320 miles

11 cm 165 km

B 50 ft2 187.5 ft2

75 ft2 150 ft2

50 ft2 525 ft2

C $265

75 feet

Type P

1.6 cm

7 feet

D[y 61 Symmetry

D Lines = 2

Order = 2

Lines = 1

Order = None

Lines = 4

Order = 4

Lines = 1

Order = None

Lines = 0

Order = 2

Lines = 1

Order = None

Lines = 2

Order = 2

Lines = 2

Order = 2

Lines = 0

Order = None

Lines = 6

Order = 6

Lines = 1

Order = None

Lines = 0

Order = None

D[y 61 Practice

A True, False, False, True, False

B H: A horizontal line of symmetry exists.

V: A vertical line of symmetry exists.

R: Rotational symmetry exists.

V H HVR V R V

HVR V H V H HVR

R V R HVR V H

C ‐20, 17, 2, 0.05


D[y 62 Transformations

B Rotation Translation Reflection

C

D[y 62 Practice

A


B (‐10, 6)

(3, ‐4)

2 vertices

Quadrant I


A (1, 2) (3, 7) (‐4, 3)

(9, ‐7) (2, ‐5) (‐2, ‐7)

(‐6, 4) (‐3, 0) (3, 5)

B (5, 3) (5, ‐3) (‐5, ‐3)

(4, ‐9) (‐4, ‐9) (‐4, 9)

C (0, 1) (‐1, 0) (1, 0)

(2, 3) (‐2, ‐3) (3, ‐2)

D (0, 2) (‐5, ‐4) (‐5, 4)

(‐3, 5) (3, 5) (7, 2)

(‐4, 0) (0, ‐4) (0, 4)

(6, ‐2) (9, 5) (‐9, ‐5)


D[y 63 Practice

A

B (1, 0) (1, 0) (9, ‐3)

(3, ‐5) (‐2, 1) (2, ‐1)

(‐2, 1) (‐1, ‐2) (1, ‐2)

(0, ‐3) (0, ‐3) (‐7, 1)

(‐5, ‐2) (‐2, ‐9) (9, ‐2)

(‐3, ‐7) (3, 7) (3, ‐7)

C

7

6

5

4

3

2

1

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9

-1

-2

-3

-4

-5

-6


A (3, 6), (3, 3), (6, 3)

(0, 2), (2, ‐3), (‐2, ‐1)

(‐6, 4), (0, 10), (4, ‐2)

B

8

7

6

5

4

3

2

1

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8

-1

-2

-3

-4

-5

D[y 64 Practice

A False, True, True, True, False

B (0, 4) (‐4, 0) (‐2, 0)

(7, ‐2) (7, ‐2) (‐7, ‐2)

(‐2, 0) (0, ‐5) (0, 5)

(8, 16) (8, ‐16) (2, ‐4)

(3, ‐1) (9, ‐3) (1, 1)

(‐9, 5) (‐2, ‐3) (‐2, 3)

C

7

6

5

4

3

2

1

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8

-1

-2

-3

-4

-5

-6

C E

A

B

D

B C

A D

F

E

C E F

B A

D



B 20 feet

90 miles

Lines = 2, Order = 2

(1, 1)

(6, ‐4)

D[y 65 Practice

A x = 20, y = 9 x = 10, y = 8

B 2 2 1 None

4 4 2 2

0 2 0 None

3 3 1 None

C (3, 5) (‐5, 3) (5, 3)

(‐4, 0) (‐2, 0) (1, ‐4)

(7, ‐5) (0, 0) (0, 0)

(0, ‐9) (0, 9) (0, ‐9)

D 6, ‐3, 0

D[y 66 Perimeter and Area of …

E 50.24 in 48 m 28 ft

F 12.56 m2 1.44 ft2 42.5 in2

21.16 m2 27 ft2 40 m2

D[y 66 Practice

A 31.4 m 25 ft 34 cm

7.2 m 43.96 cm 44 in

B 57.6 m2 254.34 in2 76 ft2

314 cm2 71.75 cm2 706.5 in2

34.8 in2 27.2 m2 78.75 m2

D[y 67 Area of Composite Shapes

C 39 in2 36.5 m2

13.42 cm2 39.25 in2

147.07 in2 185.04 ft2

D[y 67 Practice

A 81 in2 27 ft2 78.5 cm2

35 m2 135 cm2 150 in2

B 42 in2 174 ft2

8.56 m2 362.34 cm2

C 42.84 yd 51.4 cm

128.52 yd2 146.5 cm2

D[y 68 Volume of Prisms and …

D 105 in3 315 cm3

706.5 m3 160 ft3

64 cm3 502.4 cm3

630 in3 810 m3

D[y 68 Practice

A 904.32 ft3 3,375 cm3

168 in3 56 in3

405 cm3 351.68 in3

120 in3 1,260 in3

B x = 8 ft y = 4 in

D[y 69 Volume of Pyramids and …

D 125 cm3 73.5 cm3

125.6 in3 471 cm3

360 in3 1,406.72 m3

D[y 69 Practice

A 157 in3 56 cm3

64 m3 753.6 m3

254.34 in3 189 in3

120 in3 1,570 ft3

1,584 cm3 715.92 m3

D[y 70 Surface Area of Prisms and …

C 142 m2 144 ft2

299.2 in2 190.4 in2

D[y 70 Practice

A Cube, Triangular prism, Cube, Square pyramid

B 25 + 15 + 15 + 15 + 15 = 85 cm2

C 72 in2 184 ft2

480 cm2 56.4 in2

161 ft2 472 m2

D[y 71 Surface Area of Cylinders …

E 263.76 m2 505.54 cm2

94.2 in2 527.52 ft2


D[y 71 Practice

A 816.4 m2 847.8 cm2

113.04 ft2 175.84 in2

235.5 cm2 439.6 cm2

276.32 in2 477.28 cm2

642.6 m2 452.16 ft2

D[y 72 Volume and Surface Area …

A 512 in3 384 in2

226.08 in3 207.24 in2

314 ft3 282.6 ft2

300 in3 280 in2

36 m3 84 m2

401.92 cm3 452.16 cm2

288 in3 264 in2

1,130.4 in3 602.88 in2

384 ft3 384 ft2

720 cm3 516 cm2

D[y 72 Practice

A 549.5 in3 376.8 in2

180 m3 240 m2

1017.36 m3 678.24 m2

216 cm3 252 cm2

192 m3 256 m2

B 230 in3

242 in2

351.68 in3

251.2 in2

293.09 cm3

401.68 cm2

301.44 in3

401.92 in2


B 126 cm2

1,000 in3

50.24 m3

600 in2

452.16 ft2

D[y 73 Practice

A 9 cm 9.8 in

7 in 8 ft

B 2,198 in3

1,004.8 in2


C 36 in3

78 ft2

785 cm2

72 in3

1,570 cm3

6 in

D[y 74 Measures of Center

A Mean: Median: Mode:

6 6.5 8

5.2 5 3, 7

14 13 12, 13

28 27 No mode

20 21.5 21.5

D[y 74 Practice

A Mean: Median: Mode:

7 8 9, 8

7.5 8 9

5 5 4, 3, 6

9 10 10

27 28 No mode

1.9 1.4 0.9

4.66 5 No mode

64 55 55

378.5 427.5 429

D[y 75 Box-and-Whisker Plots

D 1st data set: 4, 6, 7, 9, 10

2nd data set: 30, 33, 37, 42, 44

E The 1st and 4th statements are correct.

103 4 5 11

6 7 8 9

4430 32 34 46

36 38 40 42


D[y 75 Practice

A O

O O

B The 2nd and 4th statements are correct.

C The 3rd and 4th statements are correct.

D M = $6, N = $4

Store M

75%

50%

25%

D[y 76 Practice

A 50 cups B Emily

240 cups 15 miles

40 cups/day 30 miles/runner

C Grapes D 6 students

20% Median = 3, Mode = 3

5 students 2.9 hours/student

D[y 77 Scatter Plots

B It shows a positive correlation, which means

that the hourly pay rate increases as experience

increases.

C Above $60/hr and close to $70/hr

D Negative

About 3K

The colder it gets, the more jackets the store

sells.

D[y 77 Practice

B Positive None Negative Positive

C The 2nd graph shows the best ‘line of best fit.’

D Positive

About 80%

Students good at math tend to do well in

physics also.

D[y 78 Choosing a Data Display

C First 4 answers: Next 3 answers:

Bar graph Scatter plot

Circle graph Line graph

Line graph Circle graph

Dot plot

D[y 78 Practice

A First 8 answers: Next 7 answers:

Dot plot Line graph

Circle graph Circle graph

Bar graph Bar graph

Scatter plot Scatter plot

Line graph Line graph

Bar graph Bar graph

Dot plot Dot plot

Scatter plot


A mean = 4.8, median = 4.5, mode = 3

The right plot is correct.

54 students

See Day 77, Part C.

Line graph

D[y 79 Practice

A 5.5 5 4

1.1 1.2 None

7 7 8, 6

10 11 11

110.4 109 None

B The 1st and 3rd statements are correct.

C The 1st and 3rd statements are correct.

D 5, 5, 8

4, 4, 5, 7

6, 8, 8, 9, 9

2, 4, 4, 6

D[y 80 Sets and Venn Diagrams

F {1, 2, 4} {7, 8, 9, 10}

{8} {8}

{7, 8, 9 10} {7, 9, 10}

G {1, 5}

{6, 10, 11}

{4, 9}

{2, 3, 7, 13, 14, 15}


D[y 80 Practice

A (A ∪ B)C (B − A)C

AC ∩ B BC − A

B {1, 2, 3, 5} {3, 5}

{4} {1, 3, 4, 5}

{2} {4}

C (A ∪ B ∪ C)C (A ∪ B) − C

C ∪ (A − B) (B ∪ C)C ∩ A

D {1, 2, 3, 5, 6} {3}

{4} {1, 2, 5}

{2, 3, 6} {2}

E {3} {8, 10, 14}

{2, 4, 6, 12} {3, 6, 9, 12, 15}

{6, 12} {5, 7, 11, 13}

D[y 81 Subsets

E 2, 4, 16, 32

F A set with n elements has 2n subsets.

G O O O

O O

D[y 81 Practice

A {}, {2}, {4}, {6}, {2, 4}, {2, 6}, {4, 6}, {2, 4, 6}

B {}, {3}, {5}, {3, 5}

C {4, 5, 7, 8, 10}, # of subsets = 32

D O O O

O

O O

E O O

O O

O O O

E O

O

O

O O

O

D[y 82 Sample Space and Tree …

B 123, 132, 213, 231, 312, 321

1 2 3

2 3 1 3 1 2

3 2 3 1 2 1

C 16, 25, 36, 49, 64, 81

11, 12, 13, 21, 22, 23, 31, 32, 33

HHH, HHT, HTH, HTT, THH, THT, TTH, TTT

D 24

9

12

A B BA

BA A B

A

C

B A B

C

A B

C

A B

C


D[y 82 Practice

A RT, RG, RN, BT, BG, BN

R B

T G N T G N

RR, RB, RR, RB, BR, BR

R R B

R B R B R R

B 26 alphabet letters

12, 13, 14, 21, 23, 24, 31, 32, 34, 41, 42, 43

H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6

TTT, TTF, TFT, TFF, FTT, FTF, FFT, FFF

C 36

42

25

8

20

D[y 83 Counting Principle

B 6 x 6 x 6 = 216

2 x 2 x 2 x 2 x 2 = 32

4 x 3 x 6 = 72

9 x 9 x 9 x 9 = 6,561

9 x 8 x 7 x 6 = 3,024

D[y 83 Practice

A 3 x 3 = 9

10 x 26 = 260

3 x 3 x 2 = 18

6 x 7 x 12 = 504

4 x 4 x 1 = 16

3 x 2 x 1 = 6

4 x 4 x 4 x 4 = 256

26 x 25 x 24 x 23 = 358,800

5 x 25 x 24 x 23 = 69,000

D[y 84 Factorials

B Examples will vary. Sample: 5! = 5 x 4!

D 25! 56!

8! 15!

9! 11!

E 6 720

4 56

15 12

E 4,896 19,460

5,460 1,197

D[y 84 Practice

A 4! 6!

13! 1000!

9! 48!

6! 100!

B 24 120

210 120

30 45

C 5,040 362,880

5,040 10,920

1,938 22,386

D 145 = 1! + 4! + 5!

D[y 85 Permutations and …

D P 4 x 3 x 2 x 1 =24

P 5 x 4 x 3 x 2 x 1 = 120

C (15 x 14 x 13 x 12)/(4 x 3 x 2 x 1) = 1,365

P 11 x 10 x 9 = 990

C (25 x 24 x 23)/(3 x 2 x 1) = 2,300

D[y 85 Practice

A 123, 132, 213, 231, 312, 321

B 12, 21, 13, 31, 14, 41, 23, 32, 24, 42, 34, 43

C 12, 13, 14, 23, 24, 34

D 123, 124, 134, 234

E P 6 x 5 x 4 x 3 x 2 x 1 = 720

C (52 x 51 x 50)/(3 x 2 x 1) = 22,100

P 6 x 5 x 4 x 3 = 360

C (8 x 7 x 6 x 5)/(4 x 3 x 2 x 1) = 70

C (10 x 9 x 8 x 7 x 6)/(5 x 4 x 3 x 2 x 1) = 252

P 20 x 19 x 18 x 17 = 116,280


D[y 86 Permutations and Factorials

E P 5! = 120

C 22!/17! divided by 5! = 26,334

C 15!/10! divided by 5! = 3,003

P 8!/4! = 1, 680

P 30!/27! = 24,360

D[y 86 Practice

A 42 9

252 55

102 115

B P 8! = 40,320

P 8!/5! = 336

C 10!/6! divided by 4! = 210

C 12!/6! divided by 6! = 924

P 18!/15! = 4,896

P 26!/22! = 358,800

C 40!/(40 − 2)! divided by 2! = 780


B {1, 2}

{}, {2}, {3}, {5}, {2, 3}, {2, 5}, {3, 5}, {2, 3, 5}

H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6

30 outfits

90

Combination

24 ways

D[y 87 Practice

A {1, 2} {24}

{4, 8, 12} {3, 6}

B 3 280

15 11

C 120

5,040

220

1,140

D 10, 4, 15

D[y 88 Odds

C 1:5 5:1

2:1 1:2

1:1 1:1

1:2 2:1

D[y 88 Odds (Continued)


1:1 8:0

0:6 3:1

1:2 0:9

2:1 2:3

D[y 88 Practice

A 1:1 1:1 B 1:1

6:0 0:6 9:1

0:6 6:0 0:10

1:2 2:1 10:0

5:1 1:5 1:4


6:0 2:5

1:3 2:1

7:1 1:3

0:10

D[y 89 Probability of Simple Events

A 6 1/6

1, 2, 3, 4 2/3

2, 3, 5 1/2

3, 6 1/3

B 25% C Clear

0% 20

75% 0.2

25% 0.8

0.9

0.1

D[y 89 Practice

A 0.25 B 89%

0.75 5%

0.375 19%

0.625 5%

12%

0%


5/26 7/10

3/5 3/4

5/12 2/45

3/4 2/3


D[y 90 Probability of Compound …

A 1/25 B 1/20

6/25 3/10

1/25 0

C 1/12

1/4

1/6

1/12

D[y 90 Practice

A 1/81 B 1/72

1/81 0

4/9 4/9

1/3 1/3


1/8 1/5

5/36 4/25

5/12 1/6

1/32 5/126

D[y 91 Experimental Probability


2/3 2/9

3/5 7/11

1/4 3/13

D[y 91 Practice

A 25% B 12%

50% 20%

30% 90%

45% 36%

42%


2/5 6/11

1/3 3/8

7/15 1/25


B 1/3

1/4

4/9

2/5

3/5

D[y 92 Practice

A 2/3 B 1/2

1/3 4/9

4/5 13/18

0 1/18


4/7 5/36

3/5 4/15

9 1/6


B True, True, False, True, False

True, True, False, True, True

False, True, True, False, False

True, False, False, True, True, False

D[y 93 Practice

A > > <

= < >

B O O O

O O O O

O O O O

C

‐7 18 13 15 1

710

125

28 8 ‐12 23

10 1

110

‐1

10

3 ‐2 23 45

12 2

‐1.92 4.28 3.04 √2 2√18 √50

6.76 1.8 ‐3.16 4√8 √32 0

0.56 ‐0.68 5.52 √18 √8 √98



B True, False, True, False, True

True, True, False, True, False

True, True, True, True, False

True, False, False, True, True, False

D[y 94 Practice

A V = 628 cm3

SA = 370.52 cm2

B 3/4 C 1/4 1/4

1/8 7/16 1/2

1/4 1/2 7/9

1/4

D[y 95 Writing and Evaluating …

C 15 11 10

64 16 3/16

1 1/2 2 2

6 7 1/4

D 2.9g

45 + 36h

168 − 22d

E $23.20 $153 58 pages

D[y 95 Practice

A 35 25 44

1 20 2/3

2 2 2/9 3 3/4

18 1 5/7 8

B First 3 answers: Next 3 answers:

B 0.85c 20 – 2.7b

10.4/p 68h

42 + 33h 3(n − 15)

C $5.10 $1.30 $174

$3.80 170 miles $18

D[y 96 Simplifying Expressions

D First 5 answers: Next 6 answers:

6x + 3 ‐x + 2y

9x − 3 ‐8x + y

8x + 19 5x + xy + 2

7x − 7 7x2 − x + 2

‐22x + 44 2x2 + 2x + 6

‐8x + 12

D[y 96 Practice

A

O

O

O

B O O

O O O O


5x − 2 6x − 3y − 9

7x − 9 ‐3x + 2xy +3

‐3x − 3 3x2 + x

‐12x + 36 5x2 − 7x

5x + 5y

D 7 + m + 8 = m + 15 11 − m/9

4 + m − 6 = m − 2 3(2m − 5) = 6m − 15

D[y 97 One-Step Equations

E x = 15 x = 62 x = 42

x = 1.6 x = 0.9 x = 8.2

x = 6 x = 9 x = 15

x = 63 x = 0.8 x = 4

D[y 97 Practice

A x = 44 x = 29 x = 62

x = 2.6 x = 5.7 x = 3.25

x = 9 x = 24 x = 7

x = 1.8 x = 0.6 x = 0.9

B 12.5t = 75

6 tickets

m + 255.73 = 1896

$1640.27

k − 24.99 = 33.71

$58.70

b/15 = 35

525 books

D[y 98 One-Step Equations with …

C x = ‐14 x = 31 x = 4

x = 0.2 x = 2.6 x = 0.56

x = 7 x = 7 x = ‐95

x = ‐50 x = 1.2 x = ‐4.34

x = ‐0.51 x = ‐0.09 x = 78.2


D[y 98 Practice

A x = ‐13 x = ‐5 x = ‐77

x = 8.3 x = 1.7 x = 1.05

x = ‐15 x = ‐99 x = 21

x = 27 x = 9 x = ‐8.4

B ‐247 + x = ‐128

119 feet

0.95x = 19

20 problems

4.6x = 23

5 inches

15 + 26 = 11 + x

30 crayons

D[y 99 Two-Step Equations

B x = 2 x = ‐9 x = ‐7

x = ‐5 x = ‐8 x = 7

x = 11 x = ‐25 x = ‐18

x = 16 x = ‐9 x = 12

D[y 99 Practice

A x = 6 x = ‐7 x = ‐12

x = ‐13 x = ‐9 x = 11

x = ‐12 x = 14 x = 16

x = ‐14 x = 16 x = 21

x = 49 x = ‐54 x = ‐36

x = 15 x = 27 x = ‐8

D[y 100 Two-Step Equations with …

B x = 4 x = 8 x = 1.4

x = ‐5 x = ‐1.7 x = 0.9

C x = ‐3/4 x = 9 7/12 x=1 1/4

x = ‐2/3 x = ‐4 x = ‐9

D[y 100 Practice

A x = ‐2 x = 5 x = ‐4.7

x = 0.6 x = 5 x = 0.3

x = ‐4 1/21 x = 3 7/9 x = 1/35

x= 9 1/24 x = 1/4 x = ‐4 2/3

X = 5 3/8 x = 3 x = 2 1/2

D[y 101 Multi-Step Equations

A 3x − 3 4x + 17 ‐6x + 21

B x = 8 x = 5 x = ‐0.9

x = 3 2/7 x = ‐5 x = ‐3

x = 6 x = ‐2 1/3 x = 5

x = 1.4 x = 0 x = 6 1/2

D[y 101 Practice

A x = ‐7 x = 0.9 x = ‐3

x = 6 1/3 x = 8 x = 1.3

x = ‐6 x = ‐3 x = 1 1/2

x = ‐2 x = ‐3 x = 11

x = 2 2/5 x = ‐17 x = 1.9

D[y 102 Equations with Variables …

B x = ‐4 x = 3 1/7 x = 0.15

x = ‐2 3/5 x = 2 x = 3

x = ‐3 x = ‐5 x = ‐2 1/3

D[y 102 Practice

A x = ‐1 x = ‐8 x = 0

x = 2 x = ‐9 1/2 x = ‐7

x = ‐0.05 x = 2 x = 16

x = 3 x = 2 3/4 x = ‐3

x = 0.3 x = 1 x = 6 1/2

D[y 103 Absolute Value Equations

C x = ‐1, x = ‐17 x = 10, x = 4

x = 0.6, x = ‐0.6 x = ‐3, x = 7

x = ‐2/3, x = 2/3 x = 0, x = ‐4/5

x = 31, x = ‐17 x= 17, x = ‐20 1/2

D[y 103 Practice

A x = 2, x = ‐10 x = 13, x = ‐5

x = 3, x = ‐3 x= ‐5, x = 5

x = 5/6, x = ‐5/6 x = 27, x = ‐31

x = ‐1, x = 7 x = 6/7, x = ‐2 4/7

x = 41, x = ‐29 x = 27, x = ‐27

x= 4.3, x = 0.7 x = ‐3, x = 7

D[y 104 Equations of All Types

A Incorrect.

Substitute 9 for x. 14 x 9 is 126, not 112.

C x = ‐32 x = 7.95 x = 1.8, x = ‐1.8

x = ‐70 x = ‐1/2 x = 1 11/20

x = 3 x = ‐8 x = 3, x = ‐1.7

x = ‐14 x = 1/3 x = 1 4/7

x = ‐5 x = ‐16 x = ‐2


D[y 104 Practice

A x = ‐9 x = ‐2.4 x = 6, x = 2.4

x = 84 x = ‐1/9 x = 3 3/5

x = 13 x = 1.2 x = ‐1, x = 3 2/5

x = ‐7 x = 5/8 x = ‐1 1/6

x = ‐2 x = 0.07 x = 3

x = 1 x = ‐1/2 x = ‐4

D[y 105 Equations Word Problems

B 4x = 21.2

5.3 cm

3.14 2x = 31.4

5 inches

x + (x + 1) = 13

6

x + 0.15x = 1.38

$1.20/lb

x + 3x = 112

$28

x − 1.9 = 7.6

9.5 pounds

0.75x = 43.5

$58

15 + 6x = 45

5 hours

D[y 105 Practice

A 6x = 80.4

$13.40

3x = 17.7

5.9 cm

3.14x = 94.2

30 cm

x + (x + 2) = 18

8

x + 29 = 37

8 years old

x − 26 + 17 = 30

39 paper cups

x + (x + 16) = 34.4

$9.20

30 − 2x = 4.7

$12.65

x − 0.1x = 108

$120/share

24x = 1296

$54/month

D[y 106 Rewriting Equations and …

C y = ‐x − 4 y = 2x y = ‐5x + 7

y = x/3 – 2/3 y = x + 3 y = x – 1/2

y = 2x/5 y = x/3 + 10 y = 3x/4 – 6

D h = V/(πr2) P: 10 in

h = (SA ‐ 2πr2)/(2πr) Q: 5 cm

D[y 106 Practice

A y = ‐5x y = 2x + 7 y = ‐4x + 5

y = ‐3x Y = x/2 + 12 y = ‐3x

B w = A/l h = A/b

b = 2A/h b1 = 2A/h – b2

C 192, 23, 45


B 25

‐8x + y + 5

x = 35 x = ‐13

x = ‐8 x = 0.9

x = 5 x = 3

x = 7, x = ‐2 y = 2 – x/3

9

D[y 107 Practice

A 2x + 8 = 50

x = 21

9x – 15 = 93

x = 12

3x – 10 = 116

x = 42

10x = 180

x = 18

4x – 13 = 31

x = 11

5x – 5 = 80

x = 17

6x – 3 = 75

x = 13

82 – 4x = 50

x = 8

B 14x = 126

x = 9 cm

6x/2 = 30

x = 10 in

36 + x = 60

x = 24 in

10 + 2x = 22.4

x = 6.2 m

18x = 108

x = 6 in

12 + 4x + 6x = 52

x = 4 ft

D[y 108 Writing and Graphing …

C O

O

O O O

O O

D k < 3 k ≥ ‐2 ‐5 < k ≤ 10

k > ‐8 k < 45 ‐18 ≤ k < ‐8

E x < 15

x ≥ 473

0 < x < 100

x ≤ 1,500


D[y 108 Practice

A O O

O O

O O

B 2, 3, 4, 5 5, 6, 7, 8 4, 5, 6

‐1, 0, 1, 2 ‐3, ‐2, ‐1 None

C

m > ‐6 s ≤ 8

‐10 ‐6 ‐2 5 7 9

q < 15 d ≥ ‐6

‐60 0 ‐60 ‐24 0 24

D x ≤ 10

x > 40

x ≤ 1,500

x ≥ 51

x ≥ 157

D[y 109 One-Step Inequalities

A <, <, >, >

C x ≥ ‐9 x < 43 x ≤ 41

x ≤ 6.59 x > ‐0.3 x > ‐4.03

x < 80 x ≥ ‐1 5/9 x ≥ ‐11/12

x ≥ 7/12 x < ‐5/24 x ≥ ‐2/21

x < ‐8 1/2 x > ‐3 1/8 x ≥ ‐1/10

D[y 109 Practice

A x > ‐24 x > ‐8 x ≤ 14

x ≥ 25 x ≥ ‐2.25 x > ‐0.6

x > ‐60 x ≤ ‐9.1 x ≤ 9

x ≤ ‐171 x ≥ ‐2/15 x ≤ 192

x > ‐1 1/2 x ≥ 81 x < ‐7/20

x > 1/8 x ≥ 4 7/9 x < 4 2/3

x ≤ 6 x ≥ 17 1/2 x < ‐4 3/4

D[y 110 Multi-Step Inequalities

A The second inequality.

B

x > ‐3 x ≤ 5

‐4 ‐0 4 ‐20 0 20

D[y 110 Multi-Step ... (Continued)

C x ≤ ‐6 x < 3 x > 1.7

x ≤ 15 x > ‐2 1/2 x ≤ 3/5

D[y 110 Practice

A

x ≥ 2 x < 0

‐4 ‐0 4 ‐1 0 1

B x ≤ ‐4 x > ‐9 x ≤ ‐2

x < ‐3.8 x ≥ 41 x > 1.68

x < ‐3 x < 1/5 x ≥ 3 1/4

x < ‐3/4 x ≥ 8 x ≥ 1/2

D[y 111 Inequalities of All Types

B x > 15 x ≤ ‐4 x ≤ 22.5

x < ‐1/4 x > ‐14 x < 5

x < 3 x ≤ 3 1/2 x > 1

x ≥ 34 x ≤ 4 x ≤ 1 1/5

x < 1/2 x ≤ ‐36 x ≥ ‐5/6

D[y 111 Practice

A x ≤ 44 x < 8 x < 9

x < 2.3 x > ‐0.75 x ≤ ‐1.85

x > 189 x ≤ ‐1 2/7 x > 1 1/3

x ≥ ‐1 x > ‐3 x > 1/3

x ≥ 24 x < 1/4 x < 10

x < 6 x ≤ ‐4 x > 11/15

D[y 112 Inequalities Word Problems

A Examples will vary. The solution is x ≤ 4.

B 17 + x < 42

Fewer than 25 coins

24 + x ≥ 30

At least 6 miles

14.5x ≥ 250

At least 18 hours

40x > 260

Greater than 6.5 cm

(x − 1) + x ≤ 27

At most 14

x + (x + 9) < 42

Less than $16.50

0.8x + 5 * 1.2 ≤ 20

At most 17 pencils

16 ≤ 8x/2 ≤ 36

4 cm and 9 cm


D[y 112 Practice

A 12 > y − 8 10 < 2z + 3

B 59 + x ≥ 85

At least 26 dollars

1,270 + x ≤ 2,800

Up to 1,530 pounds

18 < (1/2)x

More than 36 problems

1.9x ≤ 25

At most 13 cookies

18 + 2x ≤ 54

At most 18 cm

20 − 12x > 5

Less than $1.25

0.25x > 2000

More than $8,000

(87 + 88 + x)/3 ≥ 90

At least 95


B

m > 6 s ≤ ‐8

2 6 10 ‐11 ‐8 ‐7

x = 17 x = ‐52

x > ‐22 x ≥ ‐4

x = 9 x = 10

x ≤ 1 2/5 x < 15

0.3x + 4 * 0.15 = 3.3

9 pencils

2 * 5.5 + 2x ≤ 24

6.5 cm

D[y 113 Practice

A ‐2, ‐1, 0, 1 4, 5, 6, 7, 8 2, 3, 4

8 ‐3, ‐2, ‐1, 0 ‐2, ‐1, 0, 1

B

x > ‐3 x ≤ 5

‐4 ‐0 4 ‐20 0 20

x ≥ 2 x < 0

‐4 ‐0 4 ‐1 0 1

C 15, 300, 10, 5.5

D[y 114 Graphing Linear Equations …

B

4, 2, 1, 0, ‐2 ‐5, ‐3, ‐1, 1, 3

11

-1

0, 1, 2, 3, 4 ‐4, ‐3, ‐2, ‐1, 0

2

-4 3

-2

D[y 114 Practice

A x = ‐3, 3 x = ‐4, 12

y = 8, 4, 2 y = 3, 1, ‐3

B

‐5, ‐3, ‐1, 1, 3 5, 3, 1, ‐1, ‐3

11

-1

‐1, ‐2, ‐3, ‐4, ‐5 ‐2, ‐1, 0, 1, 2

3

-3

-3


D[y 115 Slope of a Line

D 2, ‐1/3, 3/2

E 1, ‐4, ‐1/2

F y = 10

D[y 115 Practice

A ‐1, 3, 1/2

‐4/5, 2, ‐2/3

B ‐1/2, 3, 6, ‐3/4, 0

C 1

(1, ‐2)


C

m = 1, b = 2 m = 2, b = ‐3

2

-2

-3

m = 2/3, b = ‐2 m = ‐1/2, b = 1

1 3 2

-2

m = ‐1, b = 3 m = 3/4, b = ‐1

3

3-1

D[y 116 Practice

A

m = ‐1, b = ‐1 m = 1/2, b = 3

3

-1-1

m = 4, b = 0 m = ‐2/3, b = ‐2

0 -3

-2

m = ‐2, b = 2 m = 1, b = ‐3

2

1 3

-3

m = 1/4, b = ‐1 m = 3/2, b = ‐2

4-1

-2

B y = ‐5x + 7

2√5



C

m = ‐1, b = 2 m = 1/2, b = 0

2

2 0

m = 5/3, b = ‐2 m = ‐2, b = ‐1

-1

-2

m = ‐1/3, b = ‐2 m = 3, b = 2

2

-2

D y = (‐1/2)x + 6

D[y 117 Practice

A y = ‐6x y = 2x + 5 y = ‐x + 2

B

m = 4, b = ‐4 m = 1, b = ‐2

2

-2

m = ‐2, b = 3 m = ‐1/4, b = 2

32


m = ‐2/3, b = 1 m = 5/4, b = ‐3

-3

m = 1/2, b = ‐2 m = ‐3, b = 1

1

-2


C

x‐int = ‐2, y‐int = 2 x‐int = 1, y‐int = 3

32

-2 1

x‐int = ‐2, y‐int = ‐1 x‐int = ‐3, y‐int = 4

4

-2 -3-1

x‐int = 1, y‐int = 2 x‐int = ‐4, y‐int = 1

21

1

D y = 8


D[y 118 Practice

A

x‐int = ‐3, y‐int = 2 x‐int = ‐3, y‐int = ‐3

2

-3 -3

-3

x‐int = ‐1, y‐int = 4 x‐int = ‐3, y‐int = 1

4

1-1 -3

x‐int = 1, y‐int = 2 x‐int = 1, y‐int = ‐3

2

1 1

-3

x‐int = ‐4, y‐int = ‐1 x‐int = 3, y‐int = 2

2

3-1

B y = ‐4x + 8

12 square units

D[y 119 Horizontal, Vertical, Parallel, …

G

x = ‐1 y = 4

4

-1

D[y 119 Horizontal, … (Continued)

y = ‐3 x = ‐4

-4-3

H Parallel: b and d

Slopes: b = ‐2, d = ‐2

Perpendicular: a and c

Slopes: a = 2/3, c = ‐3/2

D[y 119 Practice

A Parallel Neither

Neither Perpendicular

Perpendicular Parallel

B

42

-65

5

-3

2

7

1

-4


D[y 120 Graphing Linear Inequalities

D The first, second, and fifth pairs.

E

1-1 0

-1

-2

D[y 120 Practice

A

1 4

1 3

-2

-2

3

2


B y = 0

Trapezoid, 9 square units

D[y 121 Catch up and review!

B a = 8, b = 0

3

3

-1

3

-3 -2

D[y 121 Practice

A x + 6 = 2y

y = x/2 + 3

‐6, 3

2y + 6 = x

y = x/2 − 3

6, ‐3

y − 3 = x/‐2

y = x/‐2 + 3

6, 3

x + 2y = ‐6

y = x/‐2 − 3

‐6, ‐3

B Rhombus

5

4

3

2

x 1

-5 -4 -3 -2 -1 0 1 2 3 4 5 6

-1

-2

-3

-4 y

C 36 square units

D ‐6, 12, 3120


D[y 122 Solving Systems of Linear …

C

(0, 2) (‐2, 0)

2

-2

(‐1, 1) (3, 2)

21

-1 3

(0, ‐1) (2, ‐3)

2-1

-3

D[y 122 Practice

A True, False, False

B

(1, ‐1) (3, ‐1)

1 3-1 -1

(1, 4) (3, ‐4)

4

1 3


(‐2, 1) (3, 3)

1-2

(0, ‐1) (‐1, ‐1)

-1-1 -1


C (2, 1) (‐3, 4)

(3, ‐1) (0, 5)

(6, 2) (‐1, 7)

D[y 123 Practice

A (4, 2) (4, 0)

(3, 5) (‐3, ‐4)

(2, ‐6) (‐1, 1)

(5, ‐7) (3, 9)

(‐8, 4) (‐2, ‐5)

(9, 7) (5, ‐10)

D[y 124 Number of Solutions to …

C None One (2, 1)

One (4, 3) Infinite

One (‐3, 0) None

D[y 124 Practice

A The first and last systems.

B One (1, 5) None

None One (‐1, 2)

One (2, ‐3) Infinite

One (‐7, ‐1) None

Infinite One (9, 8)



A Incorrect. It is not a solution to x −3y + 5 = 0.

B (3, 2) None (1, ‐1)

Infinite (2, 4) (‐4, 3)

C (4, ‐5) (2, 7)

(6, ‐4) None

Infinite (‐3, 5)

D[y 125 Practice

A (0, 3) (2, ‐1) None

None (1, ‐4) Infinite

B (5, 0) (4, ‐6)

None (‐2, ‐3)

(1, 9) Infinite

None (‐7, 5)


B (2, 1)

4

1-2 2

(3, 4)

Infinitely many solutions

(2, ‐5)

D[y 126 Practice

A The second and third systems.

B The second system.

C The first and last systems.

D The second and last systems.

E (1, ‐3) None

(‐2, 4) Infinite

(1, 5) (‐4, ‐2)

D[y 127 Writing Linear Equations …

C y = ‐x + 3 y = 2x − 3 y = (‐1/2)x + 1

y = (3/4)x − 1 y = ‐x − 1 y = 4x

y = ‐2x + 2 y = (2/3)x − 2 y = (5/3)x – 2

D[y 127 Practice

A y = x + 2 y = (‐2/3)x − 2 y = (1/4)x − 1

y = ‐2x – 1 y = x − 3 y = (‐1/2)x

y = (3/2)x − 2 y = (‐1/3)x ‐ 2 y = 3x + 2

y = ‐x + 2 y = 4x ‐ 4 y = (1/2)x + 3


C y = x − 8 y = ‐5x − 6

y = ‐2x − 7 y = 3x + 13

y = ‐3x + 11 y = 4x − 15

y = (1/2)x − 9 y = (‐4/5)x − 1

y = (‐1/3)x + 6 y = (3/2)x − 10

D[y 128 Practice

A y = 3x − 8 y = ‐4x + 13

y = 7x − 12 y = 5x − 16

y = ‐2x − 10 y = ‐3x + 12

y = (1/3)x − 7 y = (1/2)x − 6

y = (‐1/4)x + 2 y = (5/4)x − 5

y = (‐2/5)x + 8 y = (‐3/2)x − 1

y = (3/7)x + 5 y = (1/5)x − 8


C y = 2x + 1 y = 4x − 5

y = ‐x + 3 y = (1/2)x − 1

y = (1/4)x + 2 y = 9x − 11

y = 7x + 5 y = (3/4)x + 9

D[y 129 Practice

A y = 3x + 2 y = ‐2x + 6

y = (‐1/2)x + 3 y = ‐4x + 8

y = 4x − 1 y = (3/2)x + 5

y = ‐3x + 4 y = 5x − 12

y = 2x + 10 y = (‐2/7)x + 15

B y = 2x + 10

y = ‐3x + 1

D[y 130 Slope-Intercept Word …

B y = 15x + 30 $210

y = 9x + 15 $42

y = 2.5x + 6.99 $36.99

y = ‐9x + 240 132 gallons


D[y 130 Practice

A y = 38x + 40 $154

y = 25x + 18 $193

y = ‐30x + 750 570 feet

y =2500x + 2800 $15,300

B y = 18x + 50 $266

y = 2x + 8 $44

D[y 131 Systems of Linear Equations …

C x = # of dimes

y = # of nickels

x + y = 17

0.1x + 0.05y = 1.3

Max has 9 dimes and 8 nickels.

x = what Leah paid

y = what Vicky paid

x + y = 550

x = 70 + y

Leah paid $310, and Vicky paid $240.

x = Max’s age

y = Dale’s age

x = y – 5

2(x – 5) = y − 5

Max is 10 years old, and Dale is 15 years old.

x = $ of an apple

x = $ of a pear

5x + 4y = 9.2

3x + 2y = 5

An apple costs $0.80, and a pear costs $1.30.

D[y 131 Practice

A x = # of fives

y = # of tens

x + y = 27

5x + 10y = 205

Mr. Kim has 13 fives and 14 tens.

x = # of roses

y = # of lilies

x + y = 24

2.2x + 1.8y = 48

Josh used 12 roses and 12 lilies.

x = # of adults

y = # of children

x + y = 10

9.5x + 7y = 80

There were 4 adults and 6 children in the group.

x = $ of a muffin

y = $ of a cookie

6x + 3y = 10.2

3x + 12y = 11.4

A muffin costs $1.40, and a cookie costs $0.60.

x = # of nickels

y = # of quarters

x = y + 5

0.5x + 0.25y = 8.5

Lynn has 13 nickels and 8 quarters.

x = Joey’s age

y = Anna’s age

x = 3y

x + 10 = y + 20

Joey is 15 years old, and Anna is 5 years old.

x = tens digit

y = ones digit

x + y = 5

10x + y – 9 = 10y + x

The number is 32.

D[y 132 Catch up and review!

B y = ‐3x + 1

y = 5x + ‐7

y = (‐1/2)x + 4

y = 1.6x + 5 $29

x = # of dimes

y = # of nickels

y = 3x

0.1x + 0.05y = 2

Mia has 8 dimes and 24 nickels.

D[y 132 Practice

A y = (1/2)x y = ‐2x − 1 y = (‐2/3)x + 1

B y = 4x − 3 y = ‐3x + 6

C y = 2x − 4 y = (1/3)x + 2

D 4, 8

2, 9

7, 15

10, 20

D[y 133 Relations, Functions, and …

D The first, second, and last relations.

E 4 10 ‐6

30 3 ‐1

D[y 133 Practice

A The first, third, and fourth relations.

B ‐23 2 8

13 3 20

C 3 ‐11

4 & 10 2 & ‐2

D 24 1 5/18

7 13 5 & 9

D[y 134 Domain and Range of …

A y = 2x − 3 y = (1/3)x − 4 y = ‐3x + 2

B 15, 10, 5 y = ‐5x + 20

Yes

C {0, 1, 2, 3, 4} {0, 5, 10, 15, 20}

D ‐6, ‐4, ‐3, ‐2, 0

{‐3, ‐1, 0, 1, 3}

{‐6, ‐4, ‐3, ‐2, 0}

3, 2, 1, 0, ‐1

{0, 2, 4, 6, 8}

{‐1, 0, 1, 2, 3}

E {0, 1, 2, 3}

{1, 2, 3}

Yes

{‐1, 0, 1}

{‐2, ‐1, 0, 1}

No


D[y 134 Practice

A 2, 1, 0, ‐1, ‐2

{3, 4, 5, 6, 7}

{‐1, ‐2, 0, 1, 2}

‐5, ‐2, 1, 4, 7

{‐1, 0, 1, 2, 3}

{‐5, ‐2, 1, 4, 7}

B {‐2, ‐1, 0, 1}

{‐2, ‐1, 1}

Yes

{‐3, ‐2, ‐1}

{1, 2, 3}

No

{0, 1, 2, 3}

{‐3, ‐2, ‐1, 0}

Yes

{‐1, 0, 1, 2}

{‐1, 1}

Yes

C 3, 9, 15, 21, 27

y = 3x

{1, 3, 5, 7, 9}

{3, 9, 15, 21, 27}

16, 14, 10, 4, 2

y = ‐2x + 20

{2, 3, 5, 8, 9}

{2, 4, 10, 14, 16}

D[y 135 Discrete and Continuous …

C ‐3 ≤ x ≤ 2

‐3 ≤ y ≤ 0

Continuous

{‐1, 0, 2}

{‐1, 1, 2}

Discrete

D f(x) = 5x g(x) = 7.5x

h(x) = 60x + 80 k(x) = ‐4x + 150

E Continuous, Discrete, Discrete, Continuous

D[y 135 Practice

A ‐3 ≤ x ≤ 1

1 ≤ y ≤ 3

Continuous

{1, 2, 3}

{‐2, ‐1}

Discrete

B Discrete Continuous

Continuous Discrete

Continuous Continuous

C f(x) = (1/3)x g(x) = (π + 2)x

h(x) = 1.5x + 5 k(x) = ‐0.8x + 24

D Continuous, Continuous, Continuous, Discrete

E {1, 2, 3} {10.28, 25.7, 51.4}

{12.5, 20, 35} {19.2, 14.4, 4.8}

D[y 136 Linear and Nonlinear …

B Linear Nonlinear Nonlinear Linear

C Linear Linear Nonlinear

Nonlinear Linear Linear

D Linear Nonlinear Linear Linear

D[y 136 Practice

A Linear Nonlinear Linear Nonlinear

B Linear Nonlinear Linear

Nonlinear Linear Linear

C Linear Linear

Nonlinear Linear

D y = (1/2)x2

Nonlinear

y = ‐1.2x + 20

Linear

D[y 137 Function Rules for …

C

x ‐2 ‐1 0 1 2 x 1 3 5 7 9

y 0 2 3 4 5 y ‐2 ‐8 ‐14 ‐20 ‐26

x ‐6 ‐4 ‐2 0 2 x 2 4 6 8 10

y 0 1 2 3 4 y 6 16 26 36 46

D Linear y = ‐x + 5

Nonlinear

Linear y = 4x + 2

D[y 137 Practice

A

x ‐1 0 1 2 3 x ‐5 ‐3 ‐1 0 1

y 3 1 ‐1 ‐3 ‐5 y ‐9 ‐7 ‐5 ‐4 ‐3

x ‐6 ‐3 0 3 6 x 1 3 5 7 9

y ‐7 ‐5 ‐3 ‐1 1 y 4 10 16 22 28

B Linear y = 2x

Linear y = 3x − 2

Nonlinear

Linear y = (‐1/2)x + 3

C y = 8x + 12

y = 5x + 7


D[y 138 Function Rules for Graphs

A

y = x y = (1/2)x + 1

1 -2

y = 3 y = 3x + 1

3

1

y = ‐x − 2 y = ‐2x

-2

-2

B y = ‐x + 1 y = 2x − 2 y = 4x

y = (‐1/2)x + 2 y = ‐1 y = (2/3)x − 2

D[y 138 Practice

A

y = ‐2 y = ‐x − 1

-1-1

-2

y = 2x y = 3x − 2

-2


y = (‐1/3)x y = ‐4x + 1

1

B y = ‐x y = 1 y = (2/3)x − 2

y = ‐2x + 1 y = (1/2)x − 2 y = ‐3x + 4

D[y 139 Function Rules for …

C d = 7 36, 43 d = 3 8, 11

d = ‐5 ‐33, ‐38 d = ‐4 ‐18, ‐22

D 8, 10, 12, 14, 16, … ‐5, ‐13, ‐21, ‐29, ‐37, …

3, 0, ‐3, ‐6, ‐9, … ‐1, 3, 7, 11, 15, …

E 5n − 10 40 ‐2n + 11 ‐9

9n − 3 87 ‐6n + 2 ‐58

D[y 139 Practice

A d = 7 41, 48 d = 3 16, 19

d = ‐2 ‐14, ‐16 d = ‐6 ‐23, ‐29

B 2, ‐3, ‐8, ‐13, ‐18, … ‐9, ‐12, ‐15, ‐18, ‐21, …

‐1, 3, 7, 11, 15, … 5, 14, 23, 32, 41, …

C 5n − 8 42 ‐7n + 10 ‐60

‐4n + 12 ‐28 6n − 8 52

D a1 = 3, d =4, x = 9

a1 = 5, d = 3, x = 13

a1 = 20, d = ‐5, x = 15

D[y 140 Direct variation

D

F No k = 5

k = 2/3 No k = ‐1

G y = ‐x y = 0.3x

y = 2x y = (7/10)x


D[y 140 Practice

A k = 2 No k = ‐3/4 No

B y = (1/2)x y = 5x

y = (1/6)x No

C y = ‐4x No No y = (3/2)x

D y = 3x

y = 5.5x

y = 18x


B Not a function.

Input 2 has two outputs, 5 and 6.

D = {‐4, ‐1, 0, 2} R = {‐2, 3, 5, 6}

Linear y = ‐x + 2

y = ‐2x + 3

nth term = 3n − 1 10th term = 29

y = 2.54x

D[y 141 Practice

A Linear y = 3x − 1

Linear y = (‐2/3)x

Nonlinear

B y = x − 2 y = ‐2x + 1 y = (1/4)x − 1

C 2n + 4 24 4n − 19 21

‐3n + 12 ‐18 ‐7n + 40 ‐30

D y = ‐6x y = (1/5)x


B False, True, True, False, True

True, True, False, False, True

True, False, True, False, False

True, True, False, True, True, True

D[y 142 Practice

A x = 3 x = 4 x = ‐5

x = ‐1 x = ‐5.75 x = ‐2 2/5

B x > 14 x ≥ ‐15 x > ‐1

x > 2 x ≤ 3 1/2 x ≤ ‐3

C 6 feet

9 pencils

4 cm, 9 cm

5 cm

D[y 143 Financial Literacy: …

D P: r: t: I: B:

$130 2% 5 $13 $143

$260 5% 4.5 $58.5 $318.5

$500 6% 2.5 $75 $575

$1,210 4% 5 $242 $1452

$3,200 3.5% 7 $784 $3984

$8,000 7.25% 2 $1160 $9160

E $750

4%

About 4.2 years

D[y 143 Practice

A P: r: t: I: B:

$550 2.8% 5 $77 $627

$300 5% 3 $45 $345

$620 3% 4 $74.4 $694.4

$400 6% 2.5 $60 $460

$740 2.25% 4 $66.6 $806.6

$800 2% 2 $32 $832

$1,900 3% 5 $285 $2185

$6,000 6% 3 $1080 $7080

B $720

$360

12%

5 years

$24,120

Mason


D 3% annual simple interest:

t: P: I: B:

2 $100 $3 $106

3 $100 $3 $109

4 $100 $3 $112

5 $100 $3 $115

3% annual compound interest:

t: P: I: B:

2 $103 $3.09 $106.09

3 $106.09 $3.18 $109.27

4 $109.27 $3.28 $112.55

5 $112.55 $3.38 $115.93


D[y 144 Practice

A 5% annual simple interest:

t: P: I: B:

2 $500 $20 $540

3 $500 $20 $560

4 $500 $20 $580

5 $500 $20 $600

5% annual compound interest:

t: P: I: B:

2 $520 $20.8 $540.8

3 $540.8 $21.63 $562.43

4 $562.43 $22.5 $584.93

5 $584.93 $23.4 $608.33

B $5,520.40 $6,094.97

$7,429.74 $2,429.74

C $800

Account B

$3,951.57


B Before

payment:

Interest

charged:

After

interest:

After

payment:

$1,817.88 $18.18 $599.94 $1,217.94

$1,217.94 $12.18 $605.94 $612.00

$612.00 $6.12 $612.00 $0.00

D $12,000

60 months

$13,260

$1,260

D[y 145 Practice

A Before

payment:

Interest

charged:

After

interest:

After

payment:

$4,187.26 $41.87 $820.87 $3,366.39

$3,366.39 $33.66 $829.08 $2,537.31

$2,537.31 $25.37 $837.37 $1,699.94

$1,699.94 $17.00 $845.74 $854.20

$854.20 $8.54 $854.20 $0.00

B $176.44 or $176.45

D $26.34 $99.24


E 216 5/16 Car pay… 95.80 1,341.86

5/19 Paycheck 520.10 1,861.96

D[y 146 Practice

A 6/3 820.00

6/8 Paycheck 1,800 2,620.00

115 6/10 Rent 124.25 2,495.75

6/15 Transfer 1,000 1,495.75

6/19 ATM 200 1,295.75

6/22 Paycheck 1,800 3,095.75

116 6/27 Car pay… 765 2,330.75

6/30 Clothing 46.28 2,284.47


D $2.11

$40.11

D[y 147 Practice

B $133.53

$187.56

$1.88

$215.68

$1.50

$23.50

$1.19

$22.31


C 80 hours

$2,400

$1,168.40

2 weeks

6.2%

22%

10%

D[y 148 Practice

A 85 hours

$30

$45

$2,625.00

$1,292.94

2 weeks

$4,798.14

10%

$162.75

$577.50

$131.25


D[y 149 Test Preparation Tips

There are no answer keys for these activities.

D[y 150 Test Taking Tips

There are no answer keys for these activities.

D[y 151 Review: Factors and Multiples

B 1, 2, 3, 4, 6, 12 1, 2, 3, 5, 6, 10, 15, 30

C 4, 8, 12, 16, 20 25, 50, 75, 100, 125

D 3, 5, 9 2, 4, 5, 10

E 25 2 x 3 x 7

32 x 7 2 x 32 x 5

F GCF = 3, LCM = 36 GCF = 9, LCM = 108

GCF = 5, LCM = 60 GCF = 24, LCM = 144

D[y 151 Practice

A 1, 2, 3, 6, 9, 18 1, 2, 3, 4, 6, 8, 12, 24

1, 2, 4, 5, 10, 20 1, 2, 4, 7, 8, 14, 28, 56

B 5, 15, 20, 25, 30 12, 24, 36, 48, 60

9, 18, 27, 36, 45 32, 64, 96, 128, 160

C 2, 3, 4, 6, 9 3, 5, 9

2, 3, 4, 6 2, 4, 5, 10

D 22 x 32 22 x 3 x 5

32 x 5 7 x 11

E GCF = 4, LCM = 48 GCF = 15, LCM = 75

GCF = 14, LCM = 84 GCF = 16, LCM = 96

GCF = 15, LCM = 90 GCF = 27, LCM = 162

D[y 152 Review: Number Properties

B (48 + 32) + 25 = 80 + 25 = 105

(17 + 23) + (6 + 34) = 40 + 40 = 80

(2 x 5) x (3 x 7) = 10 x 21 = 210

(8 x 9) x (2 x 5) = 72 x 10 = 720

C 7 x (50 + 8) = (7 x 50) + (7 x 8) = 406

(40 + 3) x 9 = (40 x 9) + (2 x 9) = 378

5 x (70 + 6) = (5 x 70) + (5 x 6) = 380

D 32 49

17 13

28 75

19 14

D[y 152 Practice

A Answers will vary.

B (26 + 14) + 58 = 40 + 58 = 98

(11 + 19) + (2 + 38) = 30 + 40 = 70

(2 x 5) x (3 x 9) = 10 x 27 = 270

(7 x 6) x (5 x 2) = 42 x 10 = 420

C (20 + 7) x 5 = (20 x 5) + (7 x 5) = 135

9 x (50 + 9) = (9 x 50) + (9 x 9) = 531

(40 + 8) x 6 = (40 x 6) + (8 x 6) = 288

7 x (60 + 4) = (7 x 60) + (7 x 4) = 448

D 11 6

8 44

9 19

D[y 153 Review: Integers

A ‐150 +10

+200 ‐14

B 3 ‐9 ‐23

‐56 ‐1 21

12 ‐63 6

C ‐5 18

23 ‐10

‐31 ‐11

D B (0, 3)

A (‐2, 1)

C (3, ‐2)

D (‐2, ‐2)

D[y 153 Practice

A +170 ‐4

+210 ‐18

B ‐8, ‐2, 0, 2, |‐7|, |‐9| ‐15, ‐9, ‐1, 3, |‐9|, |‐11|

C 12 ‐20 3

‐5 ‐7 18

‐12 ‐11 ‐45

C 7 1

23 4

‐54 ‐3

41 58

D B (3, 0)

A (‐3, 1)

C (1, ‐2)

D (1, 2)


D[y 154 Review: Fractions

A 10 8 10 5

B 3/5 3/4 5/9 2/5

C < > > =

D 0.5 1 0 1

E 1 1/2 1

1 3 1/2

6 1/2 2

D[y 154 Practice

A 2 21 3 7

B 3/5 5/7 3/8 5/9

C < > = <

D 1 1/2 0 1/2

E 1/2 1

2 1/2 1 1/2

5 2

F ≈ 4 cups

≈ 3 feet

D[y 155 Review: Operations with …

B 1 2/5

1/3 1 1/9

1 5/12 1/12

13/30 9 1/3

1 5/14 1/15

C 3 1/2 2/9

1 1/6 2 1/10

D[y 155 Practice

A 1 2/3 1/6

1/2 2 2/3

1 2/9 3/7

3/10 4 1/2

1 3/8 1/12

11/20 3/5

5/21 1/15

B 6 1/7

3 1/8 1 9/16


A 21/5 18/7 6 5/6 6 3/4

B 8 2/3 1 2/3

1 2/3 4/5

1 2/5 1 1/7

6 7/18 4 1/8

4 1/4 8

9 5/6 1 1/6

5 7/9 3 2/5

D[y 156 Practice

A 7/2 19/8 23/4 47/6

B 2 2/7 7 4/5 8 2/3 5 5/9

C 9 1/5 4 1/2

6 1/2 4

2 5/9 3 3/4

7 5/12 4/9

3 1/6 5 1/2

17/24 3 1/2

2 7/10 2 17/30

D[y 157 Review: Decimals

B 0.04 12.9

0.015 0.436

C 0.001, 0.01, 0.011, 0.1 2.04, 2.14, 2.4, 2.401

D 3 3.3 3.26 3.256

15 15.1 15.09 15.094

428 428.2 428.21 428.209

E 0.75 0.6 0.55 0.34

F 3/5 1/4 16/25 1 9/20

D[y 157 Practice

A 0.15 0.108

315.527

B 0.08, 0.085, 0.8, 0.85 5.06, 5.6, 6.005, 6.05

C 7 7 7.04 7.035

25 24.9 24.9 24.902

150 149.7 149.74 149.735

D 0.8 0.3 0.7 0.16

0.2 0.625 0.05 0.26

E 4/5 3/4 11/50 1 3/8

3/10 9/25 17/20 3 21/40



B 7.38 24.86

5.845 ‐3.87

‐1.17 ‐115.26

‐10.552 0.147

1.805 4.6

‐7.115 ‐0.9

3.172 ‐2.75

‐3.38 483

D[y 158 Practice

A 17.65 227.2

‐8.736 9.6

‐9.166 ‐213.36

‐26.43 ‐11.8

‐1.883 ‐3.33

1.583 0.999

‐21.96 ‐20.2

5.804 9.8

B $6.91

$11.82

D[y 159 Review: Percents

B 0.26 13/50

0.35 7/20

1.04 1 1/25

2.6 2 3/5

C 1.5 33 520.3

D 60%

increase

25%

decrease

250%

increase

E $45.60

$50.88

$612

$2,970

D[y 159 Practice

A 0.2 1/5

0.55 11/20

1.18 1 9/50

2.84 2 21/25

B 5.6 60 810

C 20%

decrease

35%

decrease

140%

increase


D $64.90

$1.68

$51

$28.50

$41.34

$23.60

$61.20

D[y 160 Review: Perimeter and Area

B 6.6 cm 25.12 in 28 m

C 12 ft2 1.08 yd2 113.04 m2

37.5 in2 1.96 m2 0.7 ft2

D 56.52 ft

169.56 ft2

62.8 in

257 in2

D[y 160 Practice

A 31.4 cm 10.4 ft 48 in

B 7.29 cm2 13.5 in2 8.51 ft2

200.96 in2 33 ft2 96 m2

C 40 cm2 144 in2

10.26 ft2 42.84 m2

D[y 161 Review: Surface Area of Solids

B 294 cm2 606 ft2

480 in2 156 cm2

156 in2 299.2 in2

276.32 ft2 43.96 m2

D[y 161 Practice

A 216 m2 142 m2

72 cm2 600 in2

95 in2 225 ft2

244.92 m2 204.1 cm2

114 in2 452.16 ft2

D[y 162 Review: Volume of Solids

B 343 cm3 945 ft3

420 in3 120 cm3

73.5 cm3 360 in3

351.68 ft3 125.6 in3


D[y 162 Practice

A 216 m3 105 m3

30 cm3 924 in3

56 cm3 64 m3

706.5 m3 753.6 m3

84 in3 715.92 m3

D[y 163 Review: Angles, Symmetry, …

B 21 17 16

9 114 11

C Lines = 2

Order = 2

Lines = 0

Order = None

Lines = 2

Order = 2

Lines = 1

Order = None

Lines = 2

Order = 2

Lines = 5

Order = 5

D x = 10, y = 6 x = 12, y = 10

x = 1, y = 0.8 x = 15, y = 5

D[y 163 Practice

A ∠3 ∠7 ∠1, ∠3, ∠7

B 15 9 65

18 29 18

C Lines = 1

Order = None

Lines = 4

Order = 4

Lines = 0

Order = None

Lines = 1

Order = None

Lines = 0

Order = 2

Lines = 6

Order = 6

D x = 6, y = 10 x = 24, y = 8

x = 10, y = 8 x = 12, y = 10

D[y 164 Review: Data Analysis

B Mean Median Mode

1st data set: 4.8 4.5 2

2nd data set: 2.8 2.7 2.6

C 1st data set: 0, 2, 4, 6, 7

2nd data set: 3, 5, 6, 8, 10

D[y 164 Review: Data … (Continued)

D Cookies

15%

10 students

E Bar graph

Line graph

Circle graph

D[y 164 Practice

A Mean Median Mode

Top left: 3.9 4.5 2, 5

Top right: 3 3.1 No mode

Bottom left: 14 14 15

Bottom right: 4.66 5.14 5.14

B 1st data set: 3, 4, 6, 8, 9

2nd data set: 8, 9, 10, 12, 14

C 75 mm

June

January, February

D Line graph

Scatter plot

Bar graph

Circle graph

D[y 165 Review: Measurement

A 1,200 mg 8,300 cm 0.04 kL

0.027 L 51,000 g 900 mm

B 7 ft 16 qt

792 ft 59 yd

14 lb 32 gal

C About 20 cm About 20 mi

About 68L About 7 oz

7 0 1 2 8

3 4 5 6

9 2 3 4 10

5 6 7 8

92 3 4 10

5 6 7 8

158 9 10 1611 12 13 14


D[y 165 Practice

A 0.034 km 0.066 kg 270 mL

80,000 mL 1.5 m 2.09 kg

B 24 oz 2,112 ft

228 in 36 c

5.5 lb 25.5 ft

C About 1,135 g About 800 mL

About 330 in About 12.5 gal

D 28 km

5 cups

Laura’s

D[y 166 Review: Expressions, …

B 11 25

10 32

C 5x + 10

6x − 14

8x + 30

‐7x − 7y

D k ≤ 4 k > ‐3 ‐4 < k ≤ 8

E b − 5 = 8 d + 3 ≤ 7

8m = 9 q/3 ≤ 2

5k + 6 = 12 2n + 4 > 6

D[y 166 Practice

A 4 ‐24

8 20

B 4x − 5

10x + 1

7x +22

4x + 5y

4x – 2y + 12

C m > 2 m ≥ ‐1 ‐5 < m ≤ 10

D u + 7 = 6 3p = 15

2w – 5 = 9 8 + m/3 = 7

E 12 > y − 8 5p ≤ 4

w + 6 ≥ 15 10 < 2z + 3

D[y 167 Review: Ratios, Rates, and …

B 2:5 5/9 4 to 7

C $18/hour 25 miles/gallon

D x = 9 x = 20

x = 5 x = 35

D[y 167 Review: Ratios, … (Continued)

E 20 feet

63 km

$25

900 km

D[y 167 Practice

A 2/3 4:9 5 to 4

B $5.90/pound 22 points/game

68 miles/hour 2 1/2 inches/hour

C x = 7 x = 25

x = 8 x = 60

D 5.4 feet

108 miles

91.44 cm

$25

$1,760

D[y 168 Review: Linear Equations, …

B

y = x + 2 2x + 3y = 6

2

-2

y > 2x

C y = 4x + 3

y = ‐2x + 5

y = (2/3)x − 2

y = ‐3x + 1

D y = 3x y = ‐2x + 1

E 2n + 1 21 ‐4n + 13 ‐27


D[y 168 Practice

A

y = (3/4)x − 1 2x + y ≤ 1

1

-1

y < 1

1

B y = ‐2x

y = 3x − 4

y = (‐1/2)x + 3

y = ‐x + 5

y = (1/4)x − 5

C ‐1 5 4

D y = x + 5 y = ‐3x + 5

E 3n + 2 32 ‐5n + 26 ‐24

D[y 169 Review: Sets and Counting

B {1, 2, 3, 4, 6} {2, 6}

{1, 3} {1, 2, 3, 5, 6}

C {}, {1}, {2}, {4}, {1, 2}, {1, 4}, {2, 4}, {1, 2, 4}

D 6, 42, 20, 125

E Permutation, 24

Combination, 70

Combination, 455

Permutation, 6840

D[y 169 Practice

A A ∪ B B − A


A BC − A (A ∩ B)C

B {5, 6} {1, 5, 6}

{1} {1, 2, 3, 4, 6}

C {}, {3}, {5}, {3, 5}

D 5, 52, 12, 60

E Combination, 120

Permutation, 120

Permutation, 360

Combination, 435

Permutation, 2730

D[y 170 Review: Square Roots

B 5 0.1 2

9 0.6 ‐4

11 1.4 8

C 4 9

7 10

D 3.3 6.5

4.6 8.1

E 2√5 7√6

6√7 ‐2√3

4/7 6√2

D[y 170 Practice

A 6 0.2 3

13 0.7 5

15 1.1 ‐6

B 5 9

8 11

C 3.6 8.2

5.9 9.1

D 3√2 6√3

6√6 ‐√7

8√5 2√2

3/8 ‐4√3

1 2/3 6√5

A B BA

A B A B


D[y 171 Review: Exponents

B 1 1/25 ‐1/64

‐8 81 1/10000

C 5x7 9/x4

28/x8 ‐8x11

4x3 36/x10

D 13,000 4.2 × 107

0.000058 7 × 10‐11

E 2.1 × 106 1.4 × 10‐4

6 × 103 3 × 10‐6

D[y 171 Practice

A ‐27 16 ‐1/125

196 1/16 1/100

B 2x5 36/x6

‐21x6 4x11

6/x7 3x4

4/x13 49x12

C 6,400 2.8 × 104

0.00003 9.1 × 106

0.0000052 4.07 × 10‐7

D 4.8 × 1010 3.6 × 10‐2

3 × 104 6 × 10‐8

8 × 109 7 × 103

D[y 172 Review: Triangles, …

B Acute

equilateral

Obtuse

scalene

Right

Isosceles

C Rectangle, Square

Rhombus, Square, Kite

Trapezoid, Kite

D 17 15

21 220

E 5 5

D[y 172 Practice

A Acute

isosceles

Right

scalene

Obtuse

scalene

B Rhombus, Square

Rectangle, Square

Parallelogram, Rhombus


C O O

O

O

O

O

D 92 7

13 155

E 10 5√3

D[y 173 Review: Transformations

B

C (5, 0) (‐5, 0)

(‐2, 0) (2, 0)

(‐8, 4) (‐4, 2)

(15, ‐6) (6, ‐1)

(‐9, ‐6) (‐6, ‐4)

(3, ‐2) (3, 2)


D[y 173 Practice

A

B (0, 3) (0, 9)

(‐5, 7) (5, 7)

(0, 9) (0, ‐9)

(‐3, 0) (3, ‐2)

(4, 8) (1, 2)

C (‐6, 9)

(5, ‐8)

Q2

2

D[y 174 Review: Statistics

B 1/2 1/3 1 0

C 1/36 1/4 1/6 1/9 5/12

D 25% 75% 50% 16% 80% 64%

D[y 174 Practice

A 2/3 1/3 1/6 2/3

B 25% 75% 75% 50%

C 1/60 3/5 3/5 1/10

D 0.1 0.4 0.25 0.45 0.55

D[y 175 Review: Systems of Linear …

B

(0, 2) (‐1, 1)

21

-1

C (2, 1) Infinite

None (‐3, 2)

D Oliva has 15 dimes.

Dale is 15 years old.

The bag costs $16.50.

D[y 175 Practice

B

(0, ‐1) (1, ‐1)

-1 2-1

-2

(‐2, 1) (3, 2)

4

1-2 2 -3

-2

B (‐1, 2) (2, ‐3)

None Infinite

C The numbers are 5 and 9.

A lemon costs $0.90.

Mr. Kim has 8 five‐dollar bills.

D[ys 176 ~ 180 Projects

There are no answer keys for these projects.

ep math pre-algebra workbook answers...2020/05/27 · ep math pre-algebra workbook answers d[y 4...

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