sec 1...sec 1.3 –unit measures name: 1. a measurement of electrical energy is used on power meters...

Sec 1.1 –Basic Conversions. Name:

p. 1

M. Winking (Section 1-1)

p. 2


p. 3


Sec 1.2 –Applied Conversions. Name:

Find the perimeter of the following

1. A rectangle has a length of 30 cm and

height of 53 mm. What is the perimeter of this rectangle in centimeters?

2. A rectangle has a length of 45 feet and height of 20 yards. What is the perimeter of this rectangle in feet?

3. A square has a side length of 520 meters. What is the perimeter of the square in kilometers?

4. A right triangle has legs of 2 feet and 18 inches. What is the perimeter of the triangle in inches?

M. Winking (Section 1-2) p.4

5. A rectangle has a length of 8.2 cm and a

height of 42 mm. What is the area of the square in square millimeters?

6. Find the area of the triangle shown below in square inches.

7. A square has a side of length 1.6 yards. What is the area of the square in square inches?

8. Find the area of the triangle shown below in square centimeters.

M. Winking (Section 1-2) p.5

Sec 1.3 –Unit Measures Name:

1. A measurement of electrical energy is used on power meters on most homes. E P t , where P = power

measured in Kilowatts (Kw) and t = time measured in hours.

2. Momentum is described as p m v , where p = momentum, m = mass which is measured in kilograms, and

v = velocity which is measured in meters per second (m/s). What is a possible unit measure for Momentum?

3. Force is described as F m a , where m = mass which is measured in kilograms, and a = acceleration which

is measured in meters per second squared (m/s2). What is a possible unit measure for Force?

4. Kinetic Energy is described as , where m = mass which is measured in kilograms, and v =

velocity which is measured in meters per second (m/s). What is a possible unit measure for Kinetic Energy?

p. 6


5. Power can be described as m a d

Pt

, where m = mass which is measured in kilograms, a = acceleration

which is measured in meters per second squared (m/s2), d = distance which is measured in meters, and ∆t =

change in time measured in seconds. What is a possible unit measure for Power?

6. (Challenge) Based on the tension of a string, the number of kilograms being held can be determined by the

formula:

2

T Lm

v

v = velocity of the wave in centimeters per second, and L is the length of the string measured in centimeters.

What must the value of the tension, ‘T’, be measured in, so that mass, ‘m’, is measured in grams.

p. 7


Sec 1.4 – Dimensional Analysis

(Rate Conversions) Name:

Common Conversions: SMALL LARGE

12 in

1 ft

3feet

1 yard

5280ft

1 mile

60 sec

1 min

60 min

1 hour

24 hrs

1 day

days

year

365

1

10mm

1 cm

100cm

1 m

1000m

1 km

1000g

1 kg

1000 m

1

l

l

or or or or or or or or or or or or

1 ft

12 in

1 yard

3feet

1 mile

5280ft

1 min

60 sec

1 hour

60 min

1 day

24 hrs

days

year1

365

1 cm

10 mm

1 m

100cm

1 km

1000m

1 kg

1000g

1

1000 m

l

l

1. A student is reading a book at about 370 words per minute. Convert this rate to words per hour.

2. Some female spiders have been measured spinning a web at 3 cm per second. Convert

this rate to meters per minute.

3. The average speed of a car on a stretch of interstate is 70 miles per hour. Convert this rate to feet per second.

4. A piece of data on the edge of a performance hard drive platter in a computer

moves at about 1319 inches per second. Convert this rate to miles per hour.

Standard Lengths Standard Units of Time Common Metric Measures

p. 8


Common Conversions: SMALL LARGE

12 in

1 ft

3feet

1 yard

5280ft

1 mile

60 sec

1 min

60 min

1 hour

24 hrs

1 day

days

year

365

1

10mm

1 cm

100cm

1 m

1000m

1 km

1000g

1 kg

1000 m

1

l

l

or or or or or or or or or or or or

1 ft

12 in

1 yard

3feet

1 mile

5280ft

1 min

60 sec

1 hour

60 min

1 day

24 hrs

days

year1

365

1 cm

10 mm

1 m

100cm

1 km

1000m

1 kg

1000g

1

1000 m

l

l

5. Craig Kimbrell of the Atlanta Braves, can throw his fastball at 102 miles per hour. Convert this rate to feet per

second.

(Challenge: It is exactly 60.5 feet from the pitcher’s mound to home plate. How many seconds would it take the

ball to travel from the mound to home plate?)

6. A bathroom faucet that is fully open, usually releases water at about 95 milliliters per second. How many liters of

water are released in an hour (i.e. convert the rate to liters per hour)?

7. An average typing speed for a person in a high school computer/typing class is about 44 words per minute. At this

rate how many hours would it take to re-type a novel that is 45,000 words?

8. (Challenge)Ariel noticed that her outdoor faucet was dripping. She later determined that it was dripping 10 drops

every minute. If 20 drops equals a 1 milliliter, how many liters per year is the faucet leaking?

Standard Lengths Standard Units of Time Common Metric Measures

p. 9


Sec 1.5 – Simplifying Algebraic

Expressions Name:

1. If two people had a different number of apples and bananas shown below, how much would they

have collectively?

This would be algebraically similar to simplifying:

5 5 3 8a b a b

2. Simplify the following algebraic expressions:

a. 3 8 4 2x y x y

b. 4 3 5 6 5a a b a b

c. 3 2 5p q q p

d. 4 2 3 2x y x

e. 4 2 3 5 5a b a

f. 2 5 2 6 3 2 3w w z z

3. Simplify the following algebraic expressions:

+ =

p. 10


a. 2 2 3 3 5 2 1x y x y

b. 4 2 5 3 7m n m n

c. 6 12

3

x

d. 8 2 10

2

x y

e. 5 15

3 105

aa

f. 9 3 12

2 2 43

m nn

p. 11


Sec 1.6 – Interpreting Written

Expressions Name:

Convert the following phrases and sentences to algebraic expressions:

1. “The sum of three and an unknown number.”

2. “Three less than an unknown number.”

3. “A number doubled reduced by five.”

4. “The number of five increased by three times a number.”

5. “The product of three and an unknown number diminished by eight.”

6. “Four subtracted from a number.”

7. “The quotient of a number tripled and six.”

8. “Three times the sum of a number and four.”

9. “Ten subtracted from twice a number.”

10. “Twice the difference of 7 and a number.”

p. 12


Convert the following phrases and sentences to algebraic expressions:

11. 4 of a number increased by seven.

12. Twice the total of a number and three.

13. Five add to a number squared.

14. Nine decreased by a number cubed.

15. Lori is 4 years younger than Shawn. Write an expression that represents Lori’s age in relation to Shawn.

16. Jennifer is 1 year older than twice Zack’s age. Write an expression that represents Jenifer’s age in relation to Zack.

17. Jerry worked 2 hours less than four times as many hours as Katrina worked. Write an expression that represents the number of hours Jerry worked in relation to Katrina.

p. 13


18. In a given rectangle the shorter side is 2 units less than the longer side. If we let the longer side be represented as the variable x, create an expression that represents the perimeter of the rectangle.

19. In an isosceles triangle (a triangle where two of the three sides called legs are equal), the legs are 1 unit less than twice the length of the base. If the length of the base of the triangle is represented by x, create an expression that represents the perimeter of the triangle.

20. Andrea is three times older than Eliza. Suzie is 4 years older than Eliza. If Eliza’s age can be represented by x, create an expression that represents the combined age of all three girls.

p. 14


Name:

Name Examples Non-Examples

Monomial (one term)

1. 3𝑥4 degree:4 2. 𝑎2 degree:2 3. 5 degree:0

1. 2𝑥−4

2. 5√𝑚

3. 3𝑡23

Binomial (two terms)

1. 2𝑛3 − 𝑛 degree:3 2. 𝑝 − 3 degree:1 3. −3𝑎3𝑏4 + 𝑎4𝑏5 degree:9

1. 2𝑥+1

𝑥

2. √𝑐3 − 2

Trinomial (three terms)

1. −2𝑥3 + 2𝑥 − 3 degree:3

2. 𝑑(𝑑2 + 2𝑑4 − 2) degree:5

1. 𝑥−3 + 2𝑥 − 5

2. 2𝑥 + 3𝑥 − 5

Polynomial (one or more terms)

1. 3𝑥4 + 2𝑥3 − 5𝑥 + 1 degree:4 2. 5𝑦6 degree:6 3. 1

2𝑥2+√3 𝑥3−6𝑥4 + 1𝑥 − 3 degree:4

1. 3𝑞3 +𝑝

𝑞

2. 2𝑥 + 3√𝑥

1. EXPAND and SIMIPLIFY (Also, list the degree and leading coefficient of your answer).

a. 2x)(23)(7x b. (5x3 – 3x

4 − 2x – 9x

2 – 2) + (3x

3 +2x

2 – 5x – 7)

c. xx 8)5(3 d. 7265232 xyxyx e. xxxx 2652 22

f. 51195852 233 xxxxx g. 5332 xx h. 252 x

p. 15


(1 Continued). EXPAND and SIMIPLIFY

i. yyy 24 22 j. 7)-2y-(3y6y- 22 k. 53 xx

l. m.

Determine an expression that represents: Determine an expression that represents:

Perimeter = Perimeter = Area = Area =

2. Divide the following.

a. 3

35

8a

2432a a b.

2

34

3x

321x x c.

3 5 2 3

2

36a d 72

6ad

a d

3. Factor the GCF from each expression

a. 54 315 xx b. 2416 2 x

c. 556374 423618 yxyxyx d. 3233 xxx

b.

d. c.

a.

p. 16


PRODUCT RULE: QUOTIENT RULE:

√𝑥𝑎

∙ √𝑦𝑎 = √𝑥𝑦𝑎 √𝑥

𝑎

√𝑦𝑎 = √

𝑥

𝑦

𝑎

Example: Example:

√10 ∙ √𝑥 = √10𝑥 √10

√2 = √

10

2= √5

More directly, when determining a product or quotient of radicals and the indices (the small number in front

of the radical) are the same then you can rewrite 2 radicals as 1 or 1 radical as 2.

Simplify by rewriting the following using only one radical sign (i.e. rewriting 2 radicals as 1).

1. √3 ∙ √12 2. √12

√3

3. √7𝑥 ∙ √2𝑦 4. √12𝑥23

√4𝑥3

Simplify by rewriting the following using multiple radical sign (i.e. rewriting 1 radical as 2).

5. √144

25 6. √

𝑥6

121

p. 17


Express each radical in simplified form.

7. √48 8. √450𝑥4𝑦5 9. √72𝑥5𝑦6

10. √300𝑥12 11. √675𝑥4𝑦11 12. −√81𝑥3𝑦8

13. √48𝑥7𝑦33 14. √81𝑥10𝑦33

15. √−27𝑥53

Use the letters and answers to match the answer to the riddle. Only some answers will be used.

“What is an opinion without π?”

_________ _________

_________ _________ _________ _________ _________

−9𝑥𝑦4 √𝑥 15𝑥2𝑦2 √2𝑦 10𝑥6 √3 2𝑥2𝑦 √6𝑥3

3𝑥3𝑦 √3𝑥3

6𝑥2𝑦3 √2𝑥 15𝑥2𝑦5 √3𝑦

P N O

N

O N A

I K

p. 18


Express each radical in simplified form.

16. √6𝑥 ∙ √12𝑥 17. √18𝑎5 ∙ √6𝑎4

Simplify. Assume that all variable represent positive real numbers.

18. 5√3 + √2 − 2√3 + 4√2 19. 444125108 20. 2 150 18 3 8 24

21. 𝑦√18 − 3√12𝑦4 + 2√8𝑦2 22. 𝑥 √32𝑥2 + 2 √18𝑥4 23. 283185 224 xxxx

24. 2 10 3 6 2 5 24 25. xxx 362 26. 23 6 4 2 15a a a

p. 101

p. 19


Simplify. Assume that all variable represent positive real numbers and rationalize all denominators.

18. 3

√5 19.

6

√3 20.

3√2

√6

21. √16

27 22.

2

2723812 23.

√2(√12−√3)

√3

p. 20


Rational Number: A rational number is one that can represented as a ratio of 𝑝

𝑞 , such that p and q are

both integers and 𝑞 ≠ 0. All rational numbers can be expressed as a terminating or

repeating decimal. (Examples: −0.5, 0, 7,3

2 , 0.26̅)

Irrational Number: An irrational number is one that cannot represented as a ratio of 𝑝

𝑞 , such that p

and q are both integers and 𝑞 ≠ 0. Irrational numbers cannot be expressed as a

terminating or repeating decimal. (Examples: √3, 𝜋, √5

2, 𝑒)

Irrational numbers are difficult to comprehend because they cannot be expressed easily. Consider

creating a physical representation of the √2 . Create a right triangle with each leg being exactly 1 meter.

The hypotenuse should then be the length of √2 meters.

What is interesting is, no matter how precise the ruler is, you can never measure the exact length of the hypotenuse using a metric scale. The hypotenuse will ALWAYS fall between any two lines of a metric division. This bothered early Greeks specifically the Pythagoreans. They thought it was illogical or crazy (i.e. irrational) that it was possible to draw a line of a length that could NEVER be measured precisely using a scale that was some integer division of the original measures. They even hid the fact that they may have known this as they believed it to be an imperfection of mathematics.

In the example above the hypotenuse is approximately 1.414213562373095048801688724209698…. meters. It

can NEVER be written precisely as a decimal which may seem a little IRRATIONAL. The decimal description goes

on forever without a repeating pattern.

magnified x2.5 times

p. 21


A set of numbers is said to be closed under an operation if any two numbers from the original set are than combined

under the operation and the solution is always in the same set as the original numbers.

For example, the sum of any two even numbers always results in an even number. So, the set of even numbers

is closed under addition.

For example, the sum of any two odd numbers always results in an even number. So, the set of odd numbers is

NOT closed under addition.

1. Is the set of Integers closed under addition?

2. Is the set of Integers closed under subtraction?

3. Is the set of Integers closed under multiplication?

4. Is the set of Integers closed under division?

5. Is the set of Rational Numbers closed under addition?

6. Is the set of Irrational Numbers closed under addition?

7. Is the set of Rational Numbers closed under multiplication?

8. Is the set of Irrational Numbers closed under multiplication?

9. Is the set of Even Numbers closed under division?

10. Is the set of Odd Numbers closed under multiplication?

The Set of All

EVEN NUMBERS. 4

8

24 106

–18 88

56

36

The Set of All

EVEN NUMBERS. 4

8

24 106

–18 88

56

The Set of All

ODD NUMBERS. 67

7

23

97

–17 51

37

The Set of All

EVEN NUMBERS. 4

8

24 106

–18 88

56

YES NO

Circle One: Example or Counter Example

YES NO


YES NO


YES NO


YES NO


YES NO


YES NO


YES NO


YES NO


YES NO


p. 22


Tell whether you think the following numbers are Rational or Irrational.

11. √8 12. √2 + √49 13. 2√27 − √3 − √75

14. 𝜋 15. √12 ∙ √3 16. 𝑒2

17. √643

18. √243

19. 3.2313131̅̅̅̅

20. 3.12112111211112 …. 21. 𝜑 = 1+√5

2≈ 1.618034 … 22. 81−3

4

Rational Irrational Circle One:












p. 23


sec 1...sec 1.3 –unit measures name: 1. a measurement of electrical energy is used on power meters...

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