Download All of Unit 1

Sec 1.1 –Basic Conversions.
Name:
M. Winking (Section 1-1)
p. 1
M. Winking (Section 1-1)
p. 2
M. Winking (Section 1-1)
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?
3. A square has a side length of 520
meters. What is the perimeter of
the square in kilometers?
2. A rectangle has a length of 45 feet and
height of 20 yards. What is the perimeter
of this rectangle in feet?
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?
M. Winking (Section 1-3)
p. 6
5. Power can be described as P 
mad
, where m = mass which is measured in kilograms, a = acceleration
t
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:
m
T L
v2
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.
M. Winking (Section 1-3)
p. 7
Sec 1.4 – Dimensional Analysis
(Rate Conversions)
Common
Conversions:
12 in 3feet
1 ft 1 yard
or
SMALL
LARGE
5280 ft 60 sec 60 min 24 hrs 365 days 10 mm 100 cm 1000 m
1 mile 1 min 1 hour 1 day 1 year
1 cm
1m
1 km
or
1 ft 1 yard
12 in 3feet
Name:
or
or
or
or
or
or
or
or
1 cm
1 mile 1 min 1 hour 1 day 1 year
1m
1 km
5280 ft 60 sec 60 min 24 hrs 365 days 10 mm 100 cm 1000 m
Standard Lengths
Standard Units of Time
1000 g 1000 ml
1l
1 kg
or
or
1 kg
1l
1000 g 1000 ml
Common Metric Measures
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.
M. Winking (Section 1-4)
p. 8
Common
Conversions:
12 in 3feet
1 ft 1 yard
or
SMALL
5280 ft 60 sec 60 min 24 hrs 365 days 10 mm 100 cm 1000 m
1 mile 1 min 1 hour 1 day 1 year
1 cm
1m
1 km
or
1 ft 1 yard
12 in 3feet
LARGE
or
or
or
or
or
or
or
or
1 cm
1 mile 1 min 1 hour 1 day 1 year
1m
1 km
5280 ft 60 sec 60 min 24 hrs 365 days 10 mm 100 cm 1000 m
Standard Lengths
Standard Units of Time
1000 g 1000 ml
1l
1 kg
or
or
1 kg
1l
1000 g 1000 ml
Common Metric Measures
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?
M. Winking (Section 1-4)
p. 9
Sec 1.5 – Simplifying Algebraic
Expressions
1.
Name:
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:
 5a  5b 
  3a  8b  
2. Simplify the following algebraic expressions:
a. 3x  8 y  4 x  2 y
c. 3  2 p  q   q  5 p
e. 4   2a  3b  5  5a
3. Simplify the following algebraic expressions:
b. 4a  3a  5b  6a  5b
d. 4 x  2  3 y  2 x 
f.
2  5  2w  6  3  2w  3z   z
M. Winking (Section 1-5)
p. 10
a. 2  2 x  3 y   3  5  2 x   1  y
b. 4  2m  5n   3  m  7n 
c.
6 x  12
3
d.
8 x  2 y  10
2
e.
5a  15
 3a  10
5
f.
9m  3n  12
 2  2n  4 
3
M. Winking (Section 1-5)
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.”
M. Winking (Section 1-6)
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.
M. Winking (Section 1-6)
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.
M. Winking (Section 1-6)
p. 14
Name:
Name
Monomial
Examples
1. 3𝑥 4
2. 𝑎2
3. 5
(one term)
degree:4
degree:2
degree:0
1. 2𝑛3 − 𝑛
2. 𝑝 − 3
3. −3𝑎3 𝑏4 + 𝑎4 𝑏 5
Binomial
(two terms)
Trinomial
(three terms)
Polynomial
(one or more terms)
degree:3
degree:1
Non-Examples
1. 2𝑥 −4
2. 5√𝑚
2
3. 3𝑡 3
1.
2𝑥+1
𝑥
degree:9
2. √𝑐 3 − 2
1. −2𝑥 3 + 2𝑥 − 3
degree:3
1. 𝑥 −3 + 2𝑥 − 5
2. 𝑑(𝑑2 + 2𝑑 4 − 2)
degree:5
2. 2𝑥 + 3𝑥 − 5
degree:4
1. 3𝑞3 +
1. 3𝑥 4 + 2𝑥 3 − 5𝑥 + 1
2. 5𝑦 6
3. 12𝑥 2 +√3 𝑥3 −6𝑥4 + 1𝑥 − 3
degree:6
degree:4
𝑝
𝑞
2. 2𝑥 + 3√𝑥
1. EXPAND and SIMIPLIFY (Also, list the degree and leading coefficient of your answer).
b. (5x3 – 3x4 − 2x – 9x2 – 2) + (3x3 +2x2 – 5x – 7)
a. (7x  3)  (2  2x)
d.  23x  2 y   5x  6 y   2 x  7
c. 3( x  5)  8x

 

f. 2 x 3  5x  8  5x 3  9 x 2  11x  5
g. 2 x  33x  5

 
e. 2 x 2  5x  6 x 2  2 x

h. 2 x  5
2
M. Winking (Section 1-7)
p. 15
(1 Continued). EXPAND and SIMIPLIFY

i. 4 y 2 y 2  2 y

k. x  3x  5
j. - 6y 2 (3y 2 - 2y - 7)
l.
m.
Determine an expression that represents:
Determine an expression that represents:
Perimeter =
Perimeter =
Area =
Area =
2. Divide the following.
a.
32a 5  24a 3
8a 3
b.
21x 4  3x 3
3x 2
c.
36a 3d5  72a 2 d 3
6ad 2
3. Factor the GCF from each expression
a. 15x 4  3x 5
b. 16 x 2  24
b.
a.
c. 18x 4 y 7  36 x 3 y 6  42 x 5 y 5
c.
d. 3xx  3  2x  3
d.
M. Winking (Section 1-7)
p. 16
PRODUCT RULE:
𝑎
𝑎
QUOTIENT RULE:
𝑎
√𝑥
√𝑦
𝑎
𝑥
𝑎
√𝑥 ∙ √𝑦 = √𝑥𝑦
𝑎
= √
𝑦
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
3.
√7𝑥 ∙ √2𝑦
2.
√12
√3
3
4.
√12𝑥 2
3
√4𝑥
Simplify by rewriting the following using multiple radical sign (i.e. rewriting 1 radical as 2).
144
25
5. √
6. √
𝑥6
121
M. Winking (Section 1-8)
p. 17
Express each radical in simplified form.
8. √450𝑥 4 𝑦 5
7. √48
9. √72𝑥 5 𝑦 6
P
10. √300𝑥 12
N
11. √675𝑥 4 𝑦 11
12. −√81𝑥 3 𝑦 8
O
3
13. √48𝑥 7 𝑦 3
O
N
14.
A
3
3
√81𝑥10 𝑦 3
15. √−27𝑥 5
N
I
K
Use the letters and answers to match the answer to the riddle. Only some answers will be used.
“What is an opinion without π?”
_________
−9𝑥𝑦 4 √𝑥
_________
15𝑥 2 𝑦 2 √2𝑦
_________
10𝑥 6 √3
_________
3
2𝑥 2 𝑦 √6𝑥
_________
3
3𝑥 3 𝑦 √3𝑥
_________
_________
6𝑥 2 𝑦 3 √2𝑥
15𝑥 2 𝑦 5 √3𝑦
M. Winking (Section 1-8)
p. 18
Express each radical in simplified form.
17. √18𝑎5 ∙ √6𝑎4
16. √6𝑥 ∙ √12𝑥
Simplify. Assume that all variable represent positive real numbers.
18. 5√3 + √2 − 2√3 + 4√2
19.
21. 𝑦√18 − 3√12𝑦 4 + 2√8𝑦 2

24. 2 10 3 6  2 5  24

108  5 12  4 44
23. 5 18 x 4  3x 8 x 2  x 2 2
22. 𝑥 √32𝑥 2 + 2 √18𝑥 4
25.
2x

6x  3 x
20. 2 150  18  3 8  24

26. 3 6a

4a  2 15a 2

p. 101
M. Winking (Section 1-8)
p. 19
Simplify. Assume that all variable represent positive real numbers and rationalize all denominators.
18.
3
√5
16
21. √27
19.
6
√3
22.
20.
12  8 3  2 27
2
3√2
√6
23.
√2(√12−√3)
√3
M. Winking (Section 1-8)
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
3
repeating decimal. (Examples: −0.5, 0, 7, 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
, 𝑒)
2
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.
magnified x2.5 times
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.
M. Winking (Section 1-9)
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.
56
56
The Set of All
106
24
36
EVEN NUMBERS.
4
8
88
The Set of All
106
24
EVEN NUMBERS.
4
–18
88
8
–18
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.
37
The Set of All
97
7
51
The Set of All
106
ODD NUMBERS.
67
56
23
EVEN NUMBERS.
–17
4
8
YES
YES
Example or Counter Example
NO
Example or Counter Example
Circle One:
3. Is the set of Integers closed under multiplication?
YES
NO
Example or Counter Example
Circle One:
4. Is the set of Integers closed under division?
YES
NO
Example or Counter Example
Circle One:
5. Is the set of Rational Numbers closed under addition?
YES
NO
Example or Counter Example
Circle One:
6. Is the set of Irrational Numbers closed under addition?
7. Is the set of Rational Numbers closed under multiplication?
YES
NO
Example or Counter Example
Circle One:
YES
8. Is the set of Irrational Numbers closed under multiplication?
Circle One:
9. Is the set of Even Numbers closed under division?
Circle One:
10. Is the set of Odd Numbers closed under multiplication?
Circle One:
YES
YES
YES
–18
NO
Circle One:
2. Is the set of Integers closed under subtraction?
88
Example or Counter Example
Circle One:
1. Is the set of Integers closed under addition?
24
NO
Example or Counter Example
NO
Example or Counter Example
NO
Example or Counter Example
NO
M. Winking (Section 1-9)
p. 22
Tell whether you think the following numbers are Rational or Irrational.
12. √2 + √49
√8
11.
Circle One:
Rational
Rational
3
Circle One:
Rational
Irrational
Circle One:
Circle One:
Irrational
20. 3.12112111211112 ….
Circle One:
Rational
21. 𝜑 = 1+√5
≈ 1.618034 …
2
Rational
Rational
Irrational
Circle One:
Irrational
Irrational
̅̅̅̅
19. 3.2313131
3
18. √24
Circle One:
Rational
Rational
Irrational
16. 𝑒 2
Circle One:
Irrational
17. √64
Rational
Rational
Irrational
15. √12 ∙ √3
Circle One:
Rational
Circle One:
Circle One:
Irrational
𝜋
14.
13. 2√27 − √3 − √75
Irrational
3
22. 81−4
Circle One:
Irrational
Rational
M. Winking (Section 1-9)
Irrational
p. 23