Transcript Day 2 NOTES - EOCT Review Unit 1 and 2

CCGPS Coordinate Algebra
EOCT Review
Units 1 and 2
Unit 1: Relationships Among
Quantities
Key Ideas
Unit Conversions
• A quantity is a an
exact amount or
measurement.
Examples:
• A quantity can be
exact or approximate
depending on the
level of accuracy
required.
2 – Convert 50 lbs. to
grams.
1 - Convert 5 miles to
feet.
3 -Convert 60 miles
per hour to feet per
minute.
Ex 1: Convert 5 miles to feet.
• 1 mile = 5280 feet
• 5 miles = 5 *5280 feet (does this need
to be exact?)
Ex: 2 Convert 50 grams to pounds
50 lbs. 454 grams
*

1
1 lb.
22, 700 grams
Ex: 3 Convert 60 miles per hour to feet per minute.
60miles 1hour 5280 feet
*
*

hr
60 min
1mile
5280 ft
60*5280 ft

60*1min
min
Tip
There are situations when the units in an
answer tell us if the answer is wrong.
For example, if the question called for
weight and the answer is given in cubic
feet, we know the answer cannot be
correct.
Review Examples
• The formula for density d is d = m/v
where m is mass and v is volume.
If mass is measured in kilograms and
volume is measured in cubic meters,
what is the unit rate for density?
Expressions, Equations & Inequalities
• Arithmetic expressions are comprised
of numbers and operation signs.
• Algebraic expressions contain one or
more variables.
• The parts of expressions that are
separated by addition or subtraction
signs are called terms.
• The numerical factor is called the
coefficient.
Example: 4x2 +7xy – 3
• It has three terms: 4x2, 7xy, and 3.
• For 4x2, the coefficient is 4 and the
variable factor is x.
• For 7xy, the coefficient is 7 and the
variable factors are x and y.
• The third term, 3, has no variables and
is called a constant.
Example:
The Jones family has twice as many
tomato plants as pepper plants. If there
are 21 plants in their garden, how many
plants are pepper plants?
• How should we approach the solution
to this equation?
Example:
Find 2 consecutive integers
whose sum is 225.
• How should we approach the solution
to this equation?
Example:
A rectangle is 7 cm longer than it is
wide. Its perimeter is at least 58 cm.
What are the smallest possible
dimensions for the rectangle?
• How should we approach the solution
to this equation?
Writing Linear & Exponential Equations
• If the numbers are going up or down
by a constant amount, the equation is
a linear equation and should be
written in the form y = mx + b.
• If the numbers are going up or down
by a common multiplier (doubling,
tripling, etc.), the equation is an
exponential equation and should be
written in the form y = a(b)x.
Create the equation of the line
for each of the following tables.
a)
x
0
1
2
3
y
2
6
18
54
b)
x
0
1
2
3
y
-5
3
11
19
Linear Word Problem
Enzo is celebrating his birthday and his mom
gave him $50 to take his friends out to
celebrate. He decided he was going to buy
appetizers and desserts for everyone. It cost 5
dollars per dessert and 10 dollars per
appetizer. Enzo is wondering what kind of
combinations he can buy for his friends.
a) Write an equation using 2 variables to
represent Enzo’s purchasing decision.
(let a=number of appetizers and d=number of
desserts)
Exponential Word Problem:
Ryan bought a car for $20,000 that
depreciates at 12% per year. His car is 6
years old. How much is it worth now?
Solving Exponential Equations
• If the bases are the same, you can just set
the exponents equal to each other and
solve the resulting linear equation.
• If the bases are not the same, you must
make them the same by changing one
or both of the bases.
– Distribute the exponent to the given
exponent.
– Then, set the exponents equal to each other
and solve.
Solve the exponential equation:
a)
2
4 x 8
2
x7
b)
3  27
2x
x 2
Unit 2: Solving Systems of
Equations
Key Ideas
Reasoning with Equations & Inequalities
• Understanding how to solve equations
• Solve equations and inequalities in one
variable
• Solve systems of equations
• Represent and solve equations and
inequalities graphically.
Important Tips
• Know the properties of operations
• Be familiar with the properties of
equality and inequality. (Watch out for
the negative multiplier.)
• Eliminate denominators (multiply by
denominators to eliminate them)
Properties to know
•
•
•
•
•
•
•
•
•
•
•
•
•
Addition Property of Equality
Subtraction Property of Equality
Multiplication Property of Equality
Division Property of Equality
Reflexive Property of Equality
Symmetric Property of Equality
Transitive Property of Equality
Commutative Property of Addition and
Multiplication
Associative Property of Addition and Multiplication
Distributive Property
Identity Property of Addition and Multiplication
Multiplicative Property of Zero
Additive and Multiplicative Inverses
Example
Solve the equation 8(x + 2) = 2(y + 4) for y.
Example
Karla wants to save up for a prom dress.
She figures she can save $9 each week
from the money she earns babysitting.
If she plans to spend up to $150 for the
dress, how many weeks will it take her to
save enough money?
Example
• This equation can be used to find h,
the number of hours it takes Bill and
Bob to clean their rooms.
h h

1
5 20
• How many hours will it take them?
Example
• You are selling tickets for a basketball
game. Student tickets cost $3 and
general admission tickets cost $5. You
sell 350 tickets and collect $1450.
• Use a system of linear equations to
determine how many student tickets
you sold?
Example
You sold 52 boxes of candy for a fundraiser.
The large size box sold for $3.50 each and
the small size box sold for $1.75 each. If you
raised $112.00, how many boxes of each
size did you sell?
A.
B.
C.
D.
40 large, 12 small
12 large, 40 small
28 large, 24 small
24 large, 28 small
Example
You sold 52 boxes of candy for a fundraiser. The large
size box sold for $3.50 each and the small size box sold
for $1.75 each. If you raised $112.00, how many boxes
of each size did you sell? You sold 61 orders of frozen
pizza for a fundraiser. The large size sold for $12 each
and the small size sold for $9 each. If you raised
$660.00, how many of each size did you sell?
A. 24 large, 37 small
B. 27 large, 34 small
C. 34 large, 27 small
D. 37 large, 24 small
Example
Which equation corresponds to the
graph shown?
• A. y = x + 1
• B. y = 2x + 1
• C. y = x – 2
• D. y = 3x
Example
Which graph would represent a system of
linear equations that has no common
coordinate pairs?
A
C
B
D