Transcript CC GPS Coordinate Algebra

CCGPS Coordinate Algebra
EOCT Review
Units 1 and 2
Unit 1: Relationships Among
Quantities
Key Ideas
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 5: 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 6:
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?
tomato plant: 2x
pepper plant: x
2x  x  21
x 7
Example 7:
Find 2 consecutive integers
whose sum is 225.
first: x
second: x + 1
x  x  1  225
x  112
112 &113
Example 8:
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?
4x  14  58
x  11
11 by 16
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.
9)
x
0
1
2
3
y
2
6
18
54
x
y  2(3)
10)
x
0
1
2
3
y
-5
3
11
19
y  8x  5
11. 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.
5a  10d  50
(Let a = number of appetizers and d = number of desserts.)
b) Use your equation to figure out how many desserts
Enzo can get if he buys 4 appetizers. 5 4  10d  50
 
d3
c) How many appetizers can Enzo buy if he buys 6
desserts?
a2
5a  10 6  50
 
12. 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?
y  P 1 r 
t
y  20,000 1 .12 
6
y  $9,288.08
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:
13) 2
4 x 8
2
x7
4x  8  x  7
x5
2x
14) 3
3
2x
 27
3
x 2
3 x  2 
2x  3  x  2 
x 6
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
•
•
•
•
•
•
•
•
•
•
•
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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 15
Solve the equation 8(x + 2) = 2(y + 4) for y.
y  4x  4
Example 16
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?
17weeks
Example 17
• 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
4h  h  20
h4
• How many hours will it take them?
Example 18
• 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?
Student : x
x  y  350
General :y
3x  5y  1450
150 student
Example 19
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?
large : x
small
:y
A. 40 large, 12 small
B. 12 large, 40 small
C. 28 large, 24 small
D. 24 large, 28 small
x  y  52
3.5x  1.75y  112
Example 20
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?
large : x
A. 24 large, 37 small
B. 27 large, 34 small
C. 34 large, 27 small
D. 37 large, 24 small
small :y
x  y  61
12x  9y  660
Example 21
Which equation corresponds to the
graph shown?
A. y = x + 1
B. y = 2x + 1
C. y = x – 2
D. y = -3x – 2
Example 22
Which graph would represent a system of
linear equations that has no common
coordinate pairs?
A
C
B
D
Ex. 23 Graph
y  x  2

 x  2