Download Units 1 and 5 EOCT Review

Key Ideas

A quantity is a an exact amount or
measurement.

A quantity can be exact or
approximate depending on the level
of accuracy required.
5miles 5280feet

1mile
 26,400feet
50 lbs. 454 grams


1
1 lb.
22, 700 grams
60miles 1hour 5280 feet



hr
60 min
1mile
5280 ft
min
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.
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?
kg
3
m




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.




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.

How should we approach the solution
to this equation?
tomato plant: 2x
pepper plant: x
2x  x  21
x 7
first: x
second: x + 1
x  x  1  225
x  112
112 &113
4x  14  58
x  11
11 by 16


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.
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
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.)
10a  5d  50
b) Use your equation to figure out how many desserts
Enzo can get if he buys 4 appetizers. 10 4  5d  50
 
d2
c) How many appetizers can Enzo buy if he buys 6
desserts?
a2
10a  5 6  50
 
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


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.
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 5 – Transformations in the Plane
 Precise
definitions:
 Angle
 Circle
 Perpendicular lines
 Parallel lines
 Line Segment
 Represent
the plane
transformations in
 Compare rigid and non-rigid
▪ Translations
▪ Rotations
▪ Reflections
 Understand Dilations
 Given
shapes –
 Determine which sequence of
rotations and reflections would
map it on itself
 Develop definitions of rotations,
reflections and translations

Translate C(-4, 7) by (x – 7, y – 9).
C’(-11, -2)

Reflect across the y-axis
Describe every transformation that
maps the given figure to itself.

Remember “Driving”
 90 CW – (x, y) → (y, -x)
 180 – (x, y) → (-x, -y)
 270 CW – (x, y) → (-y, x)
Practice Problems