Name __________________________________
Date _________________
State Assessment Study Guide
Directions: Complete each sentence with the words which make it true. Then complete each problem.
exponent
83
base
The _exponent tells how many times the _____ base_ is used as a factor.
‒42 ____-16________
(–6)4 = _1296____
The Product of Powers rule: To multiply powers with the same base, _add__ their exponents
Simplify. Express using exponents
__ 25_________
23 ∙ 22
2s6(7s7)
_____ 14s13___________
The Quotient of Powers rule: to divide powers with the same base, _____ subtract ____________ their
exponents.
Simplify. Express using exponents
𝑘8
𝑘
___ k7_____
i.
24 𝑥 6
4𝑥 3
______ 6x3________
Power of a Power: To find the power of a power, ____ multiply______ the exponents.
Simplify:
(53)6. ___ 518_____
Example
3 nonzero number to the zero power is ____ one_______
Any
Any nonzero number to the negative n power is the multiplicative inverse (reciprocal) of the
number to the nth power.
1
3-2 ___ 2 _____
3
(5x2y5)0___1______
A number in scientific notation is written as the __factor_ that is at least one but less than ten and a power
of __ten___.
To write numbers greater than one in scientific notation.
The decimal point moves to the __left____. The exponent is ___ positive___.
To write numbers between 0 and 1 in scientific notation:
The decimal point moves _ right____ and the exponent is ____ negative__
To multiply in scientific notation:
__Multiply the decimal numbers and _ add __ the powers of ten.
= 7.13 x 108
(3.1 × 105 )(2.3 × 103 )
To divide in scientific notations
__ Divide _ the decimal numbers and __ subtract___________ the powers of ten.
To add or subtract in scientific notation
The numbers need the _____ same__________ power of ten. Then __ add/subtract _ the decimal
numbers and ___ keep____ the power of ten.
(4.7 × 105) + (2.8 × 104) = 4.98 x 105
Solving Equations
SIMPLIFYING STEPS
1) Does the problem have parenthesis? If so use ___distributive property____
2) Combine like terms___ on the left side of the equal sign
Combine ___ like terms_____ on the right side of the equal sign
SOLVING STEPS
1) Eliminate one of the variables_
Add or Subtract the __ variable term______ to both sides of the equation.
2) Eliminate ___ lonely number_______ on the variable side of the equation
Add or subtract the _______ number _______________ to both sides of the equation
3) Eliminate the multiplication or division using the number connected to the variable.
Linear and Quadratic Equations
1. Slope, rate of change: m=
𝑟𝑖𝑠𝑒
𝑟𝑢𝑛
or m =
𝑦−𝑦
𝑥−𝑥
2. Linear equations: y=__mx + b____ where m= slope and b=y-intercept.
3. x-intercept: Where the line crosses the __x-axis__. Substitute 0 in for the y and solve for x
4. y-intercept (initial value): where the line crosses the _____ y-axis _______________
Equation in standard form: Substitute 0 in for the x and solve for the y.
Equation in y=mx+b: The __b______value is the y-intercept
5. Write a linear equation or linear function
Find the ___ slope___ .
Use one point (x,y)
Substitute the ___m___, ____x______ and ____y_____ into y=mx+b.
Solve for _____b________.
Write the equation (function)
6. Constant rate of change: Is the ___ slope____________. Calculate the ____ slope________by
choosing _____ two_____ points. Then repeat twice with other points. If all the calculations
equal the same slope then it has a constant rate of change and is a ___linear____ function.
7. System of equations. The solution of the two equations will be the Point of intersection of the
lines__
If you are testing a solution, sub the x and y values into the first equation and check it. Do the
same with the second equation. If both equations check then the coordinate is a solution.
8. Quadratics – substitute for the given value and solve for y.
DO NOT USE x2 key! Do the arithmetic x·x.
This graph is _U__ shaped.
Volume: Write the formulas for each of the following:
Volume of a rectangular prism _____L W H_________
Volume for triangular prism _____________________________________________
Volume of a cylinder ____________________________________________________
Volume of a cone _________________________________________________________
Volume of a sphere _______________________________________________________
___Surface area__ is the sum of the areas of all sides of a prism. It can also be calculated by finding the
__perimeter_of the bases times the __ height + 2 times __ the area of the base__________
e
a
c
d
b
g
h
f
Use the diagram to answer questions #1 – 5. Lines k and m are parallel and cut by transversal w.
1. Name two pair of alternate interior angles ___< C and <F
or < E and < D______
Alternate Interior angles have _____equal_________ measures.
2. Name two pair of alternate exterior angles ______< G and <B
___< A and <H __
Alternate exterior angles have equal __measures.
3. Name four pair of corresponding angles ___< C and <G
___< B and <F
___< A and <E
___< D and <H
Corresponding angles have equal measures.
4. Name two pair of vertical angles (there are a lot).__ ___< D and <A
_________________
Vertical angles have equal measures.
5. Name two pair of supplementary angles (there are a lot). ____< C and <A
______________
Supplementary angles have a sum of 180⁰
6. The sum of the measures of the angles in a triangle is _____180⁰__________
7. The sum of the remote interior angles(x and y) is equal to the measure of _____< Z_____
X
Y
Z
1. ___Translation____ is the transformation which slides a figure left, right, up and/or down the
coordinate plane.
Its transformation notation for a movement m units right and n units up is
(x,y)  (_x + m_ , __y + n_____)
Its transformation notation for movement m units left and n units down is
(x,y)  (_x − m_ , __y − n_____)
2. __Reflection__ is the transformation which makes a mirror image of the original figure.
Its transformation notation for reflection over the x-axis is (x,y)  (_x , −y)
Its transformation notation for reflection over the y-axis is (x,y)  (−x , y)
3. __Rotation____ is the transformation which turns a figure.
A turn clockwise is to the ___right____.
A turn counterclockwise is to the __left___
A quarter turn is a __90◦__ turn,
A half turn is a ___180⁰____ turn.
A three-quarter turn is a 270⁰_______ turn
4. __Dilation____ is the transformation which increases or decreases the size of a figure.
To get the coordinates of the new figure, __multiply___ the coordinates of the pre-image by the
_____ scale factor
𝐷𝑖𝑙𝑎𝑡𝑒𝑑 𝑐𝑜𝑜𝑟𝑑𝑖𝑛𝑎𝑡𝑒 𝑜𝑟 𝑙𝑒𝑛𝑔𝑡ℎ
The scale factor = 𝑂𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑐𝑜𝑜𝑟𝑑𝑖𝑛𝑎𝑡𝑒 𝑜𝑟 𝑙𝑒𝑛𝑔𝑡ℎ
1. Figures which are similar are the same shape, but ______ different sizes_________________
2. Corresponding sides of similar figures are in __ proportion__________.
3.The corresponding angles of similar figures are ____ congruent________
ΔABC ~ ΔZXW
B
X
Z
W
C
W
A  __< Z ____________ B  ____< X _______
C  ___< W ___________
̅̅̅̅ corresponds to ___XW___________
𝐵𝐶
̅̅̅̅
𝐴𝐶 corresponds to ___WZ_____
̅̅̅̅ corresponds to ____XZ___
𝐴𝐵
A
4. The scale factor of two similar figures can be calculate with the formula: _
𝐷𝑖𝑙𝑎𝑡𝑒𝑑 𝑐𝑜𝑜𝑟𝑑𝑖𝑛𝑎𝑡𝑒 𝑜𝑟 𝑙𝑒𝑛𝑔𝑡ℎ
𝑂𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑐𝑜𝑜𝑟𝑑𝑖𝑛𝑎𝑡𝑒 𝑜𝑟 𝑙𝑒𝑛𝑔𝑡ℎ
5. Two figures are similar if the ___scale factor________ of the corresponding sides is the same.
Or there are two pair of
__congruent corresponding ___angles.
A scatter plot shows the relationship between a data set with two variables graphed as ordered pairs.
The pattern of the data points determines the association between the two sets of data.
• Data points that go generally upward from left to right show a positive association.
• Data points that go generally downward from left to right show a negative association.
• Data points with no clear pattern show no association between the data sets.
Lines of Best Fit
Construct a scatter plot using the data.
Then draw and assess a line that seems to best represent the data.