Definitions, Properties, Postulates, Theorems Undefined terms: Postulate theorem Set Element (member) of a set Subset Union of two or more sets Intersection of two or more sets Empty set Natural (counting) numbers Whole numbers Integers Rational numbers I
Pfenning Algebra I
NAME: _
Properties of Real Numbers The following are true for every real number a, b, and c: Property Distributive Property Examples
a (b + c) = a b + a c
5(4 + 2) = 3( x + 2) =
a (b  c) = a b  a c
Commutative Property of Addition
a+b
Math 10 Chapter 9 Notes: Hypothesis Testing
done constantly in medicine, business, polling, education, etc. to do: set up 2 contradictory statements first statement often the accepted belief conduct a test to see whether our data supports or does not supp
Detailed Semester Final Review
real numbers natural, whole, integers, rational, irrational, etc. graph a number on the number line compare quantities using >,<,= evaluate expressions for a given variable simplify by combining like terms solve for an indi
Geometry Quiz
Name_
Complete the following statements with the word always, sometimes, or never to make a true statement. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. JK and JL are _ the same ray. Two skew lines are _ coplanar. TQ an
1
Name _ AP Statistics Chapter 6 Worksheet.
1.
Blood The probability that a person in the United States has type O positive blood is 38%.
Five unrelated people in the U.S. are selected at random. a. Find the probability that all three have type O positive
42 Measuring Angles
A) What is the difference between these two?
a. mABC = 25 ABC
b.
The first one reads as "the measure of
ABC = 25
degrees"
c. Turn to page 84 and look at the figure d. degree i. The unit of measure is called a degree e. Measure i. the
Section 8.1
Scientific Notation
Objectives
Convert numbers from scientific notation to standard notation Convert numbers from standard notation to scientific notation
Scientific Notation
Scientists often work with very small or very large numbers. To make
11 Using Variables What is a variable?
Name some?
Variable a symbol usually a letter that represents one or more numbers
Algebraic Expression a mathematical phrase that can include numbers, variables and operations (no equal sign!)
What are some words
49 Writing Up Proofs
A) Proofs a. We will always do two column b. Statements on the left and reasons on the right
B) Proofs tips a. The Given is a step/statement (a lot times the first step) and the last statement is what is to be proven b. Derive your s
12 Exponents and Order of Operations Exponents how many times the base number is used as a factor
24
23
22
Where do Exponents come in the order of operations? Simplify Expressions 1) 14 + 3 2  23
2) 4 2 + 5 2 (8  3)
3) (5 + 3) 2 + (5 2  3)
(Multiplic
Section 8.4
More Rules of Exponents
Objectives
Be able to raise a power to a power Be able to raise a product to a power
Review Simplify each expression (write each base only once, and make sure there are no 0 or negative exponents)
1) 2 x y 3
2) 2 x 0
13 Exploring Real Numbers (are there fake numbers?) Natural numbers 1,2,3,.
Whole numbers 0,1,2,3,.
Integers .2,1,0,1,2,3,4,.
Rational Numbers any number that you can write in the a form b , where a and b are integers and b 0


they can be written a
AP Calculus Final Review Sheet
When you see the words . 1. Find the zeros 2. Find equation of the line tangent to f ( x ) at (a, b ) 3. Find equation of the line normal to f ( x ) at (a, b ) 4. Show that f ( x ) is even 5. Show that f ( x ) is odd 6. Find
Section 8.5
Division of Exponents
Objectives
Be able to divide powers with the same base Be able to raise a quotient to a power
Review Simplify each expression (write each base only once, and make sure there are no 0 or negative exponents)
1) 2.8 10 3 4
Chapter 7 Graphing Review. 1) Is (1, 1) a solution to the linear inequality? 2) Is (0, 4) a solution to the linear inequality? 3) Graph
2x  5 y < 3
y 2 x  10
y x  5
4) Graph
10 x  2 y < 6
5) Is (2, 4) a solution to the system?
y < 2x  1 5 x  7
43 Some Remarks on Angles and 44 Perpendiculars, Right Angles and Related Angles, Congruent Angles
A) Does the order of naming the angle matter?
B) Order does matter in Trigonometry a. Directed Angles
i. When we use directed angles, we allow "zero angle
Fairview High School Curricular Map
Geometry
(Letters and numbers in bold print refer to the Essential Learnings from the Geometry Curriculum Essentials Document, Boulder Valley School District, May 2009)
Unit 1 (3 weeks): Tools of Geometry
Patterns and
Chapter 7 Graphing Review. 1) Is (1, 1) a solution to the linear inequality? 2) Is (0, 4) a solution to the linear inequality? 3) Graph
2x  5 y < 3
y 2 x  10
y x  5
4) Graph
10 x  2 y < 6
5) Is (2, 4) a solution to the system?
y < 2x  1 5 x  7
46 Some Theorems About Angles
A)
What do we know if the angles in a linear pair are congruent?
a. Theorem 42 i. If the angles in a linear pair are congruent, then each of them is a right angle. If,
Then,
B) Theorem 43 a. If two angles are complementary
PIB Geometry: Venn Diagram Practice (For each problem, complete a Venn diagram before answering the questions.) 1. In a group of 63 students, 22 study Biology, 26 study Chemistry, and 25 study Physics. 18 study both Physics and Chemistry, four study both
47 Vertical Angles
A) How many angles are formed when two lines intersect?
B) Vertical Angles a. Two angles are vertical angles if their sides form two pairs of opposite rays b. Quick Activity) i. With another person take out a piece of paper and draw th