Download 1-7 “Logical Reasoning and Counter Examples” p

Chapter 1 Notes
Alg 1H
1-A2 (Lesson 1-3) “Open Sentences” p. 15-17
 Open sentence:
 Solution:
 Equation:
 Inequality:
 Replacement set:
 Solution set:
1A)
1B)
T/F
T/F
1
2A)
2B)
3A)
3B)
T/F
T/F
4)
2
1-A8 (Lesson 1-7) “Logical Reasoning” Power Point
 Conditional statement: has a ________________ and a
________________ and is often written in ____________ form.
Ex.: If the heat is too high, then the popcorn burns.
1)
H:
C:
2)
H:
C:
*Note: Sometimes a conditional statement is triggered by the word “when”
instead of “if”. Example: “We earn points when it is a COTY day.”
 Deductive reasoning: is a process that uses ___________,
___________, _____________________, and
_______________________ to reach a valid conclusion.
3)
4)
 Counterexample: a ____________ case in which the
_______________ is true and the _________________ is false.
 It takes only _________ counterexample to show that a
conditional statement is ______________.
5)
6)
7)
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The Real Number System
Rational Numbers: numbers that can be written in the
a
form of . As a decimal they repeat or terminate.
b
1
1
ex:  0.3333...... repeats ex:  0.25 terminates
3
4
Integers: Whole numbers and their opposites (this
means positive and negative whole numbers). ex:
…, ‫־‬4, ‫־‬3, ‫־‬2, ‫־‬1, 0, 1, 2, 3, 4, …
Whole Numbers: Natural Numbers and zero.
ex: 0,1,2,3…
Natural or Counting: Numbers
ex: 1,2,3,4,…
So what isn’t a real number? divide by zero = undefined (  ), and
numbers) are two examples.
Irrational
Numbers:
ex:
 and
2
These must be
represented by a
symbol (ex: ), or
as a rounded
number, or in
radical form
because the
decimal doesn’t
repeat or
terminate (stop).
1 = i (imaginary
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1-A9 (Lesson 1-8) “Number Systems” p. 46-50 *calculator
Read Ex. 1
1A)
6
11
1B)  9.16
 Closure Property: determines if a solution to an operation is
found in the ________________________ as are in the problem
Read Ex. 2
2A) integers, division
2B) integers, addition
 Number line:
o Has a ___________ under the line
o Coordinate: the number that corresponds to a
___________ on a number line; labeled above the line
o includes both _________________ and
___________________ numbers (values between the
labeled values)
Read Ex. 3
3A) {-5,-4,-3,-2,…}
3B) x  8
5
 _________________: number that, when squared, results in the
given value
o Symbol is called a _____________
o Principal square root is ________________
o Only give the negative square root if there is a
_______________ sign in front of the radical
Read Ex. 4
4
121
4A)
4B)  1.69
Read Ex. 5
5)
 Compare real numbers: use a _________________ to
approximate irrational square roots
Read Ex. 6
6A)
2
2
______
3
5
6B) 0.8 _____
8
9
 Order real numbers: use decimal approximations
Read Ex. 7
7A)
0.42, 0.63,
4
9
7B) 1.46, 0.2,
2, -
1
6
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1-A10 (Lesson 1-9 “Functions and Graphs” p. 53-55
 Function: a relationship between ________________ and
_______________
 Coordinate plane: formed by the intersection of two number lines
o Horizontal axis: also called the ________________ and
the ____________________ variable
o
Vertical axis: also called the ________________ and
the ____________________ variable
o Origin: the point where the two axes
__________________;
 Ordered pair: labels a ___________ on a graph; has two
________________________, x and y
(x, y)
Read Ex. 1
1)
Read Ex. 2
2A)
I:
D:
2B)
I:
D:
Read Ex. 3
3)
 Relation: a set of ________________________ (x, y)
 Domain: set of values for the ______________________
variable; all the values of ____
 Range: set of values for the ______________________
variable; all the values of ____
 Discrete: _____________________ points
 Continuous: forms a _____________ or ______________
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