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)
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1B)
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2A) 2B)
3A)
| | |T/F |
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3B)
| | |T/F |
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4)
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)
The Real Number System
1-A9 (Lesson 1-8) “Number Systems” p. 46-50 *calculator
Read Ex. 1
1A) [pic] 1B) [pic]
⇨ 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) [pic]
⇨ _________________: 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
4A) [pic] 4B) [pic]
Read Ex. 5
5)
⇨ Compare real numbers: use a _________________ to approximate irrational square roots
Read Ex. 6
6A) [pic] 6B) [pic]
⇨ Order real numbers: use decimal approximations
Read Ex. 7
7A) [pic] 7B) [pic]
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: 2B) I:
D: 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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Irrational Numbers:
ex:
( and [pic]
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).
Integers: Whole numbers and their opposites (this means positive and negative whole numbers). ex: & , ¾4, ¾3, ¾2, ¾1, 0, 1, 2, 3, 4, &
Whole Numbers: Natural Numbers 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,…
Rational Numbers: numbers that can be written in the form of [pic]. As a decimal they repeat or terminate.
ex: [pic] repeats ex: [pic] terminates
So what isn’t a real number? divide by zero = undefined ([pic] ), and [pic] = i (imaginary numbers) are two examples.
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