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)

| | |T/F |

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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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