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CRT 1 Notes
1
Name ______________________________________________________ Hour _____________
1.1 Using Differences to Identify Patterns
Number Sequence – _____________________________________________
Constant Difference – ___________________________________________
____________________________________________________
Conjecture – ___________________________________________________
Examples:
Find the next three terms of each sequence by using constant differences.
a.
12.4, 10.7, 9, 7.3, 5.6, …
b.
49, 64, 81, 100, 121, …
The third and fourth terms of a sequence are 26 and 40. If the second
differences are a constant 4, what are the first five terms of the sequence?
Homework: p. 8 # 10-24
1.2 Variables, Expressions, and Equations
Variable – _____________________________________________________
Algebraic Expression – __________________________________________
CRT 1 Notes
2
Name ______________________________________________________ Hour _____________
Evaluations – __________________________________________________
_____________________________________________________
Equations – ____________________________________________________
Solution – _____________________________________________________
Examples:
1.
Make a table to show the value of the expression 4m – 10 when m is 8,
9, 10, and 11.
2.
The cost to rent a set of jet skis is a $20 fee plus $50 per hour. Make a
table to show the total cost to rent the skis for 1 hour through 5 hours.
Write an equation for the situation.
Use guess-and-check to solve the following equations.
3.
19x + 13 = 51
4.
7x – 12 = 44
Homework: p. 16 # 10 – 36 even, 37-39 all
CRT 1 Notes
3
Name ______________________________________________________ Hour _____________
1.3 The Algebraic Order of Operations
______________________________________________________________
________________
________________
________________
________________
________________
________________
Examples:
Evaluate each expression.
1.
72 (98) + 12
3.
4 2  2  7  32  5
 
2.

Homework: p. 21 # 18 – 64 even
91  7  6
CRT 1 Notes
4
Name ______________________________________________________ Hour _____________
2.1 The Real Numbers and Absolute Value
Real Numbers
Rationals
Irrationals
Integers
Whole Numbers
Natural Numbers
Natural Numbers – ______________________________________________
Whole Numbers – ______________________________________________
Integers – _____________________________________________________
Rationals – ____________________________________________________
Irrationals – ___________________________________________________
Absolute Value – _______________________________________________
Examples:
Use division to write each rational number as a decimal. Indicate whether it
is a terminating or repeating decimal.
a.
13
40
b.
7
12
c.
5
9
CRT 1 Notes
5
Name ______________________________________________________ Hour _____________
Insert an ordering symbol to make each statement true.
a.
-3 ___ 6
b.
-8.5 ___ -8.6
b.
-(8.6 – 1.5)
b.
16
c.
4
16
___
5
20
c.
72
Evaluate each expression.
a.
-(-10)
Simplify
8
a.
Homework: p. 58 # 20-60 even, 61-64 all
2.2-2.3 Adding and Subtracting Real Numbers
Walking on a number line
Steps:
1.
_______________________________________________________
2.
_______________________________________________________
(______________________________________________________)
3.
_______________________________________________________
(______________________________________________________)
4.
_______________________________________________________
CRT 1 Notes
6
Name ______________________________________________________ Hour _____________
Examples:
1.
3–7
2.
-5 + (-8)
Homework: Number line worksheet
2.2 More adding and subtracting
Rules:
 _________________________________________________________
_________________________________________________________
Adding Same Sign
 _________________________________________________________
Adding Opposite Signs
 _________________________________________________________
Examples:
1.
(-7) + (-15)
3.

4  7
  
15  15 
Homework: 2.2-2.3 wkst
2.
5.7 + (-3.2)
CRT 1 Notes
7
Name ______________________________________________________ Hour _____________
2.4 Multiplying and Dividing Real Numbers
Rules:
___________________________ = ___________________
___________________________ = ___________________
___________________________ = ___________________
___________________________ = ___________________
___________________________ = ___________________
___________________________ = ___________________
___________________________ = ___________________
___________________________ = ___________________
Examples:
1.
(-15) (2)
2.
(-6.1)(-9)
3.
 36
4
4.
 3.8 19
Homework: p. 78 # 18 – 58 even
CRT 1 Notes
8
Name ______________________________________________________ Hour _____________
2.5 Properties and Mental Computation
Commutative Property of Addition
For all real numbers a and b:
________________
Commutative Property of Multiplication
For all real numbers a and b:
________________
Associative Property of Addition
For all real numbers a, b, and c:
___________________
Associative Property of Multiplication
For all real numbers a, b, and c:
___________________
Distributive Property
For all real numbers a, b, and c:
____________________
____________________
Examples:
Complete each step and name the property used.
1.
(36 + 15) + 64
=(15 + ___) + 64
= 15 + (36 + ___)
= 15 + ___
= _____
Find the opposite of each expression.
2.
x+y
Homework: p. 86 # 12-36 even
CRT 1 Notes
9
Name ______________________________________________________ Hour _____________
2.6 Adding and Subtracting Expressions
Term – _______________________________________________________
Like Term – ___________________________________________________
Coefficient – __________________________________________________
Constant – ____________________________________________________
Simplify expressions – ___________________________________________
Examples:
Simplify.
1.
(4y – 5) + (-3y + 2)
2.
(a + 9) – (-3a – 7)
3.
(7x – 13y) – (8x + 6y)
Homework: p. 92 # 22 – 46 even
CRT 1 Notes
10
Name ______________________________________________________ Hour _____________
2.7 Multiplying and Dividing Expressions
Examples:
Simplify.
1.
8x (-5x – 9)
2.
(-3a – 4)(-5)
3.
(4a – b + 3) + 2(5a + 2b – 1)
4.
10 x 2  5
5
Homework: p. 101 # 18 – 46 even
Name ______________________________________________________ Hour _____________
Monday
Labor Day
11
Tuesday
Warm-ups for 9/1-9/5
Wednesday
Thursday
Friday
Name ______________________________________________________ Hour _____________
12
Monday
Tuesday
Warm-ups for 9/8-9/12
Wednesday
Thursday
Friday
Name ______________________________________________________ Hour _____________
13
Monday
Tuesday
Quiz 2.2-2.4
Warm-ups for 9/15-9/19
Wednesday
Thursday
Friday
Name ______________________________________________________ Hour _____________
14
Monday
Tuesday
CRT 1A
Wednesday
Warm-ups for 9/15-9/19
Test 1
Thursday
Friday