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Appendix A.1.1, A1.4, A1.5 and 1.1.1
Name:________________________
Core Connections Algebra: Exploring Variables and Combining Like terms
Date:_____
Vocabulary to know is indicated in bold
Alegbra: A branch of mathematics in which arithmetical operations and relationships are generalized by using
alphabetic symbols to represent unknown numbers or members of specified sets of numbers.
Expression: A mathematical expression is a combination of numbers, variables, and operation symbols. For
example, 4x2 − 3x + 6 is an expression. It has three terms: 4x2, 3x, and 6.
Variable: A variable is an alphabetic character representing a number
1. Give an example of a variable___________
Term: A term is a constant or a variable in an expression. Addition and subtraction separate expressions into
terms.
2. What are the terms in the expression: 4x2 − 3x + 6 ?_______________________
What are Like Terms?
The following are like terms because each term consists of a single variable, x, and a numeric coefficient:
2x, 45x, x, -x
Each of the following are like terms because they are all constants: 15, -2, 27, 9043, 0.6
3. Find the like terms in the following expressions and list them. State NA if there are no like terms:
a.
5x2 + 7x + 2 - 2x2 + 7 + x ______________________________
b.
9 + 7x + 4x2
_________________________________
c. 12+3x+2x2+5x-1
_________________________________
d. 17x + 17z
_________________________________
e. 15y + 19y2 + 31y5
________________________________
f. 19x + 14xy
________________________________
g. 12+5x+2x2+3x+ 4 +x2 ________________________________
Combining Like Terms - is a process used to simplify an expression or an equation using addition and
subtraction of the coefficients of terms.
Example 1: 2x2 + xy + y2 + x + 3 + x2 + 3xy + 2 ⇒ 3x2 + 4xy + y2 + x + 5
Example 2: 3x2 − 2x + 7 − 5x2 + 3x − 2
⇒ −2x2 + x + 5
4. Simplify the expressions by combining like terms:
a.
5x2 + 7x + 2 - 2x2 + 7 + x ________________________________
b.
12+5x+2x2+3x+ 4 +x2 ________________________________
Evaluate an Expression - The word evaluate indicates that the value of an expression should be calculated
when a variable is replaced by a numerical value.
For example, when you evaluate the expression x2 + 4x – 3 for x = 5, the result is:
(5)2 + 4(5) –3
25 + 20 – 3
42
2
5. Evaluate the following expression: y = 3x – 5x + 2 for x = 4
Chapter 1.1.1
Absolute value –Absolute value represents the numerical value of a number without regard to its sign. The
symbol for absolute value is two vertical bars, | | . Absolute value can represent the distance on a number
line between a number and zero. Since a distance is always positive, the absolute value is always either a
positive value or zero. The absolute value of a number is never
negative.
For example, the number −3 is 3 units away from 0, as shown on the
number line at right. Therefore, the absolute value of −3 is 3. This is
written
.
Likewise, the number 5 is 5 units away from 0. The absolute value of 5
is 5, written
.
6. Circle the expression(s) NOT equal 5:
5
2  3
5
5
2  3
1 5
5  1
Homework #1:
Appendix A.1.1: A-4. Use these directions: Simplify the expressions by combining like terms. If it is not
possible to simplify the expression, explain why not.
Appendix A1.1.2: A-17, A-18, A-19, A-22
Chapter 1.1.1: 1-5, 1.7, 1-8.