AlgebraSurvivalGuide - Glossary

Question 1

Absolute Value

Answer 1

the distance between a number and zero on the number line. Absolute Value is always positive because distance is always a positive number. Distance can never be a negative number in nature.

Question 2

Additive Identity property

Answer 2

property that says when you add zero to any number or term, you get back the number or term you started with.

Question 3

Associative property

Answer 3

property that says in addition and multiplication, the way ther terms are grouped makes no difference. In other words, a+(b+c)= (a+b) + c, and a(bc)=(ab)c.

Question 4

Base

Answer 4

the bottom number in an exponential term. Example: in the exponential term X^7, the base is X, while the exponent is 7.

Question 5

Binomial

Answer 5

a polynomial made up of two monomials.

Question 6

Cancelling

Answer 6

the act of tidying up mathematical expressions.

Question 7

Coefficient

Answer 7

the number that stands in front of the variable or variable string in a monomial. A coeffient may be position of negative. Example: in the monopial 5X^2Y, the coefficient is +5 in the monomial 5X^2Y, the coefficient is 5.

Question 8

Commutative property:

Answer 8

property that says that in addtion and multiplication, the order of the terms makes no difference. In other words, a + b is the same as b + a, and ab is the same as ba.

Question 9

Consecutive Integers

Answer 9

Integers that are one apart from one another. Example: 4,5 and 6 are consecutive integers.

Question 10

Coordinate

Answer 10

a number which, by acting as a directional tool, helps you locate a point on the coordinate plane. Each pint on the coordinate plane has both an x-coordinate and a y-coordinate.

Question 11

Coordinate plane

Answer 11

the x-y plane, used for graphing points, lines, and more.

Question 12

Denominator:

Answer 12

the quality below a fraction bar is the denominator. (Compare with numberator)

Question 13

Decending order:

Answer 13

a way of writing a polynomial so that its exponents decrease from left to right.

Question 14

Distance:

Answer 14

the measure of the length of a line between two distinct points.

Question 15

distributive property:

Answer 15

a property that says this: If you have a parenthesis containing a bunch of terms linked by addition or subtraction signs, any number or term that multiplies the parenthesis multiplies every term inside the parenthesis. That is: a(b+c)=ab+ac, and a(b-c)=ab-ac.

Question 16

Equation

Answer 16

any mathematical expression that has an equal sign and quantities on both the left and right sides of the equal sign. An equaiton tells you that these tow quantities are equal.

Question 17

Even numbers

Answer 17

the set of all numbers: {-∞…-6,-4,-2,0,2,4,6…+∞} (Compare with odd numbers.)

Question 18

Exponent

Answer 18

a little number or term that sits on the right shoulder of another number or term called the base. The exponent tells you how many times the base is mulitplying itself. For example: int eh exponential term c^7, the exponent 7 tells you that X is multiplying itself 7 times.

Question 19

Exponential term:

Answer 19

the base and the exponent, viewed as a whole.

Question 20

Factor:

Answer 20

one of two or more terms which, multiplied together, give you some product. Examples: 3 and 5 are factors of 15 because 3×5=15; and x and x^3 are factors of x^4 because x times x^3 = x^4.

Question 21

Facoring:

Answer 21

the act of splitting a methematical expression into its basic parts.

Question 22

Fraction:

Answer 22

a term made up of a numberator and a denominator. When yo see a fraction, it mens that the numerator is eing divided b the denominator.

Question 23

Greatest common factor:

Answer 23

the largest number or term that divides evenly into two or more numbers or terms.

Question 24

Infinity:

Answer 24

a way of expressing that which is the ultimate in largeness or smallness. Positive infinity means that which is large beyong our ability to count it; neative infinity means that which is small beyond our ability to couont it. The symbol for infinity is this: ∞

Question 25

integers:

Answer 25

the set of all whole numbers plus the negtive of the natural numbers: {-∞…-6,-4,-2,0,2,4,6…+∞}

Question 26

Like terms:

Answer 26

terms that represent the same kinds of things. For example, 4X and 11X are like terms; 7p^2q and 5p^2q are like terms.

Question 27

Line:

Answer 27

straight extension with no thickness. There is one and only one line between any two distinct points.

Question 28

Linear equation:

Answer 28

an equation that represents a line. One type on linear equation is the slope-intercepts equation : y=mx +b

Question 29

Mixed -sign rule:

Answer 29

the rule for combining numbers with different signs.

Question 30

Monomial:

Answer 30

a term made up of either: a) a number, or b) a coefficient along with a vairable or a variable string. Ecamples of monomials are: 3, -3, 5x, 7x^3, -7x^3.

Question 31

Multiplicative identity property:

Answer 31

property that says when you multple any number or tern by 1, you get back the number or term you started with.

Question 32

Natural numbers:

Answer 32

the set of all counting numbers: {1,2,3,4…∞}

Question 33

Negative exponent:

Answer 33

an exponent that has a negative sign.

Question 34

Negative infinity:

Answer 34

a mathematical way of referring to that which is small beyond our ability to count it. The symbol for negative infinity isthis: -∞

Question 35

Neighbor-sign rule:

Answer 35

the rule for dealing with two signs that are directly next ot each other. This rule tells you that the two signs merge to become one sign.

Question 36

Number:

Answer 36

A symbol used to indicate how many of a certain quantity you’re dealing with.

Question 37

Numerator:

Answer 37

the quantitiy above a fraction bar is the numerator. (Compare with denominator)

Question 38

Odd numbers:

Answer 38

the set of all numbers: {-∞ …-5,-3,-1,1,3,5…+∞} Compare with even numbers.

Question 39

Order of operations:

Answer 39

the set of rules that tells you which operation to perform before which other operation.

Question 40

Origin:

Answer 40

the point on a coordinate plane where the x-axis and y-axis meet.

Question 41

Percent:

Answer 41

a way of indicating how much of a quantity you’re dealing with. Percent means “out of one hundred,” so when you state a percent, you’re saying how many hundredths of something you have. Example: 12 percent means 12/100.

Question 42

Perfect square

Answer 42

what you get when you square a number or a term.

Question 43

Point:

Answer 43

a location on the coordinate plane. A point has no size.

Question 44

Polynomial:

Answer 44

a string of two or more monomials.

Question 45

Product:

Answer 45

what you get when you multiply numbers or terms together. Example: when you multiply 3 by 5, the product is 15.

Question 46

Quadratic trinomial:

Answer 46

a trinomial in which the highest exponent is 2.

Question 47

Radical:

Answer 47

the root of a number. In Algebra I, the tem radical means square root.

Question 48

Rational numbers:

Answer 48

the set of numbers that can be written as an Integer divided by another integer. There’s one exception: any number divided by zero is not a rational numebr; it is undefined.

Question 49

Real numbers:

Answer 49

Combine the rational numbers and Irrational numbers. Whe you put them together, you get the set of real numbers.

Question 50

Reciprocal:

Answer 50

the flip of a fraction. For example: 4/3 is the reciprocal of 3/4; and 5x/3y is the reciprocal of 3y/5x.

Question 51

Reflexive property:

Answer 51

a property that says that anything is equal to itself. That is a=a.

Question 52

Same-sign rule:

Answer 52

rule that tells you how to combine a group of numbers that are either all positive or all negative.

Question 53

Slope:

Answer 53

the measure of the steepness of a line on the corrdinate plane.

Question 54

Square root:

Answer 54

Choose any number or term. The find the special number or term which, when multiplied by itself, gives you the numbeer or term you started with for example, start with 9. Since 3⋅3=9, 3 is the square root of 9. Or start with 25x^2. Since 5x ⋅5x = 25x^2, 5x is the square root of 25x^2.

Question 55

Squaring:

Answer 55

the act of multiplying a number or term by itself. Example: if you square 7, you get 49.

Question 56

Symmetric property:

Answer 56

property that says the left and right sides of an equation are interchangeable. In other words, if it’s true that a=b, then it’s also true that b=a.

Question 57

Transitive property:

Answer 57

property by which you discover that two quqntities are equal because both of them are equal to a third quantity. Here’s an example with b acting as the third quantity. If a=b and b=c, then a=c.

Question 58

Trinomial:

Answer 58

a string of three monomials.

Question 59

Variable:

Answer 59

a letter that stands for a nystery quantity whose value you want to discover. In general algebraic rule and principles, variables stand for any number whatsoever.

Question 60

Variable string:

Answer 60

two or more varibales multipled together. Examples of variable string are: xyz and a^4bc^3.

Question 61

Whole numbers:

Answer 61

the set of all natural numbers, plus zero: {0,1,2,3,4,5…∞}

Question 62

X-axis:

Answer 62

the axis that runs horizontally (left to right) on the coordinate plane.

Question 63

y-coordinate:

Answer 63

the coordinate of a point that tells you how far that point stands above or below the origin.

Question 64

y-intercept:

Answer 64

point where a line crosses the y-axis.