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386 Cards in this Set
- Front
- Back
- 3rd side (hint)
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Natural Numbers are. |
{1,2,3,4,...} |
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Whole Numbers are.
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{0,1,2,3,...} |
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Integer Numbers are.
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{...,-3,-2,-1,0,1,2,3,...}
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Rational Numbers are.
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{Quotient of two integers, denominator not 0}
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The sum of two positive numbers will be a.
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Positive Number
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The sum of two negative numbers will be a.
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Negative Number
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The sum of a postive number and a negative number can be either a. |
Positive or Negative number.
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The product (or quotient) of two numbers with like signs will be a.
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Positive number.
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b^5 = ?
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b*b*b*b*b
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1st Order of Operations (1/4)
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Evaluate expressions within parentheses.
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2nd Order of Operations (2/4)
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Evaluate expressions with exponents.
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3rd Order of Operations (3/4)
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Perform Multiplications or divisions moving from left to right.
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4th Order of Operations (4/4)
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Perform additions or subtractions moving from left to right.
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Commutative Property:
a+b = a*b = |
b+a
b*a |
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Associative Property:
(a+b) + c = (a*b) * c = |
a+(b+c)
a*(b*c) |
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Distributive Property:
a(b+c) = |
a*b+a*c
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Identity Property:
a+0 = 1*a = |
0+a = a
a*1 = a |
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Inverse Property:
a + (-a) = a * 1/a = |
-a + a = 0
1/a*a = 1 |
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Variable
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a letter or symbol used to represent an unknown number
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Constant
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a value that does not change
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Numerical Expression
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contains only constants and/or operations |
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Algebraic Expression
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contains only variables, constants, and/or operations
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Evaluate an Expression
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to find its value...substitute given numbers for the variables and then simplify the expression using the order of operations
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Equation
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a mathematical statement that two expressions are equal
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Solution of an Equation
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a value of the variable that makes the equation true |
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Properties of Equalities
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you can add, subtract, multiply, or divide the same number to both sides of an equation, and the statement will still be true...used to solve equations
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Distributive Property
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for all real numbers, a, b, and c, a(b+c)=ab+ac |
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Coefficient
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a number that is multiplied by a variable...in 3x, 3 is the coefficient (x is the variable)
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Like Terms
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terms that have the same variables with the same exponents...to collect like terms, you add or subtract their coefficients (variables and exponents stay the same) |
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Identity
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an equation that is always true no matter what value is substituted for the variable...the solution is All Real Numbers |
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Formula
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an equation that states a rule for a relationship among quantities |
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Literal Equation
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an equation with two or more variables...a formula is a type of literal equation
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Absolute Value of a Number
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its distance from zero on a number line |
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Steps for Solving an Absolute Value Equation
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1. Use inverse operations to isolate the absolute–value expression |
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Ratio
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a comparison of two quantities by division (a fraction a/b or a:b) |
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Proportion
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a statement that two ratios are equal
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Rate
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a ratio with two quantities with different units
Ex: 34 km/ 2 hr |
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Unit Rate
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a rate with a denominator of 1...you can change any rate to a unit rate
Ex: 16 km/1hr or 16 km/hr |
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dimensional analysis
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a process that uses rates to convert measurements from one unit to another
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Conversion factor
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a rate in which two quantities are equal but have different units...used to convert from one set of units to another
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Proportion
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a statement that sets two ratios (fractions) equal to each other...The idea of proportions is that a ratio can be written in many ways and still be equal to the same value
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Cross Products Property
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used to solve proportions...if a/b=c/d, then ad=bc
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Scale
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a ratio between two sets of measurements such as
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1 in: 5 miles |
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Scale Drawing
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uses a scale to represent an object as much smaller or larger than the actual object...a map is an example of a scale drawing |
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Similar Figures
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figures that have exactly the same shape but not necessarily the same size
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Corresponding Sides/Angles
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sides/angles of two figures that are in the same relative position...Two figures are similar IFF the lengths of the corresponding sides are proportional and the corresponding angles have equal measures |
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Indirect Measurement
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method of measurement that allows you to solve a proportion involving similar triangles to find a length that is not easily measured..Ex: Using shadows
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Precision
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level of detail in a measurement...determined by the smallest unit or fraction of a unit that you can reasonably measure |
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Accuracy
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the closeness of a measured value to the actual or true value
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Tolerence
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describes the amount by which a measurement is permitted to vary from a specified value...Usually expressed as a range of values |
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Translate the sentence into an equation: Fifteen more than a number times six is eleven less than a different number times two.
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15 + 6z = 2y – 11
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Translate the sentence into an equation: The quotient of a number and 3 is the same as a the same number less seven.
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b/3 = b – 7
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Translate the sentence into an equation: The product of a number and 17 is the same as the number squared and then increased by 3.
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//dp11i9uvzjqmt.cloudfront.net/2/images/upload-flashcards/88/09/41/3880941_m.jpg
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Translate the equation into a sentence: 12 – 2x = –5
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Twelve minus two times a number equals the opposite of five.
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Translate the equation into a sentence: 12 – 3x = 6
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Twelve reduced by three times a number is six.
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//dp11i9uvzjqmt.cloudfront.net/2/images/upload-flashcards/88/10/22/3881022_m.jpg
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A number cubed added to three–fifths is the same as two.
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Tim's bank contains quarters, dimes, and nickels. He has three more dimes than quarters and 6 fewer nickels than quarters. If he has 63 coins, write and solve an equation to find how many quarters he has.
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x = number of quarters.
x + 3 = number of dimes x – 6 = number of nickels x + (x + 3 ) + (x – 6) = 63 3x – 3 = 63 3x = 66 x = 22 |
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Solve the equation: x – 11 = 34
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x = 45
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Solve for x: –1/3 + x = 2/3
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x = 1
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Solve for x: 5x = 25
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x = 5
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Solve for x: –3/4x = 15
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x = –20
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Solve for x: x/3 = –5/6
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x = –15/6 = –5/2
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An X–Men #1 comic book in mint condition recently sold for $45,000. An Action Comics #63 (Mile HIgh), also in mint condition, sold for $15,000.
1) Define a variable to determine the difference in selling price. 2) Write an equation using the variable from part 1. 3) Solve for how much more the X–Men comic book sold for than the Action Comics book. |
1) D = difference in price of the comic books.
2) D = $45,000 – $15,000 3) D = $30,000 |
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Solve for x: 2x + 18 = 12
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x = –3
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//dp11i9uvzjqmt.cloudfront.net/2/images/upload-flashcards/88/12/41/3881241_m.jpg
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x = 62
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Show how to use algebra to find three consecutive integers that sum to –36.
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x = 1st number
x + 1 = 2nd number x + 2 = 3rd number x + (x + 1)+ (x + 2) = –36 3x + 3 = –36 3x = –39 x = –13 –13, –12, –11 |
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The cost of a bag of potatoes is $1.50 less than 1/2 the price of apples. Write and solve an equation to find the cost of potatoes if apples cost $6.99/bag.
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P = cost of potatoes
P = 1/2($6.99) – 1.50 P = $2.00 |
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Solve for x: 3x + 2 = 7x
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x = 1/2
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5a + 2 = 6 – 7a
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a = 1/3
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Name for when an equation is true for all values of the variable.
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Identity
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–2(3x – 2) = 4 – 6x
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x = infinite solutions
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2s + 5 = 2(s – 3)
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no solution
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8 = 4(r + 4)
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r = –2
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//dp11i9uvzjqmt.cloudfront.net/2/images/upload-flashcards/88/12/89/3881289_m.jpg
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x = 4
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Solve the equation and graph the solution set.
|x + 3| = 6 |
//dp11i9uvzjqmt.cloudfront.net/2/images/upload-flashcards/91/66/71/3916671_m.jpg
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On a map the scale is 5 inches = 31 miles. What is the distance represented by 3 1/2 inches on the map.
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21.7 miles
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Evaluate the expression: 15 – |g + 9| for g = –5
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11
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Evaluate the expression: |3 – h| + 7 for h = 5
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9
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//dp11i9uvzjqmt.cloudfront.net/2/images/upload-flashcards/91/66/83/3916683_m.jpg
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|x – 1| = 3
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For a company to invest in a product, they must believe they will receive a 12% return on investment (ROI) plus or minus 3%. Write an equation to find the least and the greatest ROI they believe they will receive.
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|x – 12| = 3; x = 9% or x = 15%
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//dp11i9uvzjqmt.cloudfront.net/2/images/upload-flashcards/91/68/36/3916836_m.jpg
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yes, they are equivalent.
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//dp11i9uvzjqmt.cloudfront.net/2/images/upload-flashcards/91/68/57/3916857_m.jpg
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No, these are not equivalent.
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Find the percentage of change from 96 to 25. Round to the hundredths place. Is this an increase or decrease?
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Decrease by 73.96%
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//dp11i9uvzjqmt.cloudfront.net/2/images/upload-flashcards/91/69/32/3916932_m.jpg
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x = 2
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Mrs. B can run 3 miles in 31 minutes. If she could maintain this pace how long would it take her to run a marathon which is 26.2 miles?
1) Give your answer in minutes 2) Convert your answer to hours |
1) 270.73 minutes
2) 4.5 hours |
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Find the percent of change from 13 to 17. Round your answer to the hundredths of a percent. Indicate if this is an increase or decrease.
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Increase by 30.77%
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Find the total price of an item that costs 12.99 with a 9.5% tax rate.
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12.99 x (1.095) = $14.23
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Each bowling game costs $2.50. If Mrs. B bowled 3 games and the tax rate is 7.5% what was the total charge for bowling?
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3(2.5)(1.075) = $8.07
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What is the discounted price of an item that cost $65 if the discount is 15%?
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$65 * .85 = $55.25
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Solve the equation for g: 7h + f = 2h + g
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5h + f = g
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A car's fuel economy (E) is given by the formula E = m/g where m is the number of miles driven and g is the number of gallons of fuel. Solve the formula for m.
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m = Eg
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Mrs. B went to Guatemala. The currency there is quetzal. $1 dollar equals 7.8 quetzal. If Mrs. B took $125 on her trip. How many quetzals does that represent?
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975 quetzals
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Mrs. B returned from her trip to Guatemala with 120 quetzals. The exchange rate is $1 dollar = 7.8 quetzals. How much does this amount represent in dollars?
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$15.38
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How many cm are in 2 feet?
1 inch = 2.54 cm 12 inch = 1 foot |
//dp11i9uvzjqmt.cloudfront.net/2/images/upload-flashcards/91/72/50/3917250_m.jpg
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Grades are often computed using a weighted average. Suppose that homework counts 10%, quizzes 20%, and tests 70%.
If Pat has a homework grade of 92, a quiz grade of 68, and a test grade of 81, what is his final grade? |
Pat's overall grade = (0.10)(92) + (0.20)(68) + (0.70)(81)
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Bob had three carries of 8 yards each and five carries of 6 yards each in a recent football game. What was has rushing average (average yards per carry)?
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(3 x 8 + 5 x 6)/8 = 6.75 yards per carry
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A boat travels 16 miles due north in 2 hours and 24 miles due west in 2 hours. What is the average speed of the boat?
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16/2 + 24/2 = 20 miles per hour
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A cyclist begins traveling 18 miles per hour. At the same time and at the same starting point, an inline skater follows the cyclist's path and begins traveling 6 miles per hour. After how much time will they be 24 miles apart?
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24 = 18t – 6t where t = time |
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What is a mixed number?
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A mixed number is the sum of a whole number and a fraction.
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Why is it impossible to draw a mathematical line?
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It is impossible to draw a mathematical line because it is a straight line that has no width and no ends.
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How do we show a location on a mathematical line?
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To show the location of a mathematical line, we draw a pencil line and put arrowheads on both ends to emphasize that the mathematical line goes on and on in both directions.
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What is a line segment?
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A line segment is a part of a line. It contains the endpoints and all points between the endpoints.
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How do we show the location of a line segment?
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To show the location of a line segment, we use a pencil line with no arrowheads. We name a segment by naming the endpoints of the segment.
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Tell me about intersecting lines.
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If two lines cross, we say that the lines intersect.
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Tell me about the Point of Intersection.
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The point of intersection is the place where the lines cross.
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Tell me about parallel lines.
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Parallel lines are two lines in the same plane that do not intersect.
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Tell me about perpendicular lines.
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If two lines make square corners at the point of intersection, we say that the lines are perpendicular.
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Tell me about right angles.
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Right angles are the angles made by perpendicular lines.
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Tell me about a straight angle.
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A straight angle is formed by two right angles.
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Tell me about an acute angle.
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An acute angle is an angle that is smaller than a right angle.
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Tell me about an obtuse angle.
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An obtuse angle is an angle greater than a right angle, but less than a straight angle.
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How many degrees does a right angle measure?
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A right angle measures 90 degrees.
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How many degrees does a straight angle measure?
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A straight angle measures 180 degrees.
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How many degrees does a circle measure?
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A circle measure 360 degrees.
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Tell me about a polygon.
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A polygon is a simple, closed, flat geometric figure whose sides are line segments.
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Tell me about the attributes of a polygon.
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1. Each segment of a polygon is called a side.
2. Each endpoint of a side is called a vertex of the polygon. The plural of vertex is vertices. 3. For a polygon, the number of sides is always equal to the number of vertices. |
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Tell me about a concave polygon.
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A concave polygon is a polygon that has an indentation. (a cave)
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Tell me about a convex polygon.
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A convex polygon does not have an indentation.
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Tell me about an equilateral polygon.
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An equilateral polygon is a polygon whose sides all have equal length.
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Tell me about an equiangular polygon.
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An equiangular polygon is a polygon whose angles all have equal measure.
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Tell me about a regular polygon.
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A regular polygon is a polygon in which all sides have the same length and all angles have the same measure.
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What is the sum of the measures of the three angles in any triangle?
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The sum of the measures of the three angles in any triangle is 180 degrees.
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Tell me about a right triangle.
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A right triangle is a triangle that has a right angle.
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Tell me about an acute triangle.
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An acute triangle is a triangle in which all the angles are less than 90 degrees. (all angles are acute)
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Tell me about an obtuse triangle.
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An obtuse triangle is a triangle which contains an obtuse angle. (greater than 90 degrees)
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Tell me about an equiangular triangle.
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An equiangular triangle is a triangle in which the measures of all the angles are equal. (Each angle in an equiangular triangle must have a measure of 60 degrees.)
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Tell me about an isosceles triangle.
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An isosceles triangle is a triangle that has at least two sides of equal length.
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Tell me about an equilateral triangle.
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An equilateral triangle is a triangle in which the lengths of all sides are equal.
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Tell me about a scalene triangle.
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A scalene triangle is a triangle that has no sides of equal length.
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What are five types of quadrilaterals?
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Five types of quadrilaterals are:
1.Parallelogram 2.Trapezoid 3. Rectangle 4. Rhombus 5. Square |
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Tell me about a parallelogram.
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A parallelogram is a quadrilateral that has two pairs of parallel sides.
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Tell me about a trapezoid.
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A trapezoid is a quadrilateral that has exactly two parallel sides.
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Tell me about a rectangle.
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A rectangle is a parallelogram with four right angles.
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Tell me about a rhombus.
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A rhombus is an equilateral parallelogram.
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Tell me about a square.
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A square is a rhombus with four right angles.
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Tell me about perimeter.
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Perimeter is the distance around the outside of a closed, planar geometric figure.
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Tell me about the radius of a circle.
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The radius of a circle is the distance from the center of the circle to any given point on a circle.
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Tell me about the diameter of a circle.
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In reference to a circle, the length of a chord of a circle that passes through the center of the circle. The diameter of a circle is twice the length of the radius.
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Tell me about the circumference of a circle.
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The circumference of a circle is the distance around a circle. (the perimeter)
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What is an irrational number?
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An irrational number is a number that cannot be written as a quotient of integers.
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What is pi?
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Pi is the ratio of the circumference of a circle to the diameter of that circle. Pi ~ 3.14.
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What is a number?
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A number is an idea.
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What is a numeral?
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A numeral is a single symbol or a collection of symbols that we use to express the idea of a particular number.
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What is the value of a numeral?
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The value of a numeral is the number represented by the numeral, and we see that the words 'value' and 'number' have the same meaning.
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Tell me about the decimal system.
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The decimal system is the system of numeration that we use to designate numbers. The decimal system uses 10 symbols that we call digits.
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What are natural numbers (or counting numbers)?
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Natural numbers (or counting numbers) are the numbers that we use to count objects or things.
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What is a positive real number?
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A positive real number is any number that can be used to describe a physical distance greater than zero.
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Tell me about the number zero.
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The number zero is not a positive number. It is a real number.
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What is a real number?
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A real number isthe set of numbers that includes all members of the set of rational numbers and all members of the set of irrational numbers.
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Tell me about negative numbers.
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Negative numbers are real numbers. Every positive number has a negative counterpart, and we call these numbers negative real numbers. We must always use a minus sign when we designate a negative number.
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What is a number line?
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A number line is a line divided into units of equal length with one point chosen as the origin, or zero point. The numbers to the right of zero are the positive real numbers, and the numbers to the left of zero are the negative real numbers.
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Tell me about graphing a number.
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We graph a number when we place a dot on the number line to indicate the location of a number. The number is said to be the coordinate of the pint that we hae graphed.
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Why do we use a number line?
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We use the number line to tell if one number is greater than another number by saying that a number is greater than another number if its graph lies to the right of the graph of the other number.
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How are fractions multiplied?
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Fractions are multiplied by mutiplying the numerators to get the new numerator, and by multiplying the denominators to get the new denominator.
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How do we divide fractions?
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We divide fractions by inverting the divisor and then multiplying.
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How do we multiply or divide mixed numbers?
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We change mixed numbers to improper fractions and then multiply or divide as indicated.
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What are the four basic operations of algebra?
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The four basic operations of algebra are:
1. addition 2. subraction 3. multiplication 4. division |
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In an addition problem, what are the addends? What is the sum?
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The addends are the numbers to be added. The sum is the result of the addition problem.
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In a subtraction problem, what is the minuend, the subtrahend and the difference?
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We call the first number the minuend; the second number, the subtrahend; and the result, the difference.
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Tell me about multiplication.
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If two numbers are to be multiplied to achieve a result, each of the numbers is called a factor and the result is called a product.
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What is the product of a particular real number and the number 1?
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The product of a particular real number and the number 1 is the particular number itself.
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What is the product of any real number and the number zero?
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The product of any real number and the number zero is the number zero.
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Explain the terms dividend, divisor and quotient.
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The dividend is the number or quantity divided by another number. The divisor is a number or quantity that divides another number or quantity. The quotient is the result of dividing one number or quantity by another number or quantity.
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What is the numerator?
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The numerator is the number or quantity above the fraction bar in a fraction; i.e. the dividend of the fraction.
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What is the denominator?
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The denominator is the number or quantity under the fraction bar in a fraction; i.e. the divisor in a fraction.
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Tell me about a unit multiplier.
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A unit multiplier is a fraction that has units and has a value of 1. Unit multipliers are used to change the unit of a number. |
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Prime number
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An integer greater than one whose only positive factors are 1 and itself.
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Composite number
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A noneprime positive integer greater than 1.
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Greatest common factor
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GCF |
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Least common multiple
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LCM |
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Rational number
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It is a number that an be expressed as a ratio of 2 integers when the denominator is not equall to 0.
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Reciprocals
(multiplicative inverses) |
2 numbers whose product are 1
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Square root
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It is one of a numbers 2 equal factors.
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Cube root
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It is one of a numbers 3 equal factors.
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nth root.
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it is one of a numbers n Equal factors
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Set
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A collection of objects.
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Union of sets
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It is the set of elements that appear in any of the sets.
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Intersection of sets
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It is the set of elements common to all of the sets.
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Subset
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One set is a subset of another set if every element of the 1st is contained in the 2nd. A C B
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Natural numbers
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The set of counting numbers, beginning with 1 and going infinately.
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Real numbers |
The union of sets of rational and irrational numbers. |
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rational number
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The set of numbers expressed in the form of a fraction, a over b, where a and b are integers and b is not equal to 0.
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natural numbers
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The set [1,2,3,...] counting numbers
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whole numbers
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The set [0,1,2,3,...]
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intergers
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The set [...–2,–1,0,1,2,...]
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graph
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To draw, or plot, the points named by certain numbers or ordered pairs on a number line or coordinate plane.
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coordinate
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th number that corresponds to a point on a number line.
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àbsolute value
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The absolute value of a number n is the distance from zero on a number line and is represented by |n|.
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positive numbers
negative numbers |
+ are to the R of 0
– values less than 0, listed to the left of 0 |
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opposites
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Every positive rational number and its negative pair.
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additive inverses
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A number and its opposite are additive inverses of each other. The sum of a number and its additive inverse is 0.
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division of integers
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The quotient of two numbers having the same sign is positive, having different signs is negative.
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line plot
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A number line labled with a scale to include all the data with an X placed above a data point each time it occurs.
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measures of central tendency
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Numbers or pieces of data that can represent the whole set of data. The three basic measures of central tendency are: Mean, Median and Mode.
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mean
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The sum of the numbers in a set of data divided by the number of items.
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mode
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The middle number or numbers that appear most often in a set of data.If no item appears the most often, the set has no mode.
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median
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The middle number of a set of data when the data are arranged in numerical order. If there are an even number of data, the median is the mean of the two middle numbers.
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line plot
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A number line labled with a scale to include all the data with an X placed above a data point each time it occurs.
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frequency
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How often a piece of data occurs.
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stem–and–leaf plot
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A system used to seperate data into two numbers that are used to form a stem–and–leaf.
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back–to–back–stem–and–leaf plot
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Used to compare two related sets of data.
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probability
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The ratio of the number of favorable outcomes for an event to the number of possible outcomes of the event. P(a) = Number of favorable outcomes / total number of possible outcomes
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simple event
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A single event.
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sample space
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The list of all possible outcomes.
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equally likely
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Outcomes for which the probillity of each occuring is equal.
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odds
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The ratio that compares the number of ways an event can occur (successes) to the number of ways the event cannot occur (failures)
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square root
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One of two equal factors of a number.
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perfect square
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A number whose square root is a rational number.
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principal square root
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The nonnegative square root of a number.
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irrational numbers
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Numbers that cannot be expressed as terminating or repeating decimals.
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real numbers
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The set of rational numbers and the set of irrational numbers together.
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completeness property
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Each point on the number line corresponds to exactly one real number.
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rational approximation
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A rational number that is close to, but not equal to, the value of an irrational number.
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multiplicative property of –1
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The product of any number and –1 is its additive inverse.
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dividing integers
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The quotient of two numbers having the same sign is positive, having different signs is negative.
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multiplying integers
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Product of two numbers with same sign is positive, different signs is negative.
*even number of negative integers, product is positive, odd number of negative integers, product is negative. |
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radical sign, The radical sign is used to indicate a nonnegative square root.
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//fce-study.netdna-ssl.com/images/upload-flashcards/front/8/3/10638265_m.jpg
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Consecutive Integers
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Integers in counting order
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defining a variable
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Choosing a variable to represent on of the unspecified numbers in a problem and using it to write expressions for the other unspecified numbers in the problem.
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dimensional analysis
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The process of carrying units throughout a computation.
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equivalent equations
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Equations that have the same solutions.
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extremes
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In the rations a/b =c/d, a and d are the extremes.
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formula
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An equation that states a rule in the relationship between certain quantities.
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four–step problem solving
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1. Explore the problem
2. Plan the solution 3. Solve the problem 4. Check the solution |
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identity
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Equations that are true for all values of the variables.
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means
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The middle terms of the proportion.
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mixture problem
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Problems in which two or more parts are combined into the whole.
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multi–step equations
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Equations with more than one operation.
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number theory
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The study of numbers and the relationships between them.
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percent of change
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When an increase or decrease is expressed as a percent.
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percent of decrease
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The ration of an amount of decrease to the previous amount, expressed as a percent.
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percent of increase
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The ration of an amount of increase to the previous amount, expressed as a percent.
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Proportion
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An equation of the form a/b =c/d stating that two ratios are equivalent.
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ratio
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A comparison of two numbers by division.
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rate
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The ratio of two measurements having different units of measure.
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scale
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The ratio or rate used when making a model of something that is to large or to small to be conviently shown at actually size.
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solve an equation
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The process of finding all values of the variable that make the equation a true statement.
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uniform motion problems
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Problems in which an object moves at a certain speed, or rate.
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weighted average
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The sum of the product of the number of units and the value per unit divided by the sum of the number of units, represented by M. |
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monomial
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a number, a variable, or a product of a number and one or more variables
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constants
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monomials that are real numbers
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Product of Powers
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to multipy two powers that have the same base, add the exponents
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Power of a power
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to find the power of a power multipy the exponents
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Power of a Product
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to find the power of a product, find the power of each factor and multiply.
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Simplifying Monimial Expressions
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To simplify an expression involving monimials, write an equivalent expression in which: |
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Variable (p. 6)
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A letter or symbol used to represent a value that can change.
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Constant (p. 6)
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A value that does not change.
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Numerical Expression (p. 6)
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Contains only constants and/or operations.
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Algebraic Expression (p. 6)
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Contains variables, constants, and/or operations.
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Evaluate (p. 7)
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To find the value of an expression.
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Replacement Set (p. 7)
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A set of numbers that can be substituted for a variable.
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Real Numbers (p. 14)
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The set of all numbers that can be represented on a number line.
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Absolute Value (p. 14)
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The distance of a number from zero on a number line.
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Opposites (p. 15)
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Two numbers that have the same absolute value but have different signs.
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Additive Inverse (p. 15)
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A number and its opposite that are the same distance from zero.
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Reciprocal (p. 21)
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The product of two numbers that are equal to 1.
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Multiplicative Inverse (p. 21)
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A number and its reciprocal.
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Power (p. 26)
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An expression written with an exponent and a base.
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Base (p. 26)
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The number that is used as a factor.
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Exponent (p. 26)
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The number that indicates how many times the base is used as a factor.
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Square Root (p. 32)
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A number that is multiplied by itself to form a product.
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Principal Square Root (p. 32)
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The positive square root of a number that is represented by √.
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Perfect Square (p. 32)
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A number whose positive square root is a whole number.
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Cube Root (p. 32)
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A number that is raised to the third power to form a product.
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Natural Numbers (p. 33)
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All counting numbers.
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Whole Numbers (p. 33)
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All natural numbers and zero.
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Integers (p. 33)
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All whole numbers and their opposites.
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Rational Numbers (p. 33)
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Numbers that can be expressed in the form a/b, where a and b are both integers and b ≠ 0.
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Terminating Decimal (p. 33)
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Has a finite number of digits after the decimal point.
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Repeating Decimal (p. 33)
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Has a block of one or more digits after the decimal point that repeat continuously.
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Irrational Numbers (p. 34)
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All numbers that are not rational.
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Counterexample (p. 43)
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An example that disproves a statement, or shows that it is false.
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Closure (p. 44)
|
A set of numbers is said to be closed under an operation if the result of the operation on any two numbers in the set is also in the set.
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Order of Operations (p. 48)
|
Tells you which operation to perform first.
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Terms (p. 49)
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The parts of an expression that are added or subtracted.
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Like Terms (p. 49)
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Terms with the same variables raised to the same exponents.
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Coefficient (p. 49)
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A number multiplied by a variable. |
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Variable (p. 6)
|
A letter or symbol used to represent a value that can change.
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Constant (p. 6)
|
A value that does not change.
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Numerical Expression (p. 6)
|
Contains only constants and/or operations.
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Algebraic Expression (p. 6)
|
Contains variables, constants, and/or operations.
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Evaluate (p. 7)
|
To find the value of an expression.
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Replacement Set (p. 7)
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A set of numbers that can be substituted for a variable.
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Real Numbers (p. 14)
|
The set of all numbers that can be represented on a number line.
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Absolute Value (p. 14)
|
The distance of a number from zero on a number line.
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Opposites (p. 15)
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Two numbers that have the same absolute value but have different signs.
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Additive Inverse (p. 15)
|
A number and its opposite that are the same distance from zero.
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Reciprocal (p. 21)
|
The product of two numbers that are equal to 1.
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Multiplicative Inverse (p. 21)
|
A number and its reciprocal.
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Power (p. 26)
|
An expression written with an exponent and a base.
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Base (p. 26)
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The number that is used as a factor.
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Exponent (p. 26)
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The number that indicates how many times the base is used as a factor.
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Square Root (p. 32)
|
A number that is multiplied by itself to form a product.
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Principal Square Root (p. 32)
|
The positive square root of a number that is represented by √.
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Perfect Square (p. 32)
|
A number whose positive square root is a whole number.
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Cube Root (p. 32)
|
A number that is raised to the third power to form a product.
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Natural Numbers (p. 33)
|
All counting numbers.
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Whole Numbers (p. 33)
|
All natural numbers and zero.
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Integers (p. 33)
|
All whole numbers and their opposites.
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Rational Numbers (p. 33)
|
Numbers that can be expressed in the form a/b, where a and b are both integers and b ≠ 0.
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Terminating Decimal (p. 33)
|
Has a finite number of digits after the decimal point.
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Repeating Decimal (p. 33)
|
Has a block of one or more digits after the decimal point that repeat continuously.
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Irrational Numbers (p. 34)
|
All numbers that are not rational.
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Counterexample (p. 43)
|
An example that disproves a statement, or shows that it is false.
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Closure (p. 44)
|
A set of numbers is said to be closed under an operation if the result of the operation on any two numbers in the set is also in the set.
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Order of Operations (p. 48)
|
Tells you which operation to perform first.
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Terms (p. 49)
|
The parts of an expression that are added or subtracted.
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Like Terms (p. 49)
|
Terms with the same variables raised to the same exponents.
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Coefficient (p. 49)
|
A number multiplied by a variable. |
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abscissa
|
the distance along the horizontal axis in a coordinate graph.
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absolute value
|
the numerical value when direction or sign is not considered. the symbol for absolute value.
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additive axiom of equality
|
if a=b and c=d, then a+c=b+d.
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additive axiom of inequality
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if a>b, then a+c>b+c.
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additive inverse
|
the opposite (negative) of a number. Any number plus its additive inverse equals 0.
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algebra
|
arithmetic operations using letters and/or symbols in place of numbers.
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algebraic expressions
|
expressions composed of letters to stand for numbers.
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algebraic fractions
|
fractions using a variable in the numerator and/or denominator.
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ascending order
|
basically, when the power of a term increases for each succeeding term.
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associative property
|
grouping of elements does not make any difference in the outcome. Only true for multiplications and addition.
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axioms of equality
|
basic rules for using the equal sign
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binomial
|
an algebraic expression consisting of two terms.
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braces
|
grouping symbols used after the use of brackets. Also used to represent a set. { }
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brackets
|
grouping symbols used after parentheses. [ ]
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canceling
|
in multiplication of fractions, dividing the same number into both a numerator and a denominator.
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cartesian coordinates
|
a system of assigning ordered pairs to points on a plane.
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closed half–plane
|
a half–plane that includes the boundary line and is graphed using a solid line
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closed interval
|
an interval that includes both endpoints or fixed boundaries
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closure property
|
when all answers fall into the original set.
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coefficient
|
the number in front of a variable. For example: 9x, 9 is the coefficient
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common factors
|
factors that are the same for two or more numbers.
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commutative property
|
order of elements does not make any difference in the outcome. Only true for multiplication and addition.
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complex fraction
|
a fraction having a fraction or fractions in the numerator and/or denominator
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composite number
|
a number divisible by more than 1 and itself ( such as 4 ,6 ,8 ,9 ...). 0 and 1 are not composite numbers.
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conjugate
|
the conjugate of a binomial contains the same terms, but the opposite sign between them. (x+y) and (x–y) are conjugates.
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coordinate axes
|
two perpendicular number lines used in a coordinate graph.
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coordinate graph
|
two perpendicular number lines, the x axis and the y axis, creating a plane on which each point on a coordinate is assigned a pair of numbers.
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coordinates
|
the numbers that correspond to a point on a coordinate graph.
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cube
|
the result when a number is multiplied by itself twice. Designated by the exponent 3 (such as x3 or x–cubed)
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cube root
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the number that when multiplied by itself twice gives you the original number. For example, 5 is the cube root of 125.
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denominator
|
everything below the fraction bar in a fraction
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descending order
|
basically, when the power of a term decreases for each succeeding term.
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direct variation
|
when y varies directly as x or y is directly proportional to x.
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discriminant
|
the value under the radical sign in the quadratic formula. [b2–4ac].
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distributive property
|
the process of distributing the number on the outside of the parentheses to each number on the inside. a(b+c) = ab+ac.
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domain
|
the set of all first coordinates from the ordered pairs.
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element
|
a member of a set.
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empty set
|
a set with no members (a null set).
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equal sets
|
sets that have exactly the same members.
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equation
|
a balanced relationship between numbers and/or symbols. A mathematical sentence.
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equivalent sets
|
sets that have the same number of members.
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Euler circles
|
a method of pictorially representing sets.
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evaluate
|
to to determine the value or numerical amount.
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exponent
|
a numeral used to indicate the power of a number.
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extremes
|
outer terms.
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factor
|
to find two or more qualities whose product equals the original quantity.
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finite
|
countable. Having a definite ending.
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F.O.I.L. method
|
method of multiplying binomals in which first terms, outside terms, inside terms, and last terms are multiplied.
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function
|
a relation in which each element in the domain is paired with exactly one element in the range
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graphing method
|
a method of slving simultaneous equations by graphing each equation on a coordinate graph and finding the common point (intersection). |
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A listing from least to greatest
|
Ascending
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The sum or difference of two monomials
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Binomial
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Two lines with all points shared
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Coinciding Lines
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The sum of the exponents of the variables
|
Degree of a Monomial
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The greatest degree of any term
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Degree of a Polynomial
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Output of a function
|
Dependent Variable
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A listing from greatest to least
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Descending
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X values in a set of ordered pairs
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Domain
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Expressing a polynomial as a product
|
Factoring
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Numbers multiplied to get a product
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Factors
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|
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A set of ordered pairs in which each element of the domain is paired with exactly one element of the range
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Function
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Input for a function
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Independent Variable
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An uncountable number of solutions
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Infinite
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A point at whcih two lines cross
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Intersection
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The number in front of the term with the highest degree
|
Leading Coefficient
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Number, variable, or the product of numbers and variables
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Monomial
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Lines in the same plane with the same slope that don't intersect
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Parallel Lines
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Two lines that intersect to form right angles
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Perpendicular Lines
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The sum of four or more monomials
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Polynomial
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Of the second degree
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Quadratic
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Y values in a set of ordered pairs
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Range
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Any set of ordered pairs
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Relation
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The sum or difference of three monomials
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Trinomial
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Number that tells how many times a base is used as a factor
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Exponent
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Where a line crosses the x–axis
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x–intercept
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Where a line crosses the y–axis
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y–intercept
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Numerical value that tells how steep a line is – also rise over run
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Slope |
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