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136 Cards in this Set
- Front
- Back
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What is a prime number?
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A number that is divisble by 1 and itself. ex. 13, 17
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What is a manipulative?
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Materials that students can physically handle and move.
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What is a model?
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A means of representing mathematical concepts by relating the concepts to real world situations.
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Inductive Reasoning
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The process of finding a pattern from a group of examples. May be wrong or right.
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Deductive Reasoning
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The process of arriving at a conclusion based on other statements all known to be true, such as theorums, axioms, or postulates.
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T/F
Conclusions found by deductive thinking based on true statements will always be true???? |
True
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A statement made about a pattern or relationship between elements thought to be true, which is subsequently justified through related examples and logical reasoning.
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Valid Arguement
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Conditional Statement
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"IF" "THEN" statement
If=p then=q |
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Conditional known as the hypothesis?
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IF
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Clause known as the conclusion????
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THEN
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Inverse of a conditional statement
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If not p, then not q. Negate both the hypothesis and the conclusion from the original conditional.
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Converse of a conditional statement
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Reverse the two clauses.
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Contrapositive of a conditional statement
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Reverse both clauses and negate both.
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Conditional statements can be diagrammed using what kind of diagram?
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Venn Diagram
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Constructivism
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Prior knowledge greatly influences the learning of math and learning is cumulative and vertically structured.
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Paremeter of a polygon
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Sum of the lengths of it's sides.
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Area of a polygon
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The number of square units covered by the figure. Measure of the space inside the polygon.
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Natural Numbers
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the counting numbers.....1,2,3,4
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Whole Numbers
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Counting numbers along with Zero....0,1,2,3,4
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Integers
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The counting numbers, their opposites and zero...-2,-1,0,1,2
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Rationals
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all the fractions that can be formed by whole numbers. In decimal, these numbers will be either terminating or repeating.
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Irrationals
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Real numbers taht cannot be written as a fraction. The decimal form of these numbers are neither terminating or repeating. pie or square root of 2
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Real numbers
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The set of numbers obtained by combining the rationals and irrationals. Complex numbers such as i are not real numbers.
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Simplest form
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Numerator and denominator have no common factor except for 1 or -1.
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GCF
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The largest common factor among all the numbers given in the problem.
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LCM
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The smallest number into which all the numbers in a group will divide. Usually the quotient of all the numbers and a multiple of the largest number.
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OF
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Multiplication
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IS
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Equal
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geometric sequence formula
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An=a1+(n-1)d
n=nth term r=common ration |
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ration of geometric sequence
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r=A n+1/A n
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Relationships can be shown using?
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Table, graph, Rule
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Coordinate pair
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The relationship between a pair of values
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Linear relationship
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One in which two quantities are proportional to eachother.Doubling x also doubles y. A strait line depicts a linear equation.
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Non linear relationship
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One in which change in one quantity does not change the other quantitiy to the same extent.
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The relationship between two quantities that may be analyzed to determine how one quantity depends on another
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Funtion
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States that if there are m possible outcomes for one task and n possible outcomes for another task, there are m x n possible outcomes for the two tasks together.
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Fundamental counting principle
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The number of possible outcomes, without repetion, where order of selection is important.
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Permutation
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The number of possible outcomes, without repetition, where order of selection is not important.
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Combination
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Sample Space
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The list of all possible outcomes in an experiment.
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# of successful trials/total # of trials
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Relative frequency
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A prediciton based on experimental or theoretical probabilities.
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Relative frequency
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What are the subsets of the real number system
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Natural numbers
Whole numbers Integers Rational numbers Irrational numbers Real numbers |
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What are Natural numbers?
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counting numbers...1,2,3,4,5
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Whole Numbers
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counting numbers and zero,.... 0,1,2,3,4,5
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Integers
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Counting numbers, their opposites and zero.... -3-2-1 0 1 2 3
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Rational numbers
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All fractions that can be formed by whole numbers. Zero cannot be in the denominator. In decimal form these numbers will be either terminating or repeating decimals.
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Irrationals
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Real numbers that cannot be written as a fraction. The decimal forms of these numbers are either terminating or repeating.
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Real numbers
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The set of numbers obtained by combining the rationals and the irrationals. Complex numbers are not real numbers.
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Complex numbers???
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i or sqare of a negative.
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Closure
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a + b is a real number
a X b is a real number |
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Commutative Property
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a + b= b + a
ab =ba |
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Associative Property
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(a + b)+ c = a+(b + c)
(ab)c= a(bc) |
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Distributive Property
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a(b+c)=ab+ac
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Additive Identity
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a+0=a (Property of zero)
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Mutiplicitive Identity
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a x 1=a (Property of one)
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Additive Inverse
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a + -a = 0 (Property of Opposites)
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Multiplicative Inverse
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3 x (1/3)=0 (Property of reciprocals)
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Property of Denseness
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Between any pair of rational numbers there is at least one rational number. A set of natural numbers is NOT dense because between two consecutive natural numbers there may not exist another natural number.
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Adjacent angles
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have a common vertix and a common side but no interior points in common.
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Commplimentary angles
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Adjacent angles that add up to 90 degrees.
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Supplimentary angles
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Adjacent angles that add up to 180 degrees.
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Vertical angles
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have two sides that form two pairs of opposite rays.
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Corresponding angles
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Are in the same corresponding position on two parallel lines cut by a transversal.
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Alternate interior angles
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Opposite angles on the inside of two parralel lines cut by a transversal
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Alternate exterior angles
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Opposite anges on the outside of two parallel lines cut by a transversal.
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Acute triangle
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three acute angles
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right triangle
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has one right angle
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obtuse triangle
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has one obtuse angle. An obtuse angle is one that is greater than 90 degrees and smaller that 180 degrees.
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Equalateral triangle
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all three sides are the same lenght
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Isosceles triangle
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Two sides are the same length
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Scalene triangle
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All sides are different lengths
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The square of one side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.
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Converse of the Pythagorean Theorum
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The square of the lenght of the hypotenuse is equal to the sum of the squares of the lenghts of the legs.
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Pythagorean Theorum
c^2=a^2 +b^2 |
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A quadrilateral with EXACTLY one pair of oppisite sides parallel. The parallel sides are called bases, the non parallel sides are called legs.
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trapezoid
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An isosceles trapezid?
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the legs are congruent
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Altitude
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The hieght of the trapezoid
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Median
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The line that joins the midpoints of each leg. (parallel to the bases)
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formula for median of trapezoid
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(1/2) the sum of the lengths of the bases
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Area of a trapezoid
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[(base 1 + base 2)H]/2
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lateral area
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the area of the faces excluding the bases
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surface area
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total area of all the faces including the bases
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Volume
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The number of cubic units in a solid. The amount of space a figure holds
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Volume for right prism
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BH (where B is the area of the base of the prism. and h is the height of the prism)
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Rectangular right prism
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s= 2(lw+lh+hw)
v=lwh |
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Regular pyramid
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v= (1/3)B h
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Right circular cylinder
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s=2 pie r (r+h)
v=pie r^2 H |
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right circular cone
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v=(1/3) B h
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n(a and B)=n(a)n(b)
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Multiplication principle of counting for independent events
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n (a and b)=n(a)n(b/a)
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Multiplication principle for dependent events
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The surface area of a sphere of radius 'r' is given by:
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surface area = 4 p r^2
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Curved surface area of cylinder
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= 2prh
= 2pr(2r) = 4 p r^2 |
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Greatest possible error for measurement is:
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+/- (1/2) unit
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10 mm=?
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1 cm
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1000 m=?
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1 KM
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The area of a parallelogram is always???
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Base times height.... not base times length
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Slope intercept form
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y = mx+b
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Volume of a sphere
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V=(4/3) p r^3
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When are the volume and the surface area of a sphere equivalent?
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When the radius of the sphere is 3.
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Distance = ?
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Rate X Time
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Time =?
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Distance/Rate
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right circular cylinder
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As=2πr^2 + 2πrh
V= p r^2 h |
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12 in =?
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1 ft
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3 ft =?
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1 yd
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5280 ft =?
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1 mile
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1760 yd = ?
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1 mile
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16 oz =?
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1 pound
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2000 lb=?
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1 ton
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1 sq ft = ? sq. in.
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144 sq in
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1 sq yd. = ? sq ft
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9 sq ft
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1 sq yd = ? sq in
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1296 sq in
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1 cm =? mm
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10 mm
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1 m = ? mm
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1000 mm
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1 m= ? cm
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100 cm
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1000m =?km
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1km
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1000ml=1L
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1000 L = 1 KL
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1000 mg= ? g
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1 g
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1000 g = ? kg
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1kg
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reflexive property
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states that every number or variable is equal to itself and every segment is congruent to itself.
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What is a postulate?
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An accepted property of real numbers or geometric figures that cannot be proven.
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T/F
Point, line, plane are three undefined concepts on which plane geometry is based. |
True
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Reflexive Property
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States that every property is congruent to itself.
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Isosceles triangle theorem
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States that the base angles are congruent
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Distance formula?
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D=Sq Rt (x2-x1)^2 + (y2-y1)^2
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Midpoint Formula
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(x1+x2)/2, (y1+y2)/2
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When you begin by assuming the conclusion of a theorum is false, then show that through a sequence of logically correct steps you contradict an accepted fact.
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indirect proof
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The conclusion to be proved is shown to be true directly as a result of the other circumstances of the situation. ex.the triangles were shown to be congruent directly as a result of their sharing two equal corresponding sides and one equal included angle.
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direct proof
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Is direct proof deductive or inductive reasoning?
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Deductive Reasoning
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A form of reasoning by which each conclusion follows from the previous one; an argument is built by conclusions that progress towards a final statement.
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Deductive Reasoning
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The conclusion to be proved is shown to be true because every other possibility leads to a contradiction
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Indirect Proof
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T/F
In an ordinary parallelogram the diagnals are niether equal or perpendicular. |
True
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If the diagnals of a quadrilateral are equal and perpendicular it could be described as what shape?
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Square
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T/F
The median and the altitude of a triangle may be the same segment. |
True
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In what type of triangle are the median and the altitude to the base are the same segment?
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Isosceles triangle
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What mathmatician developed elliptic geometry?
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Reimann
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what mathmatician was the inventor of deductive reasoning and was responsible for uniting number and form in his work Geometry, which described how the motion of a point could be mapped graphically by comparing its position to planes of reference?
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Descartes
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A triangle in which each row has one more entry than the preceding row, each row begins and ends with "1," and the interior elements are found by adding the adjacent elements in the preceding row.
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Pascal's triangle
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