Praxis II: Math (5003)
Multiplicative Inverse Property
"Reciprocal"
Multiplicative Identity Property
1 is the multiplicative identity such that a x 1=a
Law of Exponents
1) Any number raised to the power of 1 is equal to itself 2) The number 1 raised to any power is equal to 1 3) Any number raised to the power of 0 is equal to 1 4) Add exponents to multiply powers of the same base number 5) Subtract exponents to divide powers of the same number 6) Multiply exponents to raise a power to a power 7) If multiplied or divided numbers inside parentheses are raised to a power it is the same as each individual term raised to that power
Transversal Line
A line that intersects at least two other lines that may or may not be parallel
Bisector
A line/line segment that divides another line segment into two equal lengths
Expected Value
A method of determining expected outcome in a random situation; sum of the weighted probabilities of the possible outcomes
Composite Number
A whole number greater than 1 that has more than two different factors
Prime Number
A whole number greater than 1 that only has two factors (itself and 1)
Triangles
Acute: 3 angles are all less than 90 degrees Right: one angle equals 90 degrees (Pythagorean Theorem) Obtuse: one angle is greater than 90 degrees Equilateral: 3 congruent sides/angles each at 60 degrees Isosceles: two congruent sides and two congruent angles opposite the two congruent sides Scalene: no congruent sides with 3 angles of different measures; angle with largest measure is opposite the longest side and angle with the smallest measure is opposite the shortest side
Angles
Acute: less than 90 degrees Right: exactly 90 degrees Obtuse: between 90 and 180 Straight: exactly 180 degrees (line) Reflex: between 180 and 360 Full: exactly 360
Rational Numbers
All integers, decimals and fractions; any terminating or repeating decimal number
Interior Angles
Angles between two parallel lines
Exterior Angles
Angles outside the parallel lines
Corresponding Angles
Angles that are in the same position relative to the transversal and a parallel line
Additive Inverse Property
Any (+) number added to its opposite (-) is equal to zero
Interior Angle
Any of the angles inside a polygon where two sides meet at a vertex
Irrational Numbers
Cannot be written as fractions or decimals because the number of decimal places is infinite and there is no recurring pattern of digits within the number (e.g. pi)
Sum of Interior Angles of a Polygon
Dependent on number of sides (n-2) 180
Probability
Desired Outcomes/Total Outcomes
Dividing Fractions
Flip the numerator and denominator of the second fraction and then multiply
Associative Property
Grouping numbers together does not change the value *THINK ASSOCIATE = group
Standard Deviation
How spread out values of a distribution are from the mean; High- values are very spread out or Low- values are close together
Side-Side-Side
If all three sides of one triangle are equal to all three sides of another triangle, they are congruent
Side-Angle-Side
If two sides and the adjoining angle in one triangle are equal to two sides and the adjoining angle of another triangle, they are congruent
Continuous Data
Info that can be expressed by any value within a given range
Discrete Data
Info that can be expressed only by a specific value
Ordinal Data
Info that can be placed in numerical order
Nominal Data
Info that cannot be placed in numerical order
Primary Data
Info that has been collected directly from a survey/experiment
Secondary Data
Info that has been collected/processed by the researcher
Qualitative Data
Information
Intersecting Lines
Lines that have exactly one point in common
Diagonals
Lines that join two nonconsecutive vertices of a polygon d=n(n-3)/2
Quantitative Data
Measurements
Common Factor
Number that divides exactly into two or more other numbers
Factors
Numbers that are multiplied together to obtain a product
Solving Percentage Problems
P=W x % or %=P/W or W=P/%
Order of Operations
PEMDAS M/D and A/S are worked left to right in order
Polygons
Planar shapes formed from line segments called sides that are joined together at points called vertices # of Sides: Triangle: 3 Quadrilateral: 4 Pentagon: 5 Hexagon: 6 Heptagon: 7 Octagon: 8 Nonagon: 9 Decagon: 10 Dodecagon: 12
Integers
Positive and Negative Whole Numbers; Includes 0
Volume Formulas
Pyramid: V=1/3Bh Prism: V=Bh Cube: V=s^3 Sphere: V=4/3pi(r)^3
Area Formulas
Rectangle: A=wl Square: A=s^2 Triangle: A=1/2bh Parallelogram: A=bh Trapezoid: A=1/2 (b1 + b2)h Circle: A=pi(r^2)
Real Numbers
Set of all rational and irrational numbers
Greatest Common Factor (GCF)
The largest number that is a factor of two or more numbers
Empirical Probability
The number of times an outcome occurs in a particular experiment or a certain number of observed events (what has happened)
Commutative Property
The order of two numbers may be switched around and the answer is the same *THINK COMMUTE = move
Vertex
The point where two segments or rays meet to form an angle
Complement of an Event
The possibility of something not happening
Conditional Probability
The probability of an event occurring once another event has already occurred
Least Common Multiple (LCM)
The smallest number that is a multiple of two or more numbers
Triangle Inequality Theorem
The sum of the measures of any two sides of a triangle is always greater than the measure of the third side
Alternate Exterior Angles
The two exterior angles that are on opposite sides of the transversal
Alternate Interior Angles
The two interior angles that are on opposite sides of the transversal
Quadrilaterals
Trapezoid: one pair of opposite parallel sides Parallelogram: two pairs of opposite parallel sides Rhombus: 4 equal sides Rectangle: 4 congruent (right) angles Square: 4 equal sides and 4 congruent (right) angles
Similar Triangles
Triangles whose corresponding angles are congruent to one another; proportional
Supplementary
Two angles whose sum is 180 degrees
Complementary
Two angles whose sum is 90 degrees
Addition Rule
Used to find the probability of a Compound Event
Multiplication Rule
Used to find the probability of two independent events occurring using the formula P (A and B) = P (A) x P (B)
Theoretical Probability
What should happen P(A) = Number of Acceptable Outcomes/Number of Possible Outcomes
Additive Identity Property
a + 0 = a
Distributive Property
a(b + c) = ab + ac
Pythagorean Theorem
a^2 (side) + b^2 (side) = c^2 (hypotenuse)
Law of Cosines
c^2 = a^2 + b^2 - 2ab(cosC)
Law of Sines
sinA/a = sinB/b = sinC/c
