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