MTEL Math Elementary (68) flashcards

31 cards. Read the term and the definition here. The deck at the top of this page is optional.

Place value

The value of a digit determined by its position in a number; each position is ten times the value of the position to its right.

Divisibility rule for 3

A whole number is divisible by 3 exactly when the sum of its digits is divisible by 3, such as 471 because 4+7+1=12.

Least common multiple

The smallest positive number that is a multiple of two or more given numbers; used to find a common denominator when adding fractions.

Order of operations

The convention for evaluating expressions: grouping symbols, exponents, multiplication and division left to right, then addition and subtraction left to right.

Percent change formula

Percent change equals the amount of change divided by the original value, multiplied by 100; a positive result is an increase.

Dividing by a fraction

Dividing by a fraction is equivalent to multiplying by its reciprocal, so a/b divided by c/d equals a/b times d/c.

Arithmetic sequence nth term

In an arithmetic sequence with first term a-one and common difference d, the nth term equals a-one plus the quantity n minus one times d.

Slope of a line

Slope equals the change in y divided by the change in x between two points; it measures the constant rate of change of a linear function.

Slope-intercept form

The equation y equals mx plus b, where m is the slope or rate of change and b is the y-intercept, the value when x is zero.

Inequality reversal rule

Multiplying or dividing both sides of an inequality by a negative number reverses the inequality symbol, so less-than becomes greater-than.

Definition of a function

A relation in which every input in the domain is paired with exactly one output; a graph passes the vertical line test.

Distributive property

Multiplying a sum by a factor gives the same result as multiplying each addend by the factor and then adding: a times the quantity b plus c.

Triangle angle sum

The three interior angles of any triangle add to 180 degrees; an exterior angle equals the sum of the two nonadjacent interior angles.

Area of a trapezoid

Area equals one-half times the sum of the two parallel bases times the height, measured perpendicular to those bases.

Circumference of a circle

The distance around a circle equals pi times the diameter, or two times pi times the radius; pi is approximately 3.14.

Volume of a cone

A cone's volume is one-third the base area times the height, which is one-third of the volume of a cylinder with the same base and height.

Pythagorean theorem

In a right triangle, the sum of the squares of the two legs equals the square of the hypotenuse: a squared plus b squared equals c squared.

Similar figures scale factor

Corresponding angles are equal and corresponding sides are proportional; a scale factor k multiplies lengths, k squared multiplies areas, k cubed multiplies volumes.

Mean, median, and mode

The mean is the sum divided by the count, the median is the middle ordered value, and the mode is the most frequent value.

Interquartile range

The difference between the third quartile and the first quartile; it describes the spread of the middle half of an ordered data set.

Theoretical probability

The ratio of favorable outcomes to the total number of equally likely outcomes in the sample space, expressed as a number from zero to one.

Independent events rule

Events are independent when one outcome does not affect the other; the probability of both occurring is the product of their individual probabilities.

Effect of an outlier

An extreme value pulls the mean toward it while leaving the median nearly unchanged, so the median better describes skewed data.

Scientific notation

A number written as a factor between 1 and 10 multiplied by a power of ten; a positive exponent shifts the decimal point to the right.

Absolute value

The distance of a number from zero on the number line, always nonnegative; the equation absolute value of x equals k has two solutions.

Proportion cross-multiplication

In the proportion a over b equals c over d, the cross products a times d and b times c are equal, allowing an unknown to be solved.

Point-slope form

An equation of a line written as y minus y-one equals m times the quantity x minus x-one, using a known point and the slope.

Interior angle sum of polygon

For a polygon with n sides, the interior angles sum to n minus two multiplied by 180 degrees; a regular polygon divides that sum equally.

Surface area of rectangular prism

The total area of all six faces, computed as two times the sum of length times width, length times height, and width times height.

Counting principle

If one choice can be made in m ways and a second in n ways, the two choices together can be made in m times n ways.

Weighted mean

The sum of each value multiplied by its weight, divided by the total of all weights; used when values occur with different frequencies.