MTEL 65 flashcards

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

Least common multiple

The smallest positive integer divisible by each of two or more given integers; find it by using the highest power of every prime appearing in their prime factorizations.

Greatest common divisor

The largest positive integer that divides each of the given integers without a remainder; use the lowest power of each shared prime or the Euclidean algorithm.

Rational number decimal form

A number expressible as p/q with integers p and q and q not zero; its decimal either terminates or eventually repeats.

Irrational square root test

The square root of a positive integer is irrational unless that integer is a perfect square; for example, sqrt(12) is irrational because 12 is not a perfect square.

Negative exponent rule

For a nonzero base a and positive integer n, a^(-n) equals 1/(a^n); the reciprocal of the positive power is used.

Percent change formula

Percent change equals the new value minus the old value, divided by the old value, then multiplied by 100; a positive result is an increase.

Scientific notation form

A number written as a times 10 to the n, where the absolute value of a is at least 1 and less than 10 and n is an integer.

Fraction division rule

To divide by a nonzero fraction, multiply by its reciprocal: a/b divided by c/d equals a/b times d/c; simplify before or after multiplying.

Slope formula

For two points (x1,y1) and (x2,y2) with x1 not equal x2, slope m equals (y2-y1)/(x2-x1), the vertical change divided by horizontal change.

Perpendicular line slopes

Two nonvertical lines are perpendicular exactly when their slopes are negative reciprocals, so their product is -1; a horizontal line is perpendicular to a vertical line.

Quadratic formula

For ax^2+bx+c=0 with a not zero, x equals negative b plus or minus the square root of b squared minus 4ac, all divided by 2a.

Discriminant test

For a quadratic with real coefficients, b^2-4ac greater than zero gives two distinct real roots, equal to zero gives one repeated real root, and less than zero gives no real roots.

Vertex of parabola

The graph of y=ax^2+bx+c has vertex x-coordinate -b/(2a); substitute that x into the equation to find the maximum or minimum y-value.

Logarithm definition

For b greater than zero and not equal to one and x greater than zero, log base b of x equals y exactly when b to the y equals x.

Compound interest formula

A equals P times (1 plus r/n) raised to n t, where P is principal, r annual rate as a decimal, n compounding periods per year, and t years.

Function domain restrictions

Exclude inputs making a denominator zero and inputs making an even-root radicand negative; for logarithms, require the argument to be greater than zero.

Circle area and circumference

A circle with radius r has area pi r squared and circumference 2 pi r, or pi times diameter; these formulas use the same radius.

Pythagorean theorem

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

Interior angle sum polygon

A polygon with n sides has interior angles summing to (n minus 2) times 180 degrees; a regular polygon has each interior angle equal to that sum divided by n.

Similar figure scale ratios

If two similar figures have scale factor k, their corresponding lengths have ratio k, areas have ratio k squared, and volumes have ratio k cubed.

Distance formula coordinates

The distance between points (x1,y1) and (x2,y2) is the square root of the sum of the squared differences in x-coordinates and y-coordinates.

Circle equation center-radius

A circle with center (h,k) and radius r has equation (x minus h) squared plus (y minus k) squared equals r squared.

Sphere volume formula

The volume of a sphere with radius r is four-thirds times pi times r cubed; its surface area is four times pi times r squared.

Complementary supplementary angles

Complementary angles have measures summing to 90 degrees; supplementary angles have measures summing to 180 degrees; these sums apply to pairs, not necessarily adjacent angles.

Interquartile range definition

The interquartile range equals the third quartile minus the first quartile; it measures the spread of the middle 50 percent of ordered data and resists extreme values.

Outlier rule quartiles

Using quartiles Q1 and Q3 and IQR equals Q3 minus Q1, values below Q1 minus 1.5 times IQR or above Q3 plus 1.5 times IQR are often flagged as outliers.

Addition rule probability

For events A and B, probability of A or B equals probability of A plus probability of B minus probability of A and B; subtract the overlap to avoid double counting.

Conditional probability formula

The probability of A given B equals the probability of both A and B divided by the probability of B, provided probability of B is greater than zero.

Independent events rule

Events A and B are independent exactly when the probability of both equals the product of their separate probabilities; conditional probability of A given B then equals probability of A.

Combinations versus permutations

Permutations count ordered arrangements using n factorial divided by (n minus r) factorial; combinations count unordered selections using n factorial divided by r factorial times (n minus r) factorial.

Empirical rule normal data

In a normal distribution, about 68 percent of values lie within one standard deviation of the mean, about 95 percent within two, and about 99.7 percent within three.

Correlation coefficient range

Correlation coefficient r measures the direction and strength of a linear association and lies between negative one and one; r near zero indicates weak linear association.