NES Essential Academic Skills Subtest III: Mathematics flashcards

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

Order of Operations

Evaluate grouping symbols first, then exponents and roots, then multiplication and division from left to right, then addition and subtraction from left to right.

Least Common Multiple

The smallest positive integer divisible by each number in a set. Found by taking the highest power of every prime appearing in the factorizations.

Greatest Common Factor

The largest integer dividing each number in a set without a remainder. It equals the product of the shared prime factors raised to their lowest powers.

Rational vs Irrational Numbers

Rational numbers can be written as a fraction of two integers and have terminating or repeating decimals. Irrational numbers, such as the square root of 2, cannot.

Percent Change Formula

Percent change equals the difference between new and old values divided by the original value, then multiplied by 100. A positive result is an increase.

Absolute Value

The distance of a number from zero on the number line. It is never negative, and the absolute value of a difference gives the distance between two points.

Scientific Notation

A number written as a factor between 1 and 10 multiplied by a power of 10. Positive exponents indicate large numbers, negative exponents small ones.

Slope Formula

Slope equals the change in y divided by the change in x between two points. It measures steepness and direction of a line.

Slope-Intercept Form

The equation y = mx + b, where m is the slope and b is the y-intercept, the point where the line crosses the vertical axis.

Quadratic Formula

For ax squared plus bx plus c equals zero, x equals negative b plus or minus the square root of b squared minus 4ac, all divided by 2a.

Discriminant

The expression b squared minus 4ac in the quadratic formula. Positive gives two real roots, zero gives one repeated root, negative gives no real roots.

Inequality Reversal Rule

Multiplying or dividing both sides of an inequality by a negative number reverses the inequality symbol, because the order of numbers on the number line flips.

Perpendicular Line Slopes

Two nonvertical lines are perpendicular exactly when their slopes are negative reciprocals, so the product of the slopes equals negative one.

Function Domain

The set of all valid input values. Exclude inputs making a denominator zero or making an even root's radicand negative.

Direct and Inverse Variation

Direct variation has the form y = kx and graphs as a line through the origin. Inverse variation has the form y = k divided by x.

Triangle Angle Sum

The three interior angles of any triangle add to 180 degrees. In an equilateral triangle each angle measures 60 degrees.

Polygon Interior Angle Sum

For a polygon with n sides, the interior angles total (n minus 2) times 180 degrees. A quadrilateral therefore totals 360 degrees.

Circle Circumference and Area

Circumference equals 2 times pi times the radius, or pi times the diameter. Area equals pi times the radius squared.

Pythagorean Theorem

In a right triangle, the sum of the squares of the two legs equals the square of the hypotenuse, the side opposite the right angle.

Similar Figure Scaling

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

Cylinder and Cone Volume

A cylinder's volume is pi times radius squared times height. A cone with the same base and height has exactly one third of that volume.

Distance and Midpoint Formulas

Distance between two points is the square root of the sum of squared differences in x and y. Midpoint coordinates are the averages of the coordinates.

Trapezoid Area

Area equals one half the height multiplied by the sum of the two parallel bases. The height is the perpendicular distance between the bases.

Mean, Median, Mode

The mean is the arithmetic average, the median is the middle ordered value, and the mode is the most frequent value. Outliers shift the mean most.

Interquartile Range

The difference between the third quartile and the first quartile. It spans the middle 50 percent of ordered data and resists distortion by outliers.

Complement Rule

The probability that an event does not occur equals 1 minus the probability that it does occur. Together the two probabilities sum to 1.

Independent Events Rule

Two events are independent when one's occurrence does not change the other's probability. Then the probability both occur is the product of their probabilities.

Permutation vs Combination

Permutations count ordered arrangements and use n factorial divided by (n minus r) factorial. Combinations count unordered selections and divide further by r factorial.

Normal Distribution Rule

A symmetric bell-shaped distribution about the mean. About 68 percent of values lie within one standard deviation, 95 percent within two, and 99.7 percent within three.

Conditional Probability

The probability of event A given that B occurred equals the probability of both divided by the probability of B, provided B has nonzero probability.

Distance Rate Time

Distance equals rate multiplied by time. Rearranged, time equals distance divided by rate and rate equals distance divided by time, with units kept consistent.

Weighted Average

Multiply each value by its weight, sum those products, then divide by the total of all weights. Grades and mixture problems use this method.