Grade 8 Mathematics flashcards

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

Irrational number

A number that cannot be written as a fraction of two integers. Its decimal expansion never terminates and never repeats, such as the square root of 2 or pi.

Rational number decimal expansion

Every rational number written as a fraction of integers has a decimal that either terminates or repeats one fixed block forever, such as 0.375 or 0.272727…

Estimating a square root

Bracket the number between consecutive perfect squares. Because 49 is less than 52 and 52 is less than 64, the square root of 52 lies between 7 and 8.

Simplifying a radical

Use the product rule for square roots to pull out perfect squares. For example, the square root of 72 equals the square root of 36 times 2, which is 6 root 2.

Negative exponent rule

For any nonzero base a and positive integer n, a raised to the negative n equals 1 divided by a to the n. So 2 to the negative 3 equals one eighth.

Scientific notation form

A number is written as c times 10 to the n, where c is at least 1 and less than 10. For example, 0.00047 becomes 4.7 times 10 to the negative 4.

Distributive property

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

Combining like terms

Terms with identical variable parts can be added by adding their coefficients. So 5x plus 3 minus 2x simplifies to 3x plus 3.

Equation with no solution

When solving ax plus b equals cx plus d, if a equals c but b does not equal d, the variable cancels and the equation is false for every value.

Slope from two points

The slope through points (x1, y1) and (x2, y2) equals the change in y divided by the change in x, written as (y2 minus y1) over (x2 minus x1).

Power of a power rule

When raising a power to a power, multiply the exponents: the quantity a to the m raised to the n equals a to the product mn.

Solving a system by substitution

Solve one equation for a variable, substitute that expression into the other equation, solve for the remaining variable, then back-substitute to find the other value.

Proportional relationship equation

A proportional relationship has the form y equals kx, where k is the constant of proportionality. Its graph is a straight line passing through the origin.

Definition of a function

A rule assigning exactly one output to each input. On a graph, a relation is a function only if every vertical line crosses it at most once.

Function notation

The symbol f of x names the output for input x. If f of x equals 2x plus 3, then f of 4 equals 11 and f of x equals 9 gives x equals 3.

Rate of change

The change in output divided by the change in input over an interval. For a linear function this ratio is constant and equals the slope of the line.

Comparing linear functions

Representations given as equations, tables, graphs, or descriptions are compared by their rates of change, which are slopes, and their starting values, which are y-intercepts.

Linear versus nonlinear function

A function is linear only when equal input differences produce equal output differences. Otherwise its rate of change varies and the graph is not a straight line.

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, where c is the longest side.

Distance formula

The distance between two points equals the square root of the sum of the squared differences of their x-coordinates and y-coordinates, derived from the Pythagorean theorem.

Cone volume formula

The volume of a cone equals one third times pi times the radius squared times the height, exactly one third the volume of a cylinder with the same base and height.

Rigid transformations

Translations, reflections, and rotations are rigid motions: they change position or orientation but preserve side lengths and angle measures, so the image is congruent to the original figure.

Similar figures scale factor

Corresponding angles of similar figures are equal and corresponding side lengths share one ratio k. Areas of the images compare by the square of that ratio.

Mean, median, and mode

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

Joint relative frequency

In a two-way table, a cell count divided by the grand total. It describes the share of all observations in one combined category.

Conditional relative frequency

A cell count divided by the total of its row or column. It gives a proportion within a subgroup rather than within the whole data set.

Probability of independent events

When two events do not affect each other, the probability both occur equals the product of their separate probabilities, as in two coin flips.

Mean absolute deviation

A measure of spread found by taking each value's distance from the mean, then averaging those distances. A larger value means data are more spread out.

Unit rate

A rate expressed per one unit of the second quantity, found by dividing. For example, 150 miles in 3 hours gives 50 miles per hour.

Solving a proportion

Set two ratios equal and cross-multiply: a over b equals c over d implies ad equals bc. Then solve the resulting equation for the unknown.

Percent equation

Percent means per 100, so part equals percent times whole. Rearranged, percent equals part divided by whole times 100.

Percent increase or decrease

The amount of change divided by the original amount, times 100. The original, earlier amount is always the denominator of the ratio.