Praxis Core Math flashcards

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

Order of Operations

The sequence for evaluating expressions: parentheses first, then exponents, then multiplication and division from left to right, then addition and subtraction from left to right.

Percent Change Formula

Percent change equals the difference between new and old values divided by the original value, then multiplied by 100. Always divide by the starting amount.

Proportion Cross-Multiplication

In a proportion a/b = c/d, multiply each numerator by the opposite denominator to get ad = bc, then solve the resulting linear equation for the unknown.

Absolute Value

The distance of a number from zero on the number line, always nonnegative. For example, the absolute value of negative seven is seven.

Negative Exponent Rule

A base raised to a negative exponent equals the reciprocal of that base raised to the positive exponent, so x to the negative n equals one over x to the n.

Scientific Notation Form

A number written as a coefficient between 1 and 10 multiplied by a power of ten. To multiply, multiply coefficients and add the exponents.

Unit Rate Conversion

Convert rates by multiplying by fractions equal to one that relate units, canceling units diagonally, such as converting miles per hour to feet per second.

Slope Formula

Slope equals the change in y divided by the change in x between two points, computed as y-two minus y-one over x-two minus x-one.

Slope-Intercept Form

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

Perpendicular Line Slopes

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

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, negative gives no real roots.

Inequality Sign Reversal

When both sides of an inequality are multiplied or divided by a negative number, the direction of the inequality symbol must be reversed to stay true.

Composite Function

A function formed by applying one function to the output of another. To evaluate f of g of x, first compute g of x, then substitute that result into f.

Linear Versus Exponential Growth

A linear function changes by adding a constant amount per unit, while an exponential function changes by multiplying by a constant factor per unit.

Solving Systems by Elimination

Add or subtract the two equations, or multiply one first, so a variable cancels; then solve for the remaining variable and back-substitute.

Triangle Area Formula

The area of a triangle equals one half times the base times the height, where the height is perpendicular to the chosen base.

Triangle Angle Sum

The three interior angles of any triangle always add to 180 degrees, which allows finding a missing angle when the other two are known.

Pythagorean Theorem

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

Circle Circumference and Area

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

Cylinder Volume

The volume of a cylinder equals pi times the radius squared times the height, since it is the circular base area multiplied by the height.

Similar Figure Scale Factor

When two figures are similar with scale factor k, corresponding lengths scale by k, areas by k squared, and volumes by k cubed.

Polygon Interior Angle Sum

The interior angles of a polygon with n sides add to (n minus 2) times 180 degrees. A regular polygon divides this equally among its angles.

Distance and Midpoint Formulas

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

Mean, Median, Mode

Mean is the sum divided by the count; median is the middle of an ordered list; mode is the most frequent value. Each describes center differently.

Range of a Data Set

The range equals the largest value minus the smallest value. It measures total spread but is sensitive to extreme outliers in the data.

Probability of Independent Events

For independent events, the probability that both occur equals the product of their individual probabilities, because one outcome does not affect the other.

Complement Rule

The probability that an event does not occur equals one minus the probability that it does occur, since the two outcomes cover all possibilities.

Mutually Exclusive Events

Events that cannot happen at the same time. Their combined probability is the sum of individual probabilities, with no overlap to subtract.

Random Sample

A sample in which every member of the population has an equal chance of selection, allowing results to be generalized to the whole population.

Correlation Versus Causation

Correlation measures the strength and direction of a linear relationship between two variables, but it does not prove that one variable causes the other.

Normal Distribution Rule

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