TASC General Mathematics Level 3 flashcards

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

Slope formula

For two points (x1, y1) and (x2, y2), slope m equals (y2 − y1) divided by (x2 − x1). It measures vertical change per unit of horizontal change.

Slope-intercept form

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

Perpendicular slopes

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

Solving a linear system

Find values satisfying all equations at once. Substitution isolates one variable; elimination adds or subtracts scaled equations to cancel a variable.

Inequality sign reversal

Multiplying or dividing both sides of an inequality by a negative number reverses the direction of the inequality symbol, so < becomes >.

Function definition

A relation assigning exactly one output to each allowed input. The vertical line test confirms that a graph represents a function.

Domain and range

Domain is the set of permitted inputs, excluding values that make denominators zero or radicands negative. Range is the set of resulting outputs.

Exponential growth model

The form y = a·b^x, where a is the initial amount, b is the growth factor, and b greater than one means growth while b between zero and one means decay.

Average rate of change

Over an interval from a to b, it equals (f(b) − f(a)) divided by (b − a), the slope of the secant line joining those two graph points.

Quadratic vertex form

The equation y = a(x − h)² + k, whose graph has vertex (h, k) and axis of symmetry x = h; the sign of a sets opening direction.

Interquartile range

IQR equals Q3 minus Q1, the spread of the middle half of ordered data. Values beyond 1.5·IQR from the quartiles are often flagged as outliers.

Complement rule

The probability an event does not occur equals one minus the probability it does occur, so P(not A) = 1 − P(A).

Independent events rule

Events are independent when one outcome does not affect the other; then the probability both occur equals the product of their separate probabilities.

Expected value

The long-run average outcome, computed by multiplying each possible value by its probability and summing all those products.

Correlation coefficient

A number r between negative one and one describing the strength and direction of a linear association; values near zero indicate weak linear relationship.

Simple interest formula

Interest equals principal times annual rate as a decimal times time in years, written I = P·r·t; the principal never changes.

Compound interest formula

A = P(1 + r/n)^(nt), where P is principal, r the annual rate, n compounding periods per year, and t years; interest earns interest.

Percent change

Divide the difference between new and old values by the original value, then multiply by 100 to express the change as a percent.

Combinations versus permutations

Combinations count selections where order does not matter, using n!/(r!(n − r)!). Permutations count arrangements where order matters.

Rule of 72

An estimate of doubling time for compounded growth: divide 72 by the annual percentage rate to approximate the number of years required.

Point-slope form

The equation y − y1 = m(x − x1) describes the line through point (x1, y1) with slope m; solve for y to get slope-intercept form.

Quadratic formula

For ax² + bx + c = 0 with a not zero, x equals negative b plus or minus the square root of b² − 4ac, all divided by 2a.

Zero product property

If the product of two factors equals zero, then at least one factor equals zero, which lets factored quadratic equations be solved for roots.

Function composition

The composition f of g at x equals f(g(x)); evaluate the inner function first, then substitute that result into the outer function.

Direct versus inverse variation

Direct variation y = kx rises steadily through the origin. Inverse variation y = k/x decreases as x grows, with neither variable zero.

Interpolation versus extrapolation

Interpolation estimates inside the observed data range and is generally reliable; extrapolation predicts outside that range and is riskier.

Weighted mean

Multiply each value by its weight, sum those products, then divide by the total of all weights; categories with more weight influence the result more.

Mutually exclusive events

Events that cannot happen at the same time, so their joint probability is zero and the probability of either equals the sum of their probabilities.

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.

Effective annual rate

The true yearly growth rate after compounding, computed as (1 + r/n)^n − 1, allowing fair comparison of accounts with different compounding frequencies.

Unit price comparison

Divide total cost by quantity to get cost per unit; the smaller unit price identifies the better value when products differ in package size.

Exponential depreciation

A fixed percent loss each period uses A = P(1 − r)^t, where r is the decimal decay rate and t counts periods; value falls quickly at first.