TSIA2 Math flashcards

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

Percent change formula

Percent change equals the amount of change divided by the original value, then multiplied by 100. The result is positive for an increase and negative for a decrease.

Solving a proportion

In a proportion written a/b = c/d, cross-multiply to obtain ad = bc, then divide by the coefficient of the unknown to isolate that variable.

Unit rate

A rate expressed per one unit of the second quantity, found by dividing the first quantity by the second, such as 150 miles ÷ 3 hours = 50 miles per hour.

Order of operations

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

Dividing by a fraction

Divide by multiplying by the reciprocal: a/b ÷ c/d becomes a/b × d/c, then multiply numerators and multiply denominators and simplify.

Scientific notation form

A number written as a × 10^n where a is at least 1 and less than 10 and n is an integer; used to express very large or very small values.

Absolute value

The distance of a number from zero on the number line, which is never negative; for example |−7| = 7 and |7| = 7.

Percent increase then decrease

Raising a quantity by p percent and then lowering it by the same p percent gives a net factor of (1 + p)(1 − p) = 1 − p², which is below the original 1.

Slope between two points

The slope is (y₂ − y₁)/(x₂ − x₁), the vertical change divided by the horizontal change between two distinct points on a line.

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 it crosses the y-axis.

Perpendicular line slopes

Two nonvertical lines are perpendicular exactly when their slopes are negative reciprocals, meaning the product of the two slopes equals −1.

Inequality sign reversal

Multiplying or dividing both sides of an inequality by the same negative number reverses the direction of the inequality symbol.

Quadratic formula

x = (−b ± √(b² − 4ac))/(2a) gives all solutions of the equation ax² + bx + c = 0 when a is not zero.

Discriminant

For ax² + bx + c = 0, the value b² − 4ac indicates the number of real solutions: positive means two, zero means one, negative means none.

Difference of squares

The expression a² − b² factors as (a − b)(a + b), a pattern used to simplify expressions and to solve certain quadratic equations quickly.

Elimination method

Multiply one or both equations so a variable has opposite coefficients, then add the equations so that variable cancels, leaving one equation to solve.

Area of a triangle

The area equals one-half times the base times the height, where the height must be measured perpendicular to the chosen base.

Circumference of a circle

The distance once around a circle, given by C = 2πr or equivalently C = πd, where r is the radius and d the diameter.

Volume of a cylinder

The volume equals the area of the circular base times the height, written V = πr²h for a radius r and height h.

Pythagorean theorem

In a right triangle, a² + b² = c², where a and b are the legs and c is the hypotenuse opposite the right angle.

Similar figure scaling

Corresponding side lengths of similar figures share a scale factor k; their areas scale by k² and their volumes scale by k³.

Triangle angle sum

The three interior angles of any triangle add to 180 degrees, and an exterior angle equals the sum of the two remote interior angles.

Distance formula

The straight-line distance between two points is √((x₂ − x₁)² + (y₂ − y₁)²), derived from the Pythagorean theorem on the coordinate plane.

Complementary and supplementary angles

Complementary angles have measures summing to 90 degrees, while supplementary angles have measures summing to 180 degrees.

Mean, median, mode

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

Probability of a complement

The probability that an event does not happen equals 1 minus the probability that it does, so the two always sum to 1.

Independent events rule

For independent events, the probability that both occur is P(A) × P(B), because the outcome of one does not change the other's probability.

Mutually exclusive events

Events that cannot happen at the same time; their combined probability is P(A) + P(B), with no overlap to subtract.

Effect of an outlier

An extreme data value shifts the mean much more than the median, so the median usually describes the center of skewed data more accurately.

Standard deviation

A measure of how far values typically lie from the mean; a larger standard deviation means the data are more spread out.

Fundamental counting principle

If one choice can be made in m ways and a second in n ways, then the two choices together can be made in m × n ways.

Combinations versus permutations

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