JCE Mathematics (Syllabus 13) flashcards

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

Order of operations

Parentheses first, then exponents and roots, then multiplication and division from left to right, and finally addition and subtraction from left to right.

Least common multiple

The smallest positive integer that is divisible by each of two or more given integers, found by multiplying the highest power of every prime factor appearing in their factorizations.

Greatest common divisor

The largest positive integer that divides each of two or more given integers with no remainder; it is the product of the shared prime factors raised to their lowest powers.

Percent change

The difference between a new value and the original value, divided by the original value, then multiplied by 100; a positive result is an increase and a negative result a decrease.

Negative exponent rule

For a nonzero base a and a positive integer n, a raised to the power negative n equals 1 divided by a raised to the power n, so the reciprocal is taken.

Proportion cross products

In a proportion a over b equals c over d with b and d nonzero, the cross products are equal: a times d equals b times c, which allows solving for an unknown term.

Scientific notation

A way of writing a number as a factor between 1 and 10 multiplied by a power of ten, such as 4.5 times 10 to the sixth.

Distributive property

For real numbers a, b and c, a times the quantity b plus c equals a b plus a c; this identity removes parentheses and underlies factoring out common factors.

Quadratic formula

For a x squared plus b x plus c equals zero with a nonzero, x equals negative b plus or minus the square root of b squared minus four a c, all over two a.

Difference of squares

The identity a squared minus b squared equals the quantity a minus b times the quantity a plus b; it factors any expression that is one perfect square subtracted from another.

Inequality reversal rule

Multiplying or dividing both sides of an inequality by a negative number reverses the inequality symbol, while adding or subtracting the same number on both sides never reverses it.

Point-slope form

An equation of a line written as y minus y one equals m times the quantity x minus x one, where m is the slope and the point x one, y one lies on the line.

Discriminant

The expression b squared minus four a c in a quadratic equation; positive means two distinct real roots, zero means one repeated real root, and negative means no real roots.

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 opposite the right angle.

Circle area and circumference

For a circle of radius r, area equals pi times r squared and circumference equals two times pi times r, which also equals pi times the diameter.

Midpoint formula

The midpoint of a segment with endpoints x one, y one and x two, y two is the average of the x-coordinates paired with the average of the y-coordinates.

Distance formula

The distance between points x one, y one and x two, y two equals the square root of the quantity x two minus x one squared plus y two minus y one squared.

Similar figure ratios

If two figures are similar with side lengths in ratio k, then their areas are in ratio k squared and their volumes are in ratio k cubed.

Triangle angle sum

The three interior angles of any triangle add to 180 degrees, and an exterior angle equals the sum of the two interior angles that are not adjacent to it.

Cylinder volume

The volume of a cylinder equals pi times the radius squared times the height, and its surface area equals two pi r squared plus two pi r h.

Mean versus median

The mean is the sum of the data divided by the count and is pulled toward outliers; the median is the middle value of ordered data and resists extreme values.

Independent events

Two events are independent when the probability of both occurring equals the product of their separate probabilities, so knowing that one happened does not change the chance of the other.

Combination formula

The number of ways to choose r objects from n distinct objects when order does not matter is n factorial divided by r factorial times n minus r factorial.

Interquartile range

The difference between the third quartile and the first quartile of ordered data, describing the spread of the middle half; values more than 1.5 times this range beyond a quartile are often outliers.

Expected value

The sum of each possible outcome multiplied by its probability; it represents the long-run average value of a random variable over many repetitions.

Complement rule

For any event A, the probability that A does not occur equals 1 minus the probability that A occurs, since an event and its complement cover all outcomes.

Vertical line test

A graph represents a function exactly when no vertical line crosses it more than once, because that condition means every input has at most one output.

Perpendicular slopes

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

Vertex form

A quadratic written as y equals a times the quantity x minus h squared plus k has vertex h, k and axis of symmetry x equals h; it opens upward when a is positive.

Inverse function

A function found by swapping x and y and solving for y; its graph is the reflection of the original over the line y equals x, and it exists only when the original is one-to-one.

Exponential growth

A function of the form f of x equals a times b to the x with a positive and b greater than one; the value multiplies by b for each unit increase in x.

Even and odd functions

A function is even when f of negative x equals f of x, giving symmetry about the y-axis; it is odd when f of negative x equals negative f of x, giving symmetry about the origin.