MTTC Mathematics (Elementary) (089) flashcards

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

Divisibility rule for 3

A whole number is divisible by 3 exactly when the sum of its digits is divisible by 3. For example, 4,281 has digit sum 15, so it is divisible by 3.

Least common multiple

The smallest positive number that is a multiple of each number in a set. Find it by writing prime factorizations and multiplying the highest power of every prime that appears.

Dividing by a fraction

Dividing by a fraction is multiplying by its reciprocal: a/b ÷ c/d = a/b × d/c. Because the reciprocal of a proper fraction exceeds 1, the quotient grows larger than the dividend.

Percent increase formula

Percent change equals the amount of change divided by the original amount, times 100. A price rising from $40 to $50 is a $10 increase over $40, a 25% increase.

Unit rate

A rate expressed per one unit of the second quantity, found by dividing both quantities by the second. If 5 pounds cost $12, the unit rate is $2.40 per pound.

Rounding decision rule

Identify the place being rounded, then look at the single digit immediately to its right. If that digit is 5 or greater, increase the target digit by one; otherwise leave it unchanged.

Subtracting negative integers

Subtracting a negative number is the same as adding its absolute value, because the two negatives cancel: 7 − (−4) = 7 + 4 = 11. On a number line this moves right, not left.

Distributive property

Multiplying a sum by a factor gives the same result as multiplying each addend separately and then adding: a(b + c) = ab + ac. Applied in reverse, it factors expressions like 6x + 9 into 3(2x + 3).

Slope of a line

The ratio of vertical change to horizontal change between two points: (y₂ − y₁)/(x₂ − x₁). It appears as m in slope-intercept form y = mx + b, where b is the y-intercept.

Inequality reversal rule

When both sides of an inequality are multiplied or divided by a negative number, the direction of the inequality symbol must flip. Adding or subtracting a negative number does not require flipping.

Arithmetic sequence nth term

In a sequence with constant difference d and first term a₁, the nth term equals a₁ + (n − 1)d. The multiplier is n − 1 because the first term already accounts for one step.

Vertical line test

A graph represents a function only if no vertical line crosses it more than once. A single x-value with two different y-values means one input has two outputs, so the relation is not a function.

Zero and negative exponents

Any nonzero base raised to the zero power equals 1. A negative exponent means the reciprocal of the positive power: x^(−a) = 1/x^a, so 2^(−3) = 1/8.

Solving a two-step equation

Undo operations in reverse order: first add or subtract to remove the constant term, then multiply or divide to remove the coefficient. Whatever is done to one side must be done to the other.

Geometric sequence ratio

Consecutive terms in a geometric sequence share a constant ratio r, found by dividing any term by the one before it. The nth term is a₁ · r^(n − 1).

Triangle angle sum

The three interior angles of any triangle add to 180 degrees. Combined with the fact that angles on a straight line add to 180 degrees, this determines missing angles in many figures.

Trapezoid area formula

The area of a trapezoid equals half the sum of the two parallel bases times the height: A = ½(b₁ + b₂)h. The height is the perpendicular distance between the bases, not a slanted side.

Pythagorean theorem

In a right triangle, the square of the hypotenuse equals the sum of the squares of the legs: a² + b² = c². The converse holds: if the equation is satisfied, the triangle has a right angle.

Scale factor and area

When similar figures have a length scale factor k, their areas scale by k² and their volumes by k³. Doubling every dimension of a rectangle multiplies its area by four.

Cylinder volume formula

The volume of a cylinder is the base area times the height: V = πr²h. A cone with the same base and height holds exactly one third as much, V = ⅓πr²h.

Supplementary and complementary angles

Two angles are complementary when their measures sum to 90 degrees and supplementary when they sum to 180 degrees. Vertical angles, formed by intersecting lines, are always equal.

Unit conversion by cancellation

Multiply by a conversion ratio equal to 1, arranged so the unwanted unit cancels. To convert 3 feet to inches, multiply by 12 in/1 ft, giving 36 inches.

Mean versus median

The mean divides the sum of values by their count and is pulled toward extreme values. The median is the middle value of ordered data and resists outliers, so it better describes skewed data.

Interquartile range

The IQR equals Q3 minus Q1, the spread of the middle half of the data. It is shown as the length of the box in a box plot and is unaffected by extreme outliers.

Complement rule

The probability that an event does not occur equals 1 minus the probability that it does. If rain has probability 0.3, no rain has probability 0.7.

Probability of independent events

When two events do not influence each other, the probability both occur is the product of their individual probabilities. Two coin flips landing heads have probability ½ × ½ = ¼.

Fundamental counting principle

If a task has stages with m and n choices respectively, the total number of outcomes is m × n. Three shirts and four pairs of pants give twelve outfits.

Permutation versus combination

A permutation counts arrangements where order matters; a combination counts selections where it does not. Choosing 2 of 5 students is a combination, while awarding first and second place is a permutation.

Correlation versus causation

Correlation measures the strength and direction of a linear association between two variables. A strong correlation does not prove that one variable causes changes in the other.

Reading a box plot

A box plot marks the minimum, first quartile, median, third quartile, and maximum. The box spans the middle half of the data, and each whisker reaches the most extreme value shown.

Effect of an outlier

An extreme value raises or lowers the mean noticeably but shifts the median little, because the median depends on position rather than magnitude. Report the median when data are skewed.

Line of best fit

A straight line drawn through a scatter plot that comes closest to the data points, used to predict one variable from another. Predictions far outside the observed data range are unreliable extrapolations.