TABE Math flashcards

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

Order of operations

Perform operations in this order: parentheses or brackets, then exponents, then multiplication and division left to right, then addition and subtraction left to right.

Common denominator

A shared multiple of two denominators. Fractions need one before they can be added or subtracted; rewrite each fraction by multiplying numerator and denominator by the same number.

Dividing fractions

To divide by a fraction, multiply by its reciprocal, which means flipping the numerator and denominator. Example: 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8.

Percent equation

part = percent × whole. To find 15% of 60, change the percent to 0.15 and multiply: 0.15 × 60 = 9.

Absolute value

The distance of a number from zero on the number line. It is never negative: |−7| = 7 and |7| = 7.

Signed number rules

A negative times a negative gives a positive. Adding two negatives gives a negative sum, and a mixed sum takes the sign of the number with the larger absolute value.

Fraction to decimal conversion

Divide the numerator by the denominator: 3/8 = 3 ÷ 8 = 0.375. To change that decimal to a percent, multiply by 100 to get 37.5%.

Multiplying by powers of ten

Multiplying by 10, 100, or 1000 moves the decimal point right by one place per zero; dividing moves it left the same number of places.

Slope formula

m = (y₂ − y₁)/(x₂ − x₁) for any two points on a line. Slope is the rise, or vertical change, divided by the run, or horizontal change.

Slope-intercept form

y = mx + b, where m is the slope and b is the y-intercept, the y-value where the line crosses the y-axis at the point (0, b).

Distributive property

a(b + c) = ab + ac. Multiply the factor outside the parentheses by every term inside: 4(x + 3) = 4x + 12.

Like terms

Terms with identical variable parts. 3x + 5x = 8x, but 3x + 5x² cannot be combined because the exponents are different.

Inequality sign reversal

Multiplying or dividing both sides of an inequality by a negative number reverses the symbol: −2x > 6 becomes x < −3.

Evaluating an expression

Substitute the given number for each variable, then follow order of operations. For 2x² + 1 with x = 3: 2(9) + 1 = 19.

Solving a proportion

Two equal ratios can be solved by cross-multiplying: a/b = c/d gives ad = bc. Then divide to isolate the unknown value.

Area of a triangle

A = ½ × base × height, where the height is perpendicular to the base. A triangle with base 10 and height 6 has area 30 square units.

Circumference of a circle

C = 2πr or C = πd, the distance around the circle. Using π ≈ 3.14, a circle with radius 5 has circumference about 31.4.

Pythagorean theorem

In a right triangle, a² + b² = c², where c is the hypotenuse opposite the right angle. Legs 3 and 4 give 9 + 16 = 25, so c = 5.

Triangle angle sum

The three interior angles of any triangle add to 180°. If two angles measure 50° and 60°, the third angle measures 70°.

Volume of a rectangular prism

V = length × width × height, which is the area of the base times the height. Volume is reported in cubic units.

Similar figures

Corresponding angles are equal and corresponding sides are proportional. A 3-4-5 triangle scaled by 2 becomes 6-8-10.

Mean of a data set

The sum of all values divided by the number of values. For the data 4, 8, and 6: (4 + 8 + 6) ÷ 3 = 6.

Median of a data set

The middle value when the data are ordered least to greatest. With an even number of values, average the two middle values.

Mode and range

The mode is the value appearing most often. The range is the highest value minus the lowest value and measures how spread out the data are.

Circle graph percentages

The whole circle represents 100% or 360°. A category at 25% covers 0.25 × 360 = 90 degrees of the graph.

Scatter plot association

If the points rise from left to right, the two variables have a positive association; if they fall from left to right, the association is negative.

Reading a data table

Each cell belongs to one row category and one column category, and those headings determine what the number inside the cell actually measures.

Probability formula

P(event) = number of favorable outcomes ÷ total number of equally likely outcomes. A probability is always between 0 and 1 inclusive.

Complement rule

P(not A) = 1 − P(A). If the probability of rain is 0.3, then the probability of no rain is 0.7.

Independent events

For independent events, P(A and B) = P(A) × P(B). Two coin flips both landing heads: ½ × ½ = ¼.

Sample space

The list of all possible outcomes. Rolling a six-sided die gives outcomes 1 through 6, so the probability of rolling a 4 is 1/6.

Effect of an outlier

An extreme value pulls the mean toward it but barely moves the median, so the median better describes a typical value in skewed data.