TABE Math cheat sheet

Order of operations: parentheses/brackets first, then exponents, then multiplication and division left to right, then addition and subtraction left to right.

a/b + c/d = (ad + bc)/(bd); a common denominator is required before fractions can be added or subtracted.

a/b ÷ c/d = a/b × d/c - dividing by a fraction is the same as multiplying by its reciprocal.

part = percent × whole, and percent = part ÷ whole × 100.

Fraction to decimal: divide numerator by denominator. Decimal to percent: multiply by 100.

Multiplying by 10^n moves the decimal point n places to the right; dividing by 10^n moves it n places to the left.

|x| is the distance from 0, so |x| ≥ 0 and |−a| = |a|.

A product or quotient of two numbers with the same sign is positive; with different signs it is negative.

Slope m = (y₂ − y₁)/(x₂ − x₁), the rise divided by the run.

Slope-intercept form y = mx + b: m is the slope and b is the y-intercept, the point (0, b).

Point-slope form: y − y₁ = m(x − x₁).

Distributive property: a(b + c) = ab + ac.

Only like terms combine: 3x + 5x = 8x, but 3x + 5x² cannot be combined.

Adding or subtracting the same value on both sides of an equation keeps it true; so does multiplying or dividing both sides by a nonzero value.

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

A direct proportion y = kx graphs as a straight line through the origin, with k = y/x constant.

Two-step equation: undo addition or subtraction first, then undo multiplication or division.

Rectangle A = lw; parallelogram A = bh; triangle A = ½bh, where h is perpendicular to the base.

Circle: A = πr² and C = 2πr = πd.

Rectangular prism V = lwh; cylinder V = πr²h; volume answers are in cubic units.

Pythagorean theorem: a² + b² = c², where c is the hypotenuse opposite the right angle.

Interior angles sum to 180° in a triangle, 360° in a quadrilateral, and 180° along a straight line.

Complementary angles sum to 90°; supplementary angles sum to 180°.

Similar figures have equal corresponding angles and proportional corresponding sides; scale factor k multiplies lengths and k² multiplies area.

Unit conversion: multiply by a ratio equal to 1 and cancel units, e.g., 3 ft × (12 in / 1 ft) = 36 in.

Metric benchmarks: 1 m = 100 cm, 1 km = 1000 m, 1 kg = 1000 g, 1 L = 1000 mL.

Mean = sum of all values ÷ number of values.

Median = middle value once data are ordered least to greatest; with an even count, average the two middle values.

Mode = most frequent value; a data set can have no mode, one mode, or several modes.

Range = maximum value − minimum value.

Circle graph: degrees = percent × 360, and percent = degrees ÷ 360 × 100.

Bar graphs compare categories, line graphs show change over time, and scatter plots show the relationship between two variables.

Positive association on a scatter plot means that as x increases, y tends to increase.

In a table, the row and column headings tell which categories each cell describes.

P(event) = favorable outcomes ÷ total equally likely outcomes, and 0 ≤ P ≤ 1.

Complement rule: P(not A) = 1 − P(A).

For independent events, P(A and B) = P(A) × P(B).

Experimental probability = number of times the event occurred ÷ number of trials.

Sample space for two coin flips is HH, HT, TH, TT, so P(two heads) = 1/4.

An outlier pulls the mean toward it more than it moves the median.

Standard deviation measures the typical distance of values from the mean; a larger value means greater spread.

Without replacement, the total number of possible outcomes decreases after each draw, changing later probabilities.