HiSET Math cheat sheet

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

Absolute value |x| is the distance from 0 on the number line, so |x| is never negative and |-7| = 7.

To add fractions, rewrite over a common denominator: a/b + c/d = (ad + bc)/(bd).

To divide by a fraction, multiply by its reciprocal: (a/b) ÷ (c/d) = (a/b) × (d/c).

Scientific notation writes a number as a × 10^n with 1 ≤ |a| < 10; the exponent n counts decimal places moved.

Percent means per 100: 15% = 0.15 = 15/100, and 'of' signals multiplication, as in 0.15 × 80.

Product of powers: a^m × a^n = a^(m+n); quotient of powers: a^m ÷ a^n = a^(m−n); power of a power: (a^m)^n = a^(mn).

Comparing fractions: cross-multiply (a/b vs c/d compares ad vs bc) or convert both to decimals.

Circle: circumference C = 2πr = πd; area A = πr².

Triangle: area A = ½bh; the interior angles of any triangle sum to 180°.

Rectangle: area A = lw and perimeter P = 2l + 2w; parallelogram area A = bh.

Trapezoid: area A = ½(b₁ + b₂)h, where b₁ and b₂ are the parallel bases.

Rectangular solid: volume V = lwh and surface area SA = 2lw + 2lh + 2wh; cylinder volume V = πr²h.

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

Similar figures have proportional sides and equal angles; if the scale factor is k, areas scale by k² and volumes by k³.

Unit conversion: multiply by a ratio equal to 1 (e.g., 12 in/1 ft) and cancel units so the unwanted unit divides out.

Mean = sum of values ÷ number of values; median is the middle value of an ordered list; mode is the most frequent value.

Range = maximum − minimum; it measures spread, not center.

Probability of an event = (number of favorable outcomes) ÷ (total equally likely outcomes), always between 0 and 1.

Complement rule: P(not A) = 1 − P(A).

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

A graph's misleading features include unequal axis intervals, truncated (non-zero) y-axes, and 3-D pie charts that distort area.

To find a percent from a two-way table, divide the cell count by the relevant row, column, or grand total named in the question.

Interquartile range IQR = Q3 − Q1; it describes the spread of the middle 50% of the data.

Slope of a line through (x₁, y₁) and (x₂, y₂): m = (y₂ − y₁)/(x₂ − x₁).

Slope-intercept form y = mx + b: m is the slope and b is the y-intercept.

Point-slope form: y − y₁ = m(x − x₁) for a line with slope m through (x₁, y₁).

Distribute and combine like terms: a(b + c) = ab + ac; only terms with identical variable parts can be added.

Solving a linear equation: undo operations in reverse order and perform the same operation on both sides.

Multiplying binomials uses FOIL: (x + a)(x + b) = x² + (a + b)x + ab.

For a system of two linear equations, the solution is the point where the graphs intersect; parallel lines (same slope) have no solution.

Exponential growth/decay: y = a(1 + r)^t grows and y = a(1 − r)^t decays, where r is the rate per period and a is the starting amount.