HiSET Math flashcards

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

Order of Operations

Evaluate grouped symbols first, then exponents, then multiplication and division from left to right, then addition and subtraction from left to right.

Absolute Value

The distance of a number from zero on the number line. It is never negative, so |−9| = 9 and |9| = 9.

Adding Fractions

Rewrite the fractions with a common denominator, then add the numerators and keep that denominator. For example, 1/3 + 1/4 = 4/12 + 3/12 = 7/12.

Dividing by a Fraction

Multiply by the reciprocal of the divisor. For example, (3/5) ÷ (2/7) equals (3/5) × (7/2) = 21/10.

Scientific Notation

A number written as a × 10^n where 1 ≤ |a| < 10. The exponent counts decimal places moved and is negative for numbers below 1.

Percent as Decimal

Percent means per 100, so divide by 100 to convert: 45% = 0.45. To find a percent of a number, multiply by that decimal.

Exponent Product Rule

When multiplying powers with the same base, add the exponents: a^m × a^n = a^(m+n). For example, 2^3 × 2^4 = 2^7.

Negative Exponent

A negative exponent means reciprocal: a^(−n) = 1/a^n. For example, 5^(−2) = 1/25, and any nonzero number to the zero power is 1.

Circle Formulas

Circumference equals 2πr, or πd, and area equals πr², where r is the radius and d is the diameter.

Triangle Area and Angles

Area equals one-half times base times height. The three interior angles of any triangle always add up to 180 degrees.

Pythagorean Theorem

In a right triangle, the squares of the two legs add to the square of the hypotenuse: a² + b² = c², where c is opposite the right angle.

Trapezoid Area

Area equals one-half times the height times the sum of the two parallel bases: A = ½(b₁ + b₂)h.

Cylinder Volume

Volume of a cylinder equals the base area times height: V = πr²h, where r is the radius of the circular base.

Rectangular Prism Surface Area

Surface area equals 2lw + 2lh + 2wh, the total area of all six rectangular faces of the solid.

Similar Figures Scaling

Corresponding angles are equal and corresponding sides are proportional. If side lengths scale by factor k, areas scale by k² and volumes by k³.

Unit Conversion Method

Multiply by a conversion ratio that equals 1, arranging units so the unwanted unit cancels. Example: 3 feet × (12 inches/1 foot) = 36 inches.

Complementary Angle Sum

Two complementary angles add to 90 degrees; two supplementary angles add to 180 degrees. Vertical angles formed by crossing lines are equal.

Mean, Median, Mode

Mean is the sum divided by the count; median is the middle of an ordered list; mode is the most frequent value.

Range of Data

The difference between the largest and smallest values in a data set. It measures spread and is sensitive to outliers.

Basic Probability

Probability equals favorable outcomes divided by total equally likely outcomes. Every probability lies between 0 and 1 inclusive.

Complement Rule

The probability an event does not happen equals 1 minus the probability it does: P(not A) = 1 − P(A).

Independent Events

When one event's outcome does not affect another, the probability both occur is the product: P(A and B) = P(A) × P(B).

Interquartile Range

IQR equals the third quartile minus the first quartile, Q3 − Q1. It gives the spread of the middle half of the data.

Misleading Graphs

Truncated vertical axes that skip zero, uneven axis intervals, and distorted 3-D pie charts exaggerate differences and misrepresent data.

Two-Way Table Percents

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

Slope Formula

For two points (x₁, y₁) and (x₂, y₂), slope m = (y₂ − y₁)/(x₂ − x₁), the change in y divided by the change in x.

Slope-Intercept Form

The equation y = mx + b describes a line with slope m and y-intercept b, the point where the line crosses the y-axis.

Point-Slope Form

y − y₁ = m(x − x₁) describes the line with slope m passing through the point (x₁, y₁). Useful when slope and one point are known.

Solving Linear Equations

Undo operations in reverse order, applying each step to both sides, to isolate the variable. Check by substituting the answer back in.

Multiplying Binomials

Use FOIL: (x + a)(x + b) = x² + (a + b)x + ab. Multiply First, Outer, Inner, Last terms, then combine like terms.

Systems of Linear Equations

The solution is the point where the two lines intersect. Lines with the same slope but different intercepts are parallel and give no solution.

Exponential Growth and Decay

y = a(1 + r)^t models growth and y = a(1 − r)^t models decay, where a is the starting amount, r the rate, and t the number of periods.