Math glossary

Every term in plain English, with the notation, an example, and the confusion it usually causes. If a word stopped you mid-lesson, it is here.

51 terms

A

Absolute value: The absolute value of a number is its distance from zero on the number line. Distance ignores direction, so it is never negative: both 5 and -5 have absolute value 5.
Area: Area is the amount of space inside a flat shape, counted in square units such as cm². It comes from multiplying two lengths, which is why the units are squared.

C

Coefficient: A coefficient is the number multiplying a variable in a term. In 3x the coefficient is 3, and in -5y it is -5, because the sign belongs to the number.
Constant: A constant is a term with a fixed value and no variable attached. In 3x + 7, the constant is 7, because it stays the same whatever x turns out to be.
Constant of proportionality: The fixed multiplier k in a proportional relationship y = kx. It equals y divided by x, gives the same value for every pair, and is the unit rate of the situation.

D

Decimal: A decimal writes a number using places smaller than one, separated from the whole part by a decimal point. 3.47 is three wholes plus four tenths plus seven hundredths.
Denominator: The denominator is the bottom number of a fraction. It says how many equal parts the whole was cut into, which fixes how big each part is.
Discriminant: The discriminant is the expression b squared minus 4ac inside the quadratic formula. Its sign tells you how many real solutions a quadratic has before you finish solving.
Distributive property: The distributive property says a(b + c) = ab + ac. The multiplier outside the parentheses multiplies every term inside, not only the first one.
Domain: The domain of a function is every input it accepts. For f(x) = 2x + 1 the domain is all real numbers, but a fraction excludes any input making the denominator zero.

E

Equation: An equation is a statement that two expressions are equal, joined by an equals sign. Solving one means finding every value of the variable that makes the statement true.
Exponent: The exponent is the small raised number in a power, and it counts how many times the base is multiplied by itself. In 2⁵ the base is 2 and the exponent is 5, so the value is 2 × 2 × 2 × 2 × 2 = 32.

F

Fraction: A fraction names a number of equal parts of a whole. It is written as one number over another, and the bar between them means divide.
Function: A function is a rule that assigns exactly one output to each input. If a single input could give two different outputs, the rule is not a function.

G

Greatest common factor: The greatest common factor of two numbers is the largest number that divides both of them exactly. The GCF of 12 and 18 is 6.

H

Hypotenuse: The hypotenuse is the side of a right triangle opposite the right angle. It is always the longest side, and it is the c in a² + b² = c².

I

Integer: An integer is a whole number or the negative of one: ... -2, -1, 0, 1, 2 ... Fractions and decimals such as 1.5 are not integers, though they are still numbers on the line.
Interest: Interest is the extra money paid for the use of money — earned on savings or owed on a loan. It is worked out as a percent of an amount, over a period of time.
Inverse operations: Inverse operations undo each other. Addition and subtraction are inverses, and so are multiplication and division. Solving an equation means applying the inverse of whatever was done to the variable.
Irrational number: An irrational number cannot be written as a fraction of two whole numbers, and its decimal never ends and never repeats. The square root of 2 and pi are the two you meet first.

L

Like terms: Like terms have exactly the same variables raised to exactly the same powers. 3x and 5x are like terms, but 3x and 3x squared are not, and neither are 3x and 7.
Linear equation: A linear equation is one whose graph is a straight line. Every variable appears to the first power only, so there are no squares, roots, or variables in a denominator.

M

Mean: The mean is the total of the values divided by how many there are. It shares the total out evenly, so it need not equal any value in the data, and a single outlier can pull it a long way.
Median: The median is the middle value once the data is in order. With an even count it is the mean of the two middle values. Because it depends on position rather than size, an outlier barely moves it.

N

Numerator: The numerator is the top number of a fraction. It counts how many parts you have. In three quarters the numerator is three, so you have three of the four parts.

O

Opposite: The opposite of a number is the number the same distance from zero on the other side. The opposite of 7 is -7, and any number plus its opposite gives zero.
Order of magnitude: An order of magnitude is a factor of ten. Two quantities differ by one order of magnitude when one is about ten times the other, which is exactly the difference between their exponents in scientific notation.
Outlier: An outlier is a value far from the rest of the data. It pulls the mean towards itself and inflates the range, while leaving the median and interquartile range almost untouched.

P

Percent: A percent is a number out of one hundred. 30% means 30 out of every 100, which is the fraction 30/100 and the decimal 0.3.
Percentage point: A percentage point is the plain difference between two percents. A rise from 4% to 6% is 2 percentage points, but a 50% increase — the two describe the same change and give different numbers.
Perfect square: A perfect square is a whole number that some whole number squares to, such as 1, 4, 9, 16, 25 and 36. Their square roots are exact whole numbers, which is what makes them worth recognising on sight.
Pi: Pi is what you get when you divide any circle's circumference by its diameter — always about 3.14159, whatever the size of the circle.
Place value: Place value is the idea that a digit's worth depends on where it sits. The 4 in 40 is worth forty; the 4 in 0.4 is worth four tenths.
Principal: The principal is the starting amount of money in an interest calculation — what was invested or borrowed, before any interest is added.

Q

Quadratic equation: A quadratic equation is one that can be written as ax squared plus bx plus c = 0, with a not equal to zero. The squared term is what makes it quadratic rather than linear.
Quartile: Quartiles cut ordered data into four equal parts. Q1 has a quarter of the values below it, Q3 has three quarters below it, and the gap between them is the interquartile range.
Quotient: The quotient is the answer to a division. In 12 ÷ 4 = 3, the 12 is the dividend, the 4 is the divisor, and the 3 is the quotient.

R

Radius: The radius of a circle is the distance from its centre to its edge. The diameter goes right across through the centre, so it is twice the radius.
Range: The range of a function is every output it produces. For f(x) = 2x + 1 the range is all real numbers, but for a horizontal line like f(x) = 5 the range is the single value 5.
Rate of change: A rate of change is how much one quantity changes compared with another: the change in output divided by the change in input. It is slope with units attached, such as miles per hour.
Ratio: A ratio compares two quantities. Written 3:2, it says there are 3 of the first thing for every 2 of the second, at any size. Order matters, so 3:2 and 2:3 describe different situations.
Rational number: A rational number is any number writable as a fraction of two integers. That covers every integer, every terminating decimal and every repeating decimal, along with the negatives of all of them.
Reciprocal: The reciprocal of a number is the number you multiply it by to get one. For a fraction it is that fraction turned upside down, so the reciprocal of three fifths is five thirds.

S

Slope: Slope measures how steep a line is: the change in y divided by the change in x. A slope of 2 means the line climbs 2 units for every 1 unit across.
Solution set: The solution set is every value that makes an equation or inequality true. An equation often has one solution, an inequality usually has infinitely many, and some have none at all.
System of equations: A system of equations is two or more equations that must all be true at once. For two lines, the solution is the point where their graphs cross.

T

Term: A term is one piece of an expression, separated from the others by plus or minus signs. The expression 4x + 12 - 2x has three terms: 4x, 12 and -2x.

U

Unit rate: A unit rate gives the amount for exactly one of something — 50 miles per hour, 75 cents per apple. Because every unit rate is measured against the same 1, two of them can be compared directly.

V

Variable: A variable is a letter standing in for a number you do not know yet, or one that can change. In x + 3 = 10, the variable x represents the single number that makes the sentence true.

Y

y-intercept: The y-intercept is where a graph crosses the vertical axis — the value of y when x is 0. In y = 2x + 3 the y-intercept is 3, so the line passes through (0, 3).

Z

Zero product property: The zero product property says that if a product equals zero, at least one of its factors must be zero. It is the reason factoring solves quadratic equations.