High-value terms

Short StudyQuest definitions, not the official glossary dictionary. For every concept that appears in a journey, use the main glossary.

• Absolute value

  Distance from zero on the number line. Always zero or positive: $|-7| = 7$.
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• Association

  A pattern in which one variable tends to change as the other changes: positive, negative, or none. An association is not proof of cause.
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• Base

  In a power such as $2^5$, the base is the number being multiplied by itself: $2^5 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2$.
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• Binomial

  A polynomial with exactly two terms, such as $x + 3$ or $2a - b$.
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• Coefficient

  The number multiplied by a variable. In $3x + 2$, the coefficient of $x$ is 3.
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• Congruent

  Same size and shape: one figure can be carried onto the other by slides, flips, and turns, so matching sides and angles are equal.
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• Constant

  A term with no variable, so its value never changes. In $5x + 20$, the constant is $20$.
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• Cube root

  The number that, multiplied by itself three times, gives the value: $\sqrt[3]{27} = 3$ because $3^3 = 27$.
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• Degree

  The largest exponent on the variable in a polynomial. $4x^3 - x + 7$ has degree $3$.
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• Dilation

  A transformation that enlarges or shrinks a figure by a scale factor from a center point. Angles stay the same and every length is multiplied by the factor.
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• Distributive property

  Multiply a sum by multiplying each part: $3(x + 4) = 3x + 12$.
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• Equation

  A statement that two expressions are equal, using $=$. Solving means finding the value that makes it true.
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• Equivalent

  Having the same value for every input even though written differently: $2(x + 3)$ and $2x + 6$ are equivalent expressions.
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• Evaluate

  Replace each variable with a number and work out the value. Evaluating $2x + 1$ at $x = 4$ gives $9$.
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• Exponent

  The small raised number that says how many times to multiply the base: in $2^5$ the exponent is $5$.
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• Expression

  A combination of numbers, variables, and operations with no equals sign, such as $4n + 1$.
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• Function

  A rule that assigns exactly one output to each input. Tables, graphs, and $y = mx + b$ can all show functions.
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• Hypotenuse

  The longest side of a right triangle, across from the right angle. In a $3$-$4$-$5$ triangle it is $5$.
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• Independent variable

  The input you choose or control, shown on the horizontal axis. The dependent variable responds to it and goes on the vertical axis.
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• Inequality

  A comparison that is not exact equality: $<$, $>$, $\leq$, or $\geq$. Solutions are often a range of numbers.
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• Input and output

  The input is the value you put into a function, usually $x$; the output is the value that comes out, usually $y$.
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• Integer

  Whole numbers and their opposites, including zero: $\ldots, -2, -1, 0, 1, 2, \ldots$
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• Irrational number

  A number that cannot be written as a fraction of integers; its decimal never ends or repeats. $\sqrt{2}$ and $\pi$ are irrational.
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• Like terms

  Terms with exactly the same variable part, which can be combined: $3x + 5x = 8x$, but $3x$ and $3x^2$ are not like terms.
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• Line of best fit

  A straight line drawn through a scatter plot to summarize the trend, with about as many points above it as below.
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• Linear

  Changing at a constant rate, so the graph is a straight line. $y = 2x + 1$ is linear; $y = x^2$ is not.
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• Mean

  The average: add the values and divide by how many there are. The mean of $4, 6, 8$ is $6$.
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• Median

  The middle value when the data are in order; with an even count, the mean of the two middle values. The median of $3, 9, 4$ is $4$.
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• Mode

  The value that appears most often in a data set. The mode of $2, 5, 5, 7$ is $5$.
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• Nonlinear

  Not changing at a constant rate, so the graph curves or bends. Doubling patterns and $y = x^2$ are nonlinear.
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• Opposite

  The number the same distance from zero on the other side of the number line: the opposite of $7$ is $-7$, and a number plus its opposite is $0$.
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• Order of operations

  The agreed order for a calculation: grouping symbols, then exponents, then multiplication and division from left to right, then addition and subtraction from left to right.
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• Outlier

  A data value that sits far from the rest. Investigate it before deciding whether it belongs.
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• Parabola

  The U-shaped graph of a quadratic function such as $y = x^2$. Its turning point is called the vertex.
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• Percent

  Out of $100$: $45\%$ means $\frac{45}{100}$, or $0.45$.
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• Perfect square

  A whole number that is the square of a whole number: $1, 4, 9, 16, 25, \ldots$ Its square root is exact.
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• Polynomial

  An expression built from terms added together, each a number times a whole-number power of a variable: $2x^3 - x + 7$.
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• Probability

  How likely an event is, from $0$ (impossible) to $1$ (certain). Rolling a $3$ on a fair die has probability $\frac{1}{6}$.
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• Proportional relationship

  Two quantities whose ratio stays the same. The graph is a straight line through the origin, $y = kx$, and $k$ is the constant of proportionality.
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• Pythagorean theorem

  In a right triangle with legs $a$ and $b$ and hypotenuse $c$, $a^2 + b^2 = c^2$.
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• Quadratic

  An expression or function whose highest power is $2$, such as $y = x^2 - 4x + 3$. Its graph is a parabola.
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• Rate of change

  How much the output changes for each one-unit change in the input. For a line it is the slope.
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• Ratio

  A comparison of two quantities, often written $a:b$ or as a fraction. A unit rate is a ratio with a denominator of 1.
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• Rational number

  A number that can be written as a fraction of integers with a nonzero denominator, including decimals that terminate or repeat.
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• Real number

  Any number on the number line, rational or irrational.
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• Reciprocal

  Flip the fraction: the reciprocal of $\frac{2}{3}$ is $\frac{3}{2}$. A number times its reciprocal is $1$.
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• Reflection

  A flip across a line, like a mirror image. Reflecting $(3, 2)$ across the $y$-axis gives $(-3, 2)$.
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• Rotation

  A turn around a fixed point. Rotating $(2, 1)$ by $90°$ counterclockwise about the origin gives $(-1, 2)$.
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• Scale factor

  The number every length is multiplied by in a dilation or scale drawing. A scale factor of $2$ doubles lengths and quadruples area.
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• Scatter plot

  A graph of paired data as points, used to spot trends, clusters, and outliers.
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• Scientific notation

  A way to write very large or very small numbers as a number from $1$ to $10$ times a power of ten: $3{,}400 = 3.4 \times 10^3$.
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• Similar

  Same shape, not necessarily the same size: equal angles and side lengths in proportion. A dilation makes similar figures.
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• Slope

  Steepness of a line: rise over run, or $\frac{y_2 - y_1}{x_2 - x_1}$ when the run is not zero.
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• Solution

  A value, or pair of values, that makes an equation or inequality true. $x = 5$ is the solution of $2x + 1 = 11$.
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• Square root

  The number that, multiplied by itself, gives the value: $\sqrt{49} = 7$. Square roots of numbers that are not perfect squares, like $\sqrt{2}$, are irrational.
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• Substitute

  Replace a variable with a number or expression. To check $x = 5$ in $2x + 1 = 11$, substitute $5$ for $x$.
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• System of equations

  Two or more equations that must be true at the same time. The solution is the point where their graphs cross.
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• Term

  A single part of an expression, separated from the others by $+$ or $-$ signs. $5x + 20$ has two terms: $5x$ and $20$.
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• Translation

  A slide: every point moves the same distance in the same direction. Translating $(1, 4)$ by $(3, -2)$ gives $(4, 2)$.
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• Two-way table

  A table that counts cases by two categories at once, such as grade level by club choice.
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• Unit rate

  A rate for one unit: $\$12$ for $3$ pounds is $\$4$ per pound.
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• Variable

  A letter that stands for a number that can change, or for an unknown you are solving for.
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• Vertex

  The turning point of a parabola, its highest or lowest point. For $y = (x - 2)^2 + 1$ the vertex is $(2, 1)$.
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• Volume

  The amount of space a solid takes up, measured in cubic units. A $2 \times 3 \times 4$ box has volume $24$ cubic units.
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• x-intercept

  Where a graph crosses the $x$-axis, so $y = 0$. For $y = 2x - 6$ the $x$-intercept is $3$.
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• y-intercept

  Where a graph crosses the $y$-axis, so $x = 0$. In $y = mx + b$ the $y$-intercept is $b$.
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