Glossary · Math
SAT and ACT math terms
SAT Math, ACT Math
By the CollegePrepRoom editorial team · Updated · How we write and check these pages
These are the math ideas that come up again and again on the SAT and ACT. Each entry gives a plain definition, a short solved problem and a note on how the idea tends to be tested, so you can recognize it quickly under time.
Index of terms
24 terms in study order
- SlopeThe rate of change of a line: how much y changes for each one-unit increase in x, calculated as rise over run.
- Slope-intercept formThe form y = mx + b of a linear equation, where m is the slope and b is the y-intercept.
- Linear functionA function whose graph is a straight line, with a constant rate of change, written f(x) = mx + b.
- System of linear equationsTwo or more linear equations with the same variables, solved together to find values that satisfy all of them.
- Linear inequalityA statement that compares two linear expressions using <, >, ≤ or ≥, with a range of solutions.
- Function notationWriting f(x) to show the output of function f for input x.
- Quadratic functionA function of the form f(x) = ax² + bx + c, whose graph is a parabola.
- Vertex formThe form f(x) = a(x − h)² + k of a quadratic, which shows the vertex (h, k) directly.
- DiscriminantThe expression b² − 4ac in a quadratic equation ax² + bx + c = 0, which tells how many real solutions the equation has.
- Exponential growth and decayChange by a constant percentage or factor per time period, modeled by y = a(1 + r)ᵗ for growth or y = a(1 − r)ᵗ for decay.
- Percent changeThe change in a quantity expressed as a percentage of the original value: (new − original) / original × 100.
- Ratio and proportionA ratio compares two quantities; a proportion states that two ratios are equal.
- Mean, median and modeMeasures of center: the mean is the average, the median is the middle value, and the mode is the most frequent value.
- Standard deviationA measure of spread showing how far data values typically are from the mean.
- Margin of errorA range around a sample estimate within which the true population value is likely to fall, at a given confidence level.
- Observational study vs. experimentAn experiment randomly assigns treatments and can show cause and effect; an observational study only observes and can show association.
- Conditional probabilityThe probability of an event given that another event has occurred, written P(A | B).
- Pythagorean theoremIn a right triangle, the square of the hypotenuse equals the sum of the squares of the legs: a² + b² = c².
- Right-triangle trigonometry (SOH-CAH-TOA)The ratios sine, cosine and tangent relate a right triangle's acute angles to its side lengths.
- Similar trianglesTriangles with the same shape: corresponding angles are equal and corresponding sides are proportional.
- Equation of a circleThe equation (x − h)² + (y − k)² = r² describes a circle with center (h, k) and radius r.
- RadianA unit of angle measure where one radian is the angle that cuts off an arc equal in length to the radius; 2π radians equal 360°.
- Absolute valueThe distance of a number from zero on the number line, always nonnegative, written |x|.
- Complex numberA number of the form a + bi, where a and b are real numbers and i² = −1.
Flashcard review
Say each definition aloud, then open the card to check your answer.
What does “Slope” mean?
The rate of change of a line: how much y changes for each one-unit increase in x, calculated as rise over run.
What does “Slope-intercept form” mean?
The form y = mx + b of a linear equation, where m is the slope and b is the y-intercept.
What does “Linear function” mean?
A function whose graph is a straight line, with a constant rate of change, written f(x) = mx + b.
What does “System of linear equations” mean?
Two or more linear equations with the same variables, solved together to find values that satisfy all of them.
What does “Linear inequality” mean?
A statement that compares two linear expressions using <, >, ≤ or ≥, with a range of solutions.
What does “Function notation” mean?
Writing f(x) to show the output of function f for input x.
What does “Quadratic function” mean?
A function of the form f(x) = ax² + bx + c, whose graph is a parabola.
What does “Vertex form” mean?
The form f(x) = a(x − h)² + k of a quadratic, which shows the vertex (h, k) directly.
What does “Discriminant” mean?
The expression b² − 4ac in a quadratic equation ax² + bx + c = 0, which tells how many real solutions the equation has.
What does “Exponential growth and decay” mean?
Change by a constant percentage or factor per time period, modeled by y = a(1 + r)ᵗ for growth or y = a(1 − r)ᵗ for decay.
What does “Percent change” mean?
The change in a quantity expressed as a percentage of the original value: (new − original) / original × 100.
What does “Ratio and proportion” mean?
A ratio compares two quantities; a proportion states that two ratios are equal.
What does “Mean, median and mode” mean?
Measures of center: the mean is the average, the median is the middle value, and the mode is the most frequent value.
What does “Standard deviation” mean?
A measure of spread showing how far data values typically are from the mean.
What does “Margin of error” mean?
A range around a sample estimate within which the true population value is likely to fall, at a given confidence level.
What does “Observational study vs. experiment” mean?
An experiment randomly assigns treatments and can show cause and effect; an observational study only observes and can show association.
What does “Conditional probability” mean?
The probability of an event given that another event has occurred, written P(A | B).
What does “Pythagorean theorem” mean?
In a right triangle, the square of the hypotenuse equals the sum of the squares of the legs: a² + b² = c².
What does “Right-triangle trigonometry” mean?
The ratios sine, cosine and tangent relate a right triangle's acute angles to its side lengths.
What does “Similar triangles” mean?
Triangles with the same shape: corresponding angles are equal and corresponding sides are proportional.
What does “Equation of a circle” mean?
The equation (x − h)² + (y − k)² = r² describes a circle with center (h, k) and radius r.
What does “Radian” mean?
A unit of angle measure where one radian is the angle that cuts off an arc equal in length to the radius; 2π radians equal 360°.
What does “Absolute value” mean?
The distance of a number from zero on the number line, always nonnegative, written |x|.
What does “Complex number” mean?
A number of the form a + bi, where a and b are real numbers and i² = −1.