MathAdvanced MathMedium frequency

SAT Math: Average Rate of Change on a Curve

20+ practice questions in Praczo

What you need to know

The concept, explained

  • 1

    The average rate of change for any function f(x) over an interval [a, b] is just the slope of the secant line connecting those two points.

  • 2

    Formula: [f(b) - f(a)] / [b - a].

  • 3

    It is identical to the slope formula (y2 - y1) / (x2 - x1).

  • 4

    Even if a curve goes up and down wildly between x=a and x=b, the average rate of change only cares about the start and end heights.

Common mistakes
  • Trying to calculate the instantaneous rate (derivative) rather than the average rate.
  • Misreading the graph and plugging in the wrong y-values for the ends of the interval.
Try a sample question

SAT-style practice

Let f(x) = x² + 2. What is the average rate of change of f(x) over the interval x = 1 to x = 3?

20+ questions ready to practice

Ready to master this concept?

Praczo tracks your mastery on all 179 SAT concepts — not just broad topics. One sample question is a start; drilling to mastery is how scores move.

3-day free trial — no credit card required