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Flashcards · Maths · Functions, Sequences and Rates of Change

Rates of Change and Areas Under Graphs

16 cards

  1. What is a tangent?

    A straight line that touches a curve at one point.

  2. How do you find the gradient of a curve at a point?

    Draw a tangent and find its gradient.

  3. What is a chord?

    A straight line joining two points on a curve.

  4. What does the gradient of a chord give?

    The average rate of change.

  5. What does the gradient of a distance-time graph represent?

    Speed.

  6. What does the gradient of a velocity-time graph represent?

    Acceleration.

  7. What does the area under a velocity-time graph represent?

    Distance travelled.

  8. What is the area of a trapezium?

    \(\dfrac{1}{2}(a + b)h\).

  9. How do you estimate the area under a curve?

    Split it into strips and add the areas of the trapezia.

  10. What is the unit of acceleration?

    m/s\(^2\).

  11. When is a trapezium estimate an underestimate?

    When the curve bends downwards.

  12. When is a trapezium estimate an overestimate?

    When the curve bends upwards.

  13. What is the average rate of change of \(y = x^2\) from \(x = 1\) to \(x = 4\)?

    5.

  14. What makes the estimate more accurate?

    More, narrower strips.

  15. Why should the two points on a tangent be far apart?

    To get a more accurate gradient.

  16. Which tier is this topic?

    Higher tier on all boards.