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Grade 12 · Functions
Average Gradient & Average Rate of Change (Grade 12)
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Answer all questions. Show all your working — marks are awarded for method as well as the final answer.

  1. 1
    Determine the average gradient of f(x) = x² + 1 between x = 1 and x = 3.
    (2)
    -1123424681012xyf(x) = x² + 1average gradient = 4(1 ; 2)(3 ; 10)
  2. 2
    Determine the average gradient of f(x) = x² + 1 between x = −1 and x = 2.
    (2)
  3. 3
    Write down the formula for average gradient between x = a and x = b.
    (2)
  4. 4
    Is the average gradient the same as the gradient at a point? Explain.
    (2)
  5. 5
    Determine the average gradient of f(x) = x² between x = 2 and x = 2,001 (three decimals).
    (2)
  6. 6
    What does the average gradient become as the two points move together?
    (2)
  7. 7
    A car travels 240 km in 3 hours. What is its average rate of change of distance?
    (2)
  8. 8
    Determine the average gradient of f(x) = 2x + 5 between any two points.
    (2)
TOTAL: 16 marks
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