Practice Example (1.4.2) - Rates of Change - IB 10 Mathematics

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6 sample questions

Question 1.
Calculate the AROC for f(x) = 2x + 3 from x = 1 to x = 4.
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Use the slope formula for secant line.
Question 2.
What is the IROC of f(x) = 1/x at x = 1?
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Calculate the limit as h approaches 0.
3Question 3.
What is the formula for Average Rate of Change?
- (f(b) - f(a)) / (b - a)
- (b - a) / (f(b) - f(a))
- (f(a) + f(b)) / (b - a)
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Think about how distance is divided by time.
4Question 4.
True or False: The instantaneous rate of change is found by evaluating the slope of the tangent line.
- True
- False
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Recall the definitions of tangent lines.
Question 5.
A cyclist travels along a path described by the equation D(t) = t^3 - 12t^2 + 36t, where D is distance in meters and t is time in seconds. Calculate the AROC from t = 1 to t = 5 and the IROC at t = 3.
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Calculate function values first for AROC and derive before substituting for IROC.
Question 6.
The height of a projectile is given by h(t) = -4.9t^2 + 20t + 5. Determine the AROC from t = 0 to t = 3 and the IROC at t = 2.
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Apply the same approach: compute heights, then find derivatives.

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