Practice Key Concepts Covered (1.2) - Rates of Change - IB 10 Mathematics – Group 5, Calculus

Practice: Key Concepts Covered

Lesson 1.2Rates of Change

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8 questions

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Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
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Quiz
2 questions · about 1 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
Calculate the average rate of change of $f(x) = 4x - 3$ from $x = 2$ to $x = 5$ .
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Use the AROC formula with $a = 2$ and $b = 5$.
Question 2.
What is the slope of the secant line for $f(x) = x^2$ from $x = 0$ to $x = 2$ ?
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Calculate using the AROC formula.
3Question 3.
What is the formula for average rate of change?
- $$\\frac{f(b) + f(a)}{b + a}$$
- $$\\frac{f(b) - f(a)}{b - a}$$
- $$f'(x)$$
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Think about how we derive the slope between two points.
4Question 4.
True or False: The tangent line gives us the average rate of change.
- True
- False
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Remember the difference between average and instantaneous.
Question 5.
A car travels a distance described by $d(t) = 4t^2 + 2t$ km in hours. Find the average speed from $t = 1$ to $t = 3$ .
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Use the AROC formula on distance.
Question 6.
Given the function $g(x) = x^3 - 3x^2 + 4$ , calculate the IROC at $x = 1$ and interpret its significance.
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Differentiate $g(x)$ then evaluate at $x = 1$.

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