ME-C1
Rates of Change
Solve related rates problems; model and interpret motion using calculus.
Sample questions
- 1.A spherical balloon is inflated so that its radius increases at 2 cm/s. Find the rate of increase of volume when r = 5 cm.
Exam weighting
3–5 marks.
Common student mistakes
- ·Forgetting the chain rule in related rates (dV/dt = dV/dr × dr/dt)
- ·Incorrect sign for displacement vs distance
ME-C2
Further Integration
Integrate using substitution and partial fractions; apply integration by parts.
Sample questions
- 1.Use the substitution u = x² + 1 to find ∫ x(x² + 1)⁴ dx.
- 2.Find ∫ x·eˣ dx using integration by parts.
Exam weighting
4–6 marks.
Common student mistakes
- ·Forgetting to adjust the differential when making a substitution (du = f'(x)dx)
- ·Incorrect partial fraction decomposition setup
ME-C3
Differential Equations
Solve separable differential equations; model logistic growth; interpret slope fields.
Sample questions
- 1.Solve dy/dx = y(1 − y) given y(0) = 0.25. Describe the long-term behaviour.
Exam weighting
3–5 marks.
Common student mistakes
- ·Not separating variables correctly before integrating
- ·Confusing logistic growth curve shape with exponential growth
Other Extension 1 topics
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