Unit 5: Calculus
Topic 5.14: Implicit & related rates (HL only) Questions
Practice 20 exam-style questions for IB Math AA SL Topic 5.14. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
11 mark
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d/dx(5y) where y is a function of x equals:
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A negative value of dh/dt for a draining tank means:
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The first step to differentiate x² + y² = 25 implicitly is to:
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The correct ORDER of steps for a related-rates problem is:
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At a stationary point f″(x) > 0. The point is a:
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Write down the derivative of with respect to .
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If dy/dt = dy/dx · dx/dt and dy/dx = 6, dx/dt = 2, then dy/dt =
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The stationary points of f are found by solving:
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A rectangle of fixed perimeter has maximum area when it is:
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Find the equation of the tangent to x² + y² = 10 at the point (1, 3).
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On a curve dy/dx = (x − 1)/(y + 2). A vertical tangent occurs where:
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An open box V = x(10 − 2x)² has domain:
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In a cone with r = h/3, V = (1/3)πr²h becomes, in terms of h:
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The curve x² − xy + y² = 3 passes through (1, −1). Find the gradient there.
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A square's side length increases at 0.2 cm s⁻¹. Find the rate its area increases when the side is 8 cm.
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Find the point on the line y = 2x + 1 closest to the origin. (Minimise the squared distance.)
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A rectangle has perimeter 40 cm. Find the dimensions giving the maximum area, and the maximum area.
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