Unit 5: Calculus
Topic 5.15: Slope fields (HL only) Questions
Practice 12 exam-style questions for IB Math AI SL Topic 5.15. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
11 mark
2026
A solution curve of dy/dx = f(x, y) is decreasing exactly where:
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2026
A population model gives dy/dx = 0.1y − x, where y is the population (thousands) and x is the time (years). Find the gradient of the slope field at the point (3, 50).
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2026
For the slope field dy/dx = 2x − y, the gradient of the segment at (3, 1) is:
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2026
The flat (horizontal) segments of dy/dx = f(x, y) occur where:
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Unlock Question5Sketch1 mark
2026
Sketch the slope field's line segments along the line .
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2026
For dy/dx = x + y, find the equation of the isocline along which every segment has gradient 2.
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2026
To sketch a solution curve of dy/dx = f(x, y) through a given point, you should:
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An isocline of a slope field is a curve along which:
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2026
For the slope field dy/dx = x − 2y, find the equation of the curve on which all segments are flat (horizontal), and state what such points mean for a solution curve.
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2026
A chemical concentration follows dy/dx = 4 − y (y in mg/L, x in hours). The equilibrium is where the segments are flat. Find the equilibrium concentration and the gradient at (0, 1).
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2026
A spread-of-rumour model gives dy/dx = 0.3y(1 − y), where y is the fraction of people who know (0 ≤ y ≤ 1) and x is the time (days). Find the two lines on which all segments are flat, and say what they represent.
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Unlock Question12Describe4 marks
2026
A solution curve of dy/dx = x − y passes through (0, 3). Determine whether it is initially increasing or decreasing, and describe what happens as it approaches the line y = x.
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