Unit 2: Functions
Topic 2.10: Log-log & semi-log graphs (HL only) Questions
Practice 12 exam-style questions for IB Math AI SL Topic 2.10. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
11 mark
2026
Comparing two linearisations of the same data, you should pick the model whose R² is:
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2026
If log y vs x is a straight line (and log y vs log x is curved), the underlying model is:
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2026
A scientist measures a reaction rate k against temperature. log k vs 1/T is a straight line, gradient −2000 and intercept 5.
Given log k = (intercept) + (gradient)(1/T), find log k when T = 400 K, then k.
Given log k = (intercept) + (gradient)(1/T), find log k when T = 400 K, then k.
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2026
A power law y = a·xⁿ is plotted as log y against log x, giving a straight line of gradient 1.5 through the point (0, 0.9). Find a and n.
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2026
A semi-log line for y = a·bˣ has gradient 0.4771. The base b is:
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2026
A puppy's mass y (kg) at age x weeks is modelled. Semi-log (log y vs x) regression gives R² = 0.94; log-log (log y vs log x) gives R² = 0.998.
State, with reason, which model fits better and give its general form.
State, with reason, which model fits better and give its general form.
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2026
On a log-log graph of y = a·xⁿ the intercept (where log x = 0) equals 0.7. The value of a is:
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2026
Christmas-tree stock y (thousands) at distance d (km) follows a power law. Log-log regression of log y on log d gives gradient m = −0.8 and intercept b = 2.1.
(a) Write the power-law model y = a·dⁿ.
(b) Estimate y when d = 25.
(a) Write the power-law model y = a·dⁿ.
(b) Estimate y when d = 25.
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2026
Two consecutive points on a log-log graph of a power law y = a·xⁿ are (log x, log y) = (1, 2.4) and (2, 3.0). Find n and a.
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2026
An exponential model y = a·bˣ is linearised as log y against x: straight line, gradient 0.2, intercept 1.5. Find a and b and interpret b.
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