Unit 2: Functions
Topic 2.5: Exponential and Sinusoidal Models Questions
Practice 20 exam-style questions for IB Math AI SL Topic 2.5. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
1find5 marks
A printing service charges $20 plus $0.15 per page.
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A gym membership costs M(t) = 35t + 90, where t is months and M is dollars.
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A quantity decays as Q(t) = 200 × (0.5)ᵗ. Find Q(4).
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A sinusoidal model has amplitude 4 and midline 3. State the maximum and minimum values.
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For y = a sin(bx), the amplitude is 6 and the period is 8. Find a and b (a > 0, b > 0).
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The number of users of an app is U(t) = 2000 × (1.4)ᵗ thousand, t in months. Find the number of users after 2 months.
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A sinusoidal model has period 6. Find the exact value of b.
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A projectile is launched from ground level. Its height (m) is h(t) = −5t² + 30t, where t is time in seconds. Find the time at which the projectile lands.
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The mass m of certain marbles is m = 5d³, where d is the diameter in cm and m is in grams. Find the mass of a marble with diameter 2 cm.
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A daily temperature model has maximum 28 °C and minimum 12 °C. Find the amplitude a and the midline d for a sinusoidal model y = a·sin(bt) + d.
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State the maximum and minimum values of g(x) = −4 sin(2x) + 9.
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Find the vertex of f(x) = 2x² − 8x + 5 and state whether it is a maximum or minimum.
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State whether the range of y = sin(x) is bounded or unbounded. Justify.
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For y = 6 cos(2x) − 3, write down the midline.
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A population grows as P(t) = 5000 × (1.03)ᵗ. State the annual percentage growth rate.
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For y = 4 sin(πx) + 1, write down the amplitude.
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State the range of f(x) = 7 sin(2x) − 1.
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A taxi charges a fixed fee of $3.50 plus $1.80 per kilometre.
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