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.
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A sinusoidal model has amplitude 4 and midline 3. State the maximum and minimum values.
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The graph of y = sin(x) is stretched vertically by a factor of 3, then shifted up by 2 units. State the new equation.
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State whether the range of y = sin(x) is bounded or unbounded. Justify.
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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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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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For y = 4 sin(πx) + 1, write down the amplitude.
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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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A sinusoidal model has period 6. Find the exact value of b.
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The maximum value of a sinusoidal model is 11 and the minimum is 3. Find the amplitude and the midline.
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For y = 3 sin(x) + 5, state the maximum and minimum values.
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State the range of f(x) = 7 sin(2x) − 1.
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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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State the maximum and minimum values of g(x) = −4 sin(2x) + 9.
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The period of f(x) = a sin(bx) + d is 12 seconds. The model completes one full cycle every 12 seconds. Find the frequency (cycles per second).
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For y = 2 sin(πx) + 6, find the y-value when x = 0.5.
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For y = 6 cos(2x) − 3, write down the midline.
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