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Trigonometric modelling - MYP Questionbank | RevisionDojo

Practice Trigonometric modelling with authentic MYP MYP Extended Mathematics exam questions for both SL and HL students. This question bank mirrors Paper 1, 2, 3 structure, covering key topics like core principles, advanced applications, and practical problem-solving. Get instant solutions, detailed explanations, and build exam confidence with questions in the style of MYP examiners.

Type

Difficulty

Question 1

Fill in the Blank: A Ferris wheel completes one full rotation every 90 seconds. To model the height in degrees using $h(t) = A\cos(Bt) + D$ where $t$ is in seconds, the value of the parameter $B$ is ________.

Question 2

The tide in a harbor reaches a maximum height of $5\text{ m}$ at $t = 0$ hours and a minimum height of $1\text{ m}$ at $t = 6$ hours. Which of the following equations best models the height $h(t)$ for $t \ge 0$ ?

Question 3

Which of the following functions represents the graph of $y = \sin x$ after it has been translated 5 units up and then stretched vertically by a factor of 2?

Question 4

An object's vertical position is modeled by the function

y = 10\sin\left(\frac{\pi}{4}(t - C)\right) + 20

where $t$ is time in seconds. If the object is at its midline (principal axis) and moving upward at $t = 1$ , find the smallest non-negative value for the phase shift $C$ .

Question 5

True or False: The sinusoidal function $y = \sin(2x - 10)$ has a phase shift of 10 units to the right relative to $y = \sin(2x)$ .

Question 6

A researcher models daylight hours using a sine function. If the longest day has $16$ hours of light and the shortest has $8$ hours, what is the value of the vertical shift $D$ in the model?

Question 7

The height of the tide in a harbor follows a periodic pattern that repeats every 12 hours. If the model is written in the form $h(t) = A \sin(B(t - C)) + D$ , where $t$ is measured in hours, what is the value of the parameter $B$ in radians?

Question 8

A sinusoidal model $y = A\sin(Bt) + D$ starts at its midline value of $10$ at $t = 0$ . It reaches its first maximum value of $14$ at $t = 1$ . Determine the values of $A$ and $B$ (in radians).

Question 9

Identify the phase shift and direction of the function $y = \cos(3x + \pi)$ relative to the parent function $y = \cos(3x)$ .

Question 10

A periodic function $f(x)$ has a range of $[-12, 2]$ . What is the equation of the principal axis for this sinusoidal model?

Type

Difficulty

Question 1

Question 2

Question 3

Which of the following functions represents the graph of $y = \sin x$ after it has been translated 5 units up and then stretched vertically by a factor of 2?

Question 4

An object's vertical position is modeled by the function

y = 10\sin\left(\frac{\pi}{4}(t - C)\right) + 20

where $t$ is time in seconds. If the object is at its midline (principal axis) and moving upward at $t = 1$ , find the smallest non-negative value for the phase shift $C$ .

Question 5

True or False: The sinusoidal function $y = \sin(2x - 10)$ has a phase shift of 10 units to the right relative to $y = \sin(2x)$ .

Question 6

A researcher models daylight hours using a sine function. If the longest day has $16$ hours of light and the shortest has $8$ hours, what is the value of the vertical shift $D$ in the model?

Question 7

Question 8

A sinusoidal model $y = A\sin(Bt) + D$ starts at its midline value of $10$ at $t = 0$ . It reaches its first maximum value of $14$ at $t = 1$ . Determine the values of $A$ and $B$ (in radians).

Question 9

Identify the phase shift and direction of the function $y = \cos(3x + \pi)$ relative to the parent function $y = \cos(3x)$ .

Question 10

A periodic function $f(x)$ has a range of $[-12, 2]$ . What is the equation of the principal axis for this sinusoidal model?

Type

Difficulty

Question 1

Question 2

Question 3

Which of the following functions represents the graph of $y = \sin x$ after it has been translated 5 units up and then stretched vertically by a factor of 2?

Question 4

An object's vertical position is modeled by the function

y = 10\sin\left(\frac{\pi}{4}(t - C)\right) + 20

where $t$ is time in seconds. If the object is at its midline (principal axis) and moving upward at $t = 1$ , find the smallest non-negative value for the phase shift $C$ .

Question 5

True or False: The sinusoidal function $y = \sin(2x - 10)$ has a phase shift of 10 units to the right relative to $y = \sin(2x)$ .

Question 6

A researcher models daylight hours using a sine function. If the longest day has $16$ hours of light and the shortest has $8$ hours, what is the value of the vertical shift $D$ in the model?

Question 7

Question 8

A sinusoidal model $y = A\sin(Bt) + D$ starts at its midline value of $10$ at $t = 0$ . It reaches its first maximum value of $14$ at $t = 1$ . Determine the values of $A$ and $B$ (in radians).

Question 9

Identify the phase shift and direction of the function $y = \cos(3x + \pi)$ relative to the parent function $y = \cos(3x)$ .

Question 10

A periodic function $f(x)$ has a range of $[-12, 2]$ . What is the equation of the principal axis for this sinusoidal model?

Trigonometric modelling Questionbank