Lesson 1.07t
1.07t Differential equations Quiz: OCR Maths, Unit 7
20 questions
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Lesson 1.07t, Differential equations: 20 multiple choice questions for the OCR Maths (H240), Unit 7: Differentiation, written with Revision Ninja.
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The 20 questions
-
In the differential equation dy/dt = ky, what is the rate of change of y proportional to?
- t
- t^2
- y
- k
-
Which equation models a population P growing at a rate proportional to P?
- dP/dt = k
- dP/dt = k/P
- dP/dt = kP
- P = kt
-
Which is the definition of acceleration a in terms of velocity v?
- a = ds/dt
- a = v/t
- a = d^2v/dt^2
- a = dv/dt
-
A tank of depth h drains at a rate proportional to h. Which equation models this?
- dh/dt = -k h
- dh/dt = -k
- dh/dt = k h
- h = -k t
-
A population grows at a rate of 4% of its size per year. Which equation models this?
- dP/dt = 0.4P
- P = 0.04t
- dP/dt = 0.04
- dP/dt = 0.04P
-
Newton's law of cooling for temperature T above ambient T0 is:
- dT/dt = k(T - T0)
- dT/dt = -k(T - T0)
- dT/dt = -k T0
- dT/dt = -kT
-
The price p rises at a rate proportional to excess demand, given by 100 - 2p. Which equation models this?
- dt/dp = k(100 - 2p)
- dp/dt = k(100 - 2p)
- p = k(100 - 2t)
- dp/dt = 100k - 2p^2
-
A body moving through resistance has deceleration proportional to velocity. Which equation models it?
- dv/dt = -k
- dv/dt = -kv
- v = -kt
- dv/dt = kv
-
Which function satisfies dy/dt = 3y with y(0) = 5?
- 15t
- 5 + 3t
- 5e^(3t)
- 3e^(5t)
-
A curve has dy/dx = 2x and passes through (1, 4). What is y?
- y = x^2 + 3
- y = x^2 + 4
- y = 2x^2 + 2
- y = 2x + 2
-
In the model dP/dt = kP - H, what does the constant term H represent?
- Proportional growth rate
- Constant removal rate
- Carrying capacity
- Initial population
-
For dv/dt = g - kv, what is the terminal velocity?
- k/g
- g - k
- g/k
- gk
-
A price p falls at a rate proportional to p. Which equation models this?
- dp/dt = -k
- dp/dt = -kp
- p = -kt
- dp/dt = kp
-
In the rate equation dh/dt = -0.5 sqrt(h), what does the negative sign indicate?
- h is negative
- h is increasing
- h is decreasing
- h is constant
-
For dp/dt = k(100 - 2p), what is the equilibrium price?
- p = 100
- p = 25
- p = 2
- p = 50
-
Which is the order of the differential equation dy/dt = ky?
- First order
- Second order
- Third order
- Zero order
-
What term describes a differential equation model where growth slows as population approaches a limit?
- Linear model
- Exponential model
- Polynomial model
- Logistic model
-
If dy/dt = 2y and y(0) = 1, what is y when t = ln 2 / 2?
- 4
- 2
- 1
- e
-
Which equation models money A growing at 3% per year?
- A = 0.03t
- dA/dt = 0.03A
- dA/dt = 0.3A
- dA/dt = 0.03
-
Which equation models simple harmonic motion with acceleration -4x?
- d^2x/dt^2 = 4x
- dx/dt = -4x
- d^2x/dt^2 = -4
- d^2x/dt^2 = -4x
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