Lesson 4.10h
4.10h Simple systems of linear first order differential equations Quiz: OCR Further Maths, Unit 1
20 questions
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Lesson 4.10h, Simple systems of linear first order differential equations: 20 multiple choice questions for the OCR Further Maths (H245), Unit 1: Pure Core (Y540, Y541), written with Revision Ninja.
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The 20 questions
-
How many coupled first-order differential equations form a standard two-variable linear system?
- One
- Two
- Three
- Four
-
What method converts two coupled first-order linear differential equations into one second-order equation?
- Separation of variables
- Variable elimination
- Integration by parts
- Partial fractions
-
What damping type occurs when the auxiliary equation of the reduced second-order DE has two distinct real roots?
- Underdamping
- Overdamping
- Critical damping
- Zero damping
-
What damping type occurs when the auxiliary equation of the reduced second-order DE has complex conjugate roots?
- Critical damping
- Underdamping
- Overdamping
- Infinite damping
-
What damping type occurs when the auxiliary equation of the reduced second-order DE has a repeated real root?
- Overdamping
- Undamped oscillation
- Underdamping
- Critical damping
-
In the system dx/dt = ax + by and dy/dt = cx + dy, what does x represent?
- Constant parameter
- Integrating factor
- Independent variable
- Dependent variable
-
In the coupled system dx/dt = 2x + 3y and dy/dt = x - y, what is t?
- Dependent variable
- Dummy variable
- Constant parameter
- Independent variable
-
If dx/dt = 3x and dy/dt = -2y, how are the variables x and y described?
- Non-linear
- Uncoupled
- Second-order
- Coupled
-
For dx/dt = y and dy/dt = -4x, what single second-order differential equation for x is formed?
- d²x/dt² - 4x = 0
- d²x/dt² + 4x = 0
- d²x/dt² - 4 = 0
- d²x/dt² + 4 = 0
-
For dx/dt = y and dy/dt = 2x + y, what is the auxiliary equation for x?
- m² + m + 2 = 0
- m² + 2m + 1 = 0
- m² - 2m - 1 = 0
- m² - m - 2 = 0
-
What popular ecological model uses a system of coupled first-order differential equations?
- Predator-prey model
- Newton-Raphson model
- Normal distribution
- Markov chain
-
What is the order of the coupled differential equation system dx/dt = 4x - y and dy/dt = 2x + y?
- Zero order
- First order
- Second order
- Third order
-
Eliminating y from dx/dt = x + y and dy/dt = 3x - y yields which second-order equation?
- d²x/dt² - 2x = 0
- d²x/dt² + 4x = 0
- d²x/dt² + 2x = 0
- d²x/dt² - 4x = 0
-
What general solution form arises when the reduced DE has a repeated real root k?
- A e^(kt) + B e^(-kt)
- A cos kt + B sin kt
- (A + Bt)e^(kt)
- A e^(kt) + B e^(2kt)
-
In continuous population modeling of two competing species, what do coupled differential equations track?
- Individual ages
- Geographic areas
- Genetic mutations
- Population sizes
-
If dx/dt = -3x + y and dy/dt = -3y, what is the repeated auxiliary root for x?
- 0
- -3
- 3
- -9
-
For the equation dx/dt = ax + by + f(t), what term describes f(t)?
- Eigenvalue
- Homogeneous term
- Integrating factor
- Non-homogeneous term
-
If f(t) = 0 and g(t) = 0 in a linear system, what is the system called?
- Non-homogeneous
- Singular
- Homogeneous
- Uncoupled
-
In a two-tank industrial mixing problem, what physical quantity do the dependent variables usually represent?
- Tank temperature
- Flow rate
- Mass of solute
- Liquid density
-
How many independent variables are present in a standard two-variable linear differential system?
- Zero
- Two
- One
- Three
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