Free Printable Wk7 0B2 Review Session MCQs (Matrix Inverses and ODEs)

1.

An $n\times n$ matrix A is invertible if...

a)

a) When going through the Gaussian Elimination process to find an inverse of A you obtain a matrix on the left of an augmented matrix in REF with no zero rows.

b)

b) When going through the process to find an inverse of A you get a row of 1s on the left of an augmented matrix.

c)

c) If A represents the left-hand-side (LHS) of equations that has a unique solution.

2.

A differential equation can be (roughly) defined to be...

a)

a) an equation.

b)

b) an equation that involves derivatives.

c)

c) an equation with two variables.

d)

d) an integral.

3.

Suppose F(x,y) is a function in x and y. What do we mean by "a solution of a differential equation $\frac{\text{d}y}{\text{d}x}=F\left(x,y\right)$ "?

a)

a) Numbers for x and y that satisfy the equation.

b)

b) Another equation in x and y that satisfies the differential equation.

c)

c) A function y(x) such that, when it is substituted into $\frac{\text{d}y}{\text{d}x}=F\left(x,y\right)$ for y, satisfies the equation.

d)

d) A simplification of the differential equation.

4.

A solution of an ODE where all the constants have a specific values for the constants of integration is called a (a) solution.

5.

Is the following ODE directly integrable

$\frac{\text{d}^2y}{\text{d}x^2}=12x^2$ ?

a)

Yes

b)

No

6.

What is a separable ODE?

a)

a) An ODE that we can (re)write as $\frac{\text{d}x}{\text{d}y}=f\left(x\right)g\left(y\right)$ where $f\left(x\right)$ is a function of x only, and $g\left(y\right)$ is a function of y only.

b)

b) An ODE that we can (re)write as $\frac{\text{d}x}{\text{d}y}=f\left(x\right)g\left(y\right)$ where $f\left(x\right)$ is a function of x only.

c)

c) An ODE that we can (re)write as $\frac{\text{d}x}{\text{d}y}=f\left(x\right)g\left(y\right)$ where $g\left(y\right)$ is a function of y only.

d)

d) An ODE that we can (re)write as $\frac{\text{d}x}{\text{d}y}=\frac{f\left(x\right)}{g\left(y\right)}$ where $f\left(x\right)$ is a function of x only, and $g\left(y\right)$ is a function of y only.

7.

What do we mean by a linear (first order) ODE.

a)

a) A differential equation that can be written in the form y=mx+c, for some constants m and c.

b)

b) An ODE that can be written in the form $\frac{\text{d}y}{\text{d}x}=F\left(x,y\right)$ where F(x,y) is a linear function.

c)

c) An ODE that can be written in the form $\frac{\text{d}y}{\text{d}x}+P\left(x\right)y=Q\left(x\right)$ where P(x) and Q(x) are linear functions in x only.

d)

d) An ODE that can be written in the form $\frac{\text{d}y}{\text{d}x}+P\left(x\right)y=Q\left(x\right)$ where P(x) and Q(x) are functions in x only.

8.

What is an integrating factor of the ODE $\frac{dy}{dx}+\frac{y}{x-1}=x+1$ ?

a)

a) $e^{x-1}$

b)

b) x-1

c)

c) $\ln\left|x-1\right|$

d)

d) $x+1$

9.

What do we do with an integrating factor (IF) to solve an ODE?

a)

a) Multiply the LHS of the ODE by the IF.

b)

b) Multiply the RHS of the ODE by the IF.

c)

c) Multiply the both sides of the ODE by the IF.

d)

d) Multiply the IF by the ODE.

Wk7 0B2 Review Session MCQs (Matrix Inverses and ODEs)

Total questions: 9

Worksheet time: 9mins

Similar Resources on Wayground