Module 9 Module Quiz Extension 1

Module 9 Quiz

15 multiple choice questions covering area, volumes, differential equations, direction fields and modelling applications.

Q11 MARK

The area between $y = f(x)$ and $y = g(x)$ from $x = a$ to $x = b$ is found by integrating:

Aupper function minus lower function Blower function minus upper function only Cthe product $f(x)g(x)$ Dthe derivative of $f(x)$ only

Q21 MARK

When finding area with respect to the y-axis, the integral is usually written in terms of:

A$dx$ with $x$-functions only B$dy$ with right curve minus left curve C$dt$ only Darc length

Q31 MARK

The disk method for rotating $y = f(x)$ about the x-axis uses:

A$\pi \int f(x)\, dx$ B$2\pi \int f(x)\, dx$ C$\pi \int [f(x)]^2\, dx$ D$\int \sqrt{1 + f'(x)^2}\, dx$

Q41 MARK

The washer method subtracts:

Ainner radius squared from outer radius squared Bouter radius from inner radius Carea from volume Ddy from dx

Q51 MARK

A differential equation relates a function to:

Aonly its x-intercepts Bone or more of its derivatives Cits graph colour Dits denominator only

Q61 MARK

A direction field represents:

Athe roots of a polynomial Bthe area under a graph Clocal slopes from a differential equation Donly maximum points

Q71 MARK

Solving $dy/dx = f(x)$ generally requires:

Aintegrating $f(x)$ with respect to $x$ Bintegrating y with respect to y only Cusing combinations Dfinding a dot product

Q81 MARK

A separable differential equation can be rearranged so that:

Aall constants disappear B$x$ and $y$ terms are separated onto opposite sides Cthere are no integrals Dthe derivative becomes zero

Q91 MARK

The differential equation $dP/dt = kP$ models:

Alinear decrease only Bconstant acceleration Cexponential growth or decay Dcircular permutations

Q101 MARK

Newton's law of cooling commonly has the form:

A$dT/dt = kT^2$ B$T = kt + A$ only C$dT/dt = A/T$ D$dT/dt = -k(T - A)$

Q111 MARK

In a logistic model $dP/dt = kP(1 - P/M)$, the value $M$ represents:

Ainitial gradient Bcarrying capacity Ctime period Darea between curves

Q121 MARK

A mixing problem usually tracks:

Aangle between vectors Bcoefficient of $x^3$ Camount of solute in a tank Dsector area

Q131 MARK

For a volume of revolution about the y-axis, it may be useful to express:

A$x$ as a function of $y$ Bonly $y$ as a function of $x$ Cthe derivative as zero Dthe answer in degrees

Q141 MARK

Before integrating area between curves, intersection points are used to find:

Athe axis of rotation only Bthe carrying capacity Cthe slope field Dthe integration limits

Q151 MARK

A model solution to a differential equation with an initial condition should:

Aleave the arbitrary constant unknown Bignore units Calways be linear Duse the initial condition to determine the constant