This quiz tests the work covered in Lecture 7 and corresponds to Section 2.1 of the
textbook Calculus: Single and Multivariable (Hughes-Hallett, Gleason, McCallum et
al.).

There is a web quiz at Wiley. It is the same quiz for each section of Chapter 2
and you should probably wait until the end of lecture 9 before you attempt
it.

Be aware that it doesn’t seem to accept the written answers so you will have to check
whether your answers are correct when they print the correct answer. Questions 11
and 12 were illegible on 14/11/05.

The Learning Hub (Mathematics) has a booklet on differentiation Introduction to
Differential Calculus which covers all of the topics for the next few lectures. In
particular, Chapter 1 of the booklet covers this topic.

The distance, $s\phantom{\rule{0.3em}{0ex}},$
a car has travelled from its starting point on a trip is shown in the table below as a function
of time, $t\phantom{\rule{0.3em}{0ex}},$
since the trip started.

$t$ (hours)

0

1

2

3

4

5

$s$ (km)

0

45

135

220

300

400

Which of the following is the average velocity between
$t=1$ and
$t=3\phantom{\rule{0.3em}{0ex}}?$
Exactly one option must be correct)

Choice (a) is incorrect

Try again, this is the average velocity
over the whole trip.

Choice (b) is incorrect

Try again, this is the average velocity between
$t=2$ and
$t=5\phantom{\rule{0.3em}{0ex}}.$

Choice (c) is correct!

Average velocity = $\frac{220-45}{2}=\frac{175}{2}=87.5$
km/hr.

Choice (d) is incorrect

Try again, this is the average velocity between
$t=2$ and
$t=3\phantom{\rule{0.3em}{0ex}}?$

In a time of $t$ seconds, a particle
moves a distance of $s$ metres
from its starting point, where $s=3{t}^{2}+4$. Which one of the following sets of statements is correct? Exactly
one option must be correct)

Choice (a) is correct!

The average velocity =$\frac{3{\left(1+h\right)}^{2}+4-7}{h}=\frac{3+6h+3{h}^{2}+4-7}{h}=3h+6$

Choice (b) is incorrect

Try again, you may not have expanded
$3{\left(1+h\right)}^{2}$ correctly.

Choice (c) is incorrect

Try again, you may not have expanded
$3{\left(1+h\right)}^{2}$ correctly.

Choice (d) is incorrect

Try again, you seem to have forgotten to substitute
$t=1$ into
the formula.

Consider the graph below

At which labelled points does the graph have negative slope? Exactly one
option must be correct)

Choice (a) is incorrect

Try again, B has zero slope which
we do not consider to be negative.

Choice (b) is incorrect

Try again, all of these
slopes are greater than, or equal to zero.

Choice (c) is correct!

The graph is decreasing as
$x$
increases at these points so the slope is negative.

Choice (d) is incorrect

Try again, these slopes are
all positive.

Using algebra which of the following evaluates the limit
$\underset{h\to 0}{lim}\frac{{\left(2+h\right)}^{3}-8}{h}\phantom{\rule{1em}{0ex}}$
correctly?
Exactly one option must be correct)

Choice (a) is incorrect

Try again, you seem to have expanded ${\left(2+h\right)}^{3}$
incorrectly.