Alice is a computer system that assists in the teaching of
some parts of University mathematics. Your comments and suggestions
will be very welcome; you can send them by email to Ken
Monks.
The basic idea is that you follow the obvious links from the
Alice login page, and
then Alice will present you with a list of questions. There is
detailed advice below on how to enter your
answers. You can then click the Mark button at the
bottom of the page to mark your work. The details of how this works
depend on whether Alice is running in
practice mode or
assessment mode.
If a test is set up in practice mode, it will say so in the test
selection menu, and also at the top of the test page. If so, you
can do the same set of questions repeatedly, and mark them by
clicking the Mark button at the bottom of the page. The
system will tell you whether your answers are right or wrong (except
for multiple choice questions) and may give some feedback about any
answers that are wrong, but it will not tell you the right answers.
You can click the Back button on your browser to get back to
the page where you filled in your answers, correct any mistakes, and
try again. Alternatively, you can go away and come back some other
time; Alice will remember your previous answers, so you can
correct any that were wrong, and leave the others as they are. The
system will give you a numerical mark for your work which you may
find informative, but it does not officially count for anything.
For more information about the marking system, see the section on
assessment mode.
If you want to see the solutions, you can click the Solutions
button at the bottom of the page instead of the Mark button.
If you try the test again after doing this, you will get slightly
different questions.
Assessment mode is used for formal testing, and also for some
practice tests that do not fit naturally in the framework of the
practice mode.
The questions will involve some randomly generated parameters, so
different students will get slightly different questions.
A test in assessment mode will usually have a "Due date"
listed in the test selection menu and at the top of the test page.
Before the due date, when you access the test you will be asked to
enter your answers. If you have tried the test before, your
previous answers will be filled in so that you can modify them if
you wish. When you have entered your answers, you should click the
Validate button at the bottom of the page to see how the
system will interpret it. If there are any syntax errors or the
system has misunderstood what you meant then you can fix the problem
before proceeding. When you are satisfied with your answers, you
can click the Mark button. Alice will tell you whether
your answers are right or wrong (except for multiple choice
questions) and may give some feedback about any answers that are
wrong, but it will not tell you the right answers.
Usually, no credit will be given for partially correct
answers. Instead, you are allowed to try again on any questions
that you got wrong. However, a penalty (usually 10%) is charged for
each incorrect attempt. For example, suppose a question is worth 5
marks and you get it wrong three times and then get it right on the
fourth attempt. You will be penalized 3 x 10% = 30%, so your score
is 70% of 5 marks, which is 3.5 marks. If you submit the same wrong
answer several times in a row, you will only be penalized once. You
will not be penalized if you leave the answer blank, or if you make
a syntax error rather than a mathematical error.
Thus, it would make sense to:
Do the first five questions, and then press the mark button.
Find that you have got Q1 and Q5 wrong
Try Q1 and re-mark it a couple more times, leaving your answer to Q5
unchanged
Then fix Q5 in the same way
Then go on to do the remaining questions.
If you access the test after the due date, then Alice will tell
you your marks and give the solutions to the questions.
Alice generally displays mathematics in a good approximation to
traditional notation. (Formulas are translated into HTML, so they
can be displayed in most browsers without any kind of plugin. This
does impose some limits on the quality of the display, however.) If
you see gibberish instead of mathematics, then you may have a font
encoding problem, which can be fixed by the steps explained in the
TtH
manual. This should only be necessary if you are using a
Macintosh, or using Netscape under Unix or Linux.
You may find that subscripts and superscripts are too small to read
easily. If so, you can just increase the font size in your
browser. If you are using Internet Explorer, click on View
at the top of the browser, then Text Size,
then Larger or Largest. For Netscape, click
Edit, then Preferences, then Appearance, then
Fonts, then change the variable width font size.
Apart from these font issues, there is one feature that may cause
confusion. An expression like 1/3 (x + y) always means
1
3
(x + y),
or equivalently (x + y)/3. Similarly, an expression like
1/2 Ö3 always means
You should type in your answers using the same syntax used in the
symbolic mathematics package Maple. This is broadly similar
to the syntax used for mathematical formulae in general programming
languages such as Java, C and Basic and in spreadsheet programs such
as Excel, so you will find it useful to master it. If you are
taking the Applied Mathematics Core course AMA101 then you will
learn to use Maple there. If you are not, the advice below should
be sufficient. Alice tries quite hard to give helpful information
about syntax errors. You can also learn about the right syntax by
doing tests in practice mode and asking for
the solutions; as well as displaying the right answers in ordinary
mathematical notation, Alice will tell you how they could be
entered. (However, there are often several possible ways, and Alice
will not always suggest the easiest one.)
When you have entered your answer, you can always click on the
Validate button at the bottom of the page to see how Maple will
interpret it. If there are any syntax errors or Maple has
misunderstood what you meant then you can fix the problem before
asking Alice to mark your work.
Numbers like 1/4 should be entered as
1/4, not as
0.25, which can cause some
subtle problems.
Use a star for multiplication: for example,
3x should be
entered as 3*x. Forgetting this
is by far the most
common source of syntax errors. Note that you do not need
a semicolon at the end, unlike when you are using Maple directly.
Use a caret (^) for raising something to a power: for example,
x2 should be entered as
x^2. You can get
a caret by holding down the SHIFT key and pressing the 6 key
on most keyboards. Negative or fractional powers need brackets:
enter x-2 as
x^(-2)
and x1/3 as
x^(1/3).
More generally, when in doubt, use brackets. For example,
a + b
c + d
should be entered as
(a+b)/(c+d).
Note that in this context you should always use ordinary round
bracket (like (a+b)), not
square or curly ones (like [a+b]
or {a+b}).
If you type
a+b/(c+d), then Alice
will think that you mean
a +
b
c + d
If you type (a+b)/c+d, then Alice
will think that you mean
a + b
c
+ d
If you type a+b/c+d, then Alice
will think that you mean
a +
b
c
+ d
Some other examples:
2a+b should be entered as
2^(a+b)
2 cos 3x should be entered as
2*cos(3*x)
eaxsin(bx) should be entered as
exp(a*x)*sin(b*x)
(a x2 + b x + c)-1
should be entered as
(a*x^2 + b*x + c)^(-1).
Maple is case-sensitive. Do not enter
X instead of
x, or
a instead of
A, or
Log(Z) instead of
log(z).
The absolute value of x, which is
written as |x| in traditional notation,
must be entered as abs(x).
Standard functions such as sin, cos, tan, exp, log and so on can
be entered using their usual names. However, the argument must
always be enclosed in brackets:
sin x should be entered as
sin(x),
ln 3 should be entered as
ln(3) and so on. You can use
either log(x) or
ln(x) for
the natural logarithm of x (note that both of these start with a
lower case l, not a capital I). The function
1/sin(x) must be
referred to as csc(x) rather
than cosec(x) (or you can just call
it 1/sin(x) if you prefer). You
should always write
exp(x) for
ex.
sin2x should be entered as
sin(x)^2 (which is
what it really means, after all). Similarly for
tan2(x),
sinh2(x) and so on.
Recall that sin-1(x)
traditionally means the number t such that
sin(t) = x, which is of
course completely different from the number
sin(x)-1 = 1/sin(x). This
traditional notation is really rather unfortunate and is not used
by Maple; instead, sin-1(x)
should be entered as arcsin(x).
Similarly, tan-1(x) should be
entered as arctan(x) and so on.
Greek letters can be entered using their English names: for
example, enter
a+b
as alpha+beta, and
2p
as 2*pi.
When you work directly with Maple, the vector (1,2,3) must be entered as
vector([1,2,3]). Many AIM
questions are set up so that you can just enter [1,2,3] instead.
When you work directly with Maple, the matrix
é ê
ë
1
2
3
4
5
6
ù ú
û
must be entered as
matrix([[1,2,3],[4,5,6]]).
Many AIM questions are set up so that you can just enter
[[1,2,3],[4,5,6]] instead.
Note that there are double square brackets at the beginning and
the end, and there is no comma after the 3 or the 6.
Sometimes, Alice will check the type of your answer (eg whether
it is a constant, a function of x, a vector, a matrix ...) before
working out whether it is correct. If your answer has the wrong
type Alice will allow you to go back and change it without any
penalty. Unfortunately, the warning messages for type errors are
not as comprehensible as they might be. Here are some examples that
illustrate how they work.
Suppose that the correct answer is x2 + y2,
but your answer is x2 + y2 + z2.
You might get the following message:
Your last answer was:
x2 + y2 + z2.
Wrong type.
Your answer should have type
polynom(constant,[x,y])
but it does not.
This means that your answer was supposed to be a polynomial
function of x and y, but in fact it depends on z as well. For
example, the expressions x2 + y and
(x2 + y2)/6 are polynomials in x and y, so
these answers would have the right type, although they are not of
course the right answer.
Suppose that the correct answer is 2 sin(3 x)
but your answer is just the number 5.
You might get the following message:
Your last answer was:
5
Wrong type.
Your answer should have type
dependent(x)
but it does not.
This means that your answer was supposed to depend on x.
Suppose that Alice asked you to calculate
sin(p/4) (for which the answer is of course
2-1/2). One cunning plan that might occur to you would
be to just enter sin(pi/4) as your
answer, leaving Maple to do all the real work. If this worked, it
would remove the whole point, so Alice prevents it. For each
question, there are certain "forbidden words" that you are
not allowed to use as part of your answer; in the example above, the
word "sin" would be forbidden. If you give an answer
involving a forbidden word, Alice will tell you, and you will be
able to go back and change it without any penalty.
You are doubtless intelligent enough to realize that there are
ways of cheating on the formal tests. Equally obviously, this will
not help you in the written exam, which carries much more weight.
