Help with AIM system

• Overview
• How do I enter my answers?
• Penalty for wrong answers
• Minimum number of answers
• Maximum number of attempts
• Hints and subquestions
• Types
• Multiple Response questions
• Forbidden words

Overview

The basic idea is that you follow the obvious links from the AIM home page, and then the system will present you with a list of questions. There is detailed advice below on how to enter your answers. Once you give your answers, you can then click the Validate button at the bottom of the page to mark your work.

Most tests have a "Due date" listed in the test selection menu and at the top of the test page. In this case you must get them done before the due date; thereafter your answers will not be recorded. After the due date the system will tell you your marks and give the solutions to the questions.

The questions are randomly generated, so different students will get different questions.

How do I enter my answers?

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 the system to mark your work.

• Use a star for multiplication: for example, 3x should be entered as 3*x. Forgetting this is probably 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.

 
• When in doubt, use brackets. For example,

a + b c + d

should be entered as (a+b)/(c+d). If you type a+b/(c+d), then the computer will think that you mean

a + b c + d

If you type (a+b)/c+d, then the computer will think that you mean

a + b c + d

If you type a+b/c+d, then the computer will think that you mean

a + b c + d

Some other examples:
• 2^a+b should be entered as 2^(a+b)
• 2 cos 3x should be entered as 2*cos(3*x)
• e^axsin(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).
• 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) and so on. You can use either log(x) or ln(x) for the natural logarithm of x. 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 e^x.

 
• 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.

 
• Vectors can be entered simply as a Maple list. For example, enter the vector (1,2,3) as [1,2,3].
• Matrices can be entered using Maple's "matrix" command. For example, enter

    [ 1  2  3 ]
    [         ]
    [ 4  5  6 ]

as matrix([[1,2,3],[4,5,6]]) or matrix(2,3,[1,2,3,4,5,6]). Sometimes you will be given the form of a matrix; in this case you can just fill in its entries.
• Sets can be entered with curly brackets: {}. For example enter

                              [1    0]  [1    0]  [0    1]
                             {[      ], [      ], [      ]}
                              [0    1]  [1    0]  [0    1]

as {matrix([[1,0],[0,1]]), matrix([[1,0],[1,0]]), matrix([[0,1],[0,1]])}.

Penalty for wrong answers

You will not be penalized for syntax errors or type mismatches. Also, the penalty system keeps track of your answers: even if you have entered the same wrong answer twice you will be penalized only once.

Minimum number of answers

Maximum number of attempts

Hints and subquestions

 

Before viewing the hint	After viewing the hint
Evaluate the following integral     /   |   |  exp(-x) sin(2 x) dx   |  / at a point x= p /2. Answer:  Click here:  for a hint. Penalty=20%, value=0% of question value.	Evaluate the following integral    /  |  |  exp(-x) sin(2 x) dx  | / at a point x= p /2. Answer:  Hint (Penalty=20%, value=0% of question) Use integration by parts.

Each hint has a value and a penalty associated to it, as a percentage of the question value. For the above example the penalty is 20% and the value is zero. This means that if you gave a correct answer without viewing the hint, you would get 100% for this question, but if you viewed the hint, then you would be able to obtain a maximum of 80%.

If you expand a hint whose value is non-zero, then such hint will ask you a question which you will have to answer. The value of such a subquestion is expressed as the percentange of the value of the question itself. For example:

Before viewing the hint	After viewing the hint
Find a derivative of               2             x  sin(x) at a point x= p /2. Answer:  Click here:  for a hint. Penalty=10%, value=50% of question value.	Find a derivative of               2             x  sin(x) at a point x= p /2. Answer:  Hint (Penalty=10%, value=50% of question) Find the derivative of          2         x  sin(x) Answer:

For this example:

If you give a correct answer without viewing the hint, you would get 100% for this question.

If you view the hint and then give a correct answer to both the question and its hint (as done above), you would get 90%.

If you view the hint, then answer the hint correctly and the question incorrectly, you would get (0+0.5)/(1+0.5)*90% = 30%.

If you view the hint, then answer the hint incorrectly and the question correctly, you would get (1+0)/(1+0.5)*90% = 60%.

Subquestions may contain further subhints or questions, in which case this grading scheme is applied recursively.

Penalties are additive: for example if you use one wrong trial and one hint with penalty 10% before correctly answering the question, you would get 100-10-15 = 75%.

Types

Suppose that the correct answer is the matrix

    [ 1 2 ]
    [     ]
    [ 3 4 ]

but you enter the number 7 as your answer. You will get the following message:
Your answer has the following error:
Wrong type. Your answer was
7
It should be of type matrix but it is not.
Try again.
This means that your answer was a matrix, but in fact it is just a single constant.
• Suppose that the correct answer is x² + y², but your answer is x² + y² + z². You might get the following message:

Your answer has the following error:
Wrong type. Your answer was
x^2 + y^2 + z^2
It should be of type polynom(constant,[x,y]) but it is not.
Try again.
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 te following message:

Your answer has the following error:
Wrong type. Your answer was
5
It should be of type dependent(x) but it is not. Try again.
This means that your answer was supposed to depend on x.

Multiple response questions

 
Consider the following matrix:

                               [cos( q  )    -sin( q  )]
                           A = [                   ]
                               [sin( q  )    cos( q  ) ]

Which of the following properties does this matrix posess?

symmetric
anti-symmetric
orthogonal
singular
non-singular

 

where Rs is the number of right choices and Rs (Ws) is the number of right (wrong) choices that the student had selected. For the above question, the right answer is "orthogonal" and "non-singular". If you answer "orthogonal", "non-singular" and "anti-symmetric" then you would get only 50%. You will usually get a penalty of 15% for each answer which is not 100% correct. Since there are 2ⁿ possible answers for a multiple response question, guessing is not to your advantage.

Forbidden words