I agree with Bill in USMA 18575 that the first question is too difficult
for Grade 11 and the second question is trivial.
If one knows the formula for the sum of of an infinite number of terms of a
convergent geometric sequence, the result is simple. It is
0.4/(1 - 0.75) = 1.6
>That's an inteeresting pair of questions from Yvonne. My reaction is that
>the first question is too difficult and the second is too easy for 11th
>graders.
>
>The problem with the first question (reprinted at the end below) is that, I
>don't think 11th graders (or many adults) would understand how to handle an
>equilibrium situation when the question is given in such a way that the
>reader is led to think about calculating from the beginning. At the
>beginiining the amount is zero an this is long before before equilibrium is
>established. If one does that (easy with a simple spread sheet routine) one
>finds that it takes 85 days before equilibrium is established to 10 decimal
>places. (Amount in blood is 1.6 on the 85th day and all subsequent days,
>but was only 1.599 999 9999 g on the 84th day.) If one is satisfied with
>three decimal place accuracy, it still takes 29 days to reach equilibrium.
>(The amount is 1.6 g on the 29th day and all following days, but was only
>1.599 g on the 28th day.)
>
>Even on the 29th day, the final value of 1.6 is approximate and not exact.
>It is equal to 1.6 ONLY if rounded off to three decimal places. I don't
>think most 11th graders are comfortable with giving answers that they know
>aren't exact. (Maybe they should be!) The more exact figure
>for 28 days is 1.599 492 0332 g and
>for 29 days is 1.599 619 0249 g.
>The answer of EXACTLY 1.6 g is mathematically correct ONLY in the limit as
>the number of days approaches infinity. Do we expect 11th graders to
>understand the concept of limits? That's a concept that is often not learned
>until a calculus course in college.
>
>One could also find fault with the question's use of the word
>"concentration" when it must be asking for the AMOUNT of the drug in the
>system, not Its concentration (in grams per litre ot something). But I won't
>quibble.
>
>The second question is poor because it is too easy. The equation is given
>as:
>H = 44 - 5.5t
>and the student is asked to find the answer when t = 0. That's trivially
>simple.
>
>Regards,
>Bill Hooper
>=========
>
>Questions from Yvonne were:
>
>>> 1) A medical prescription requires a patient to take 0.4 grams of
>>> a drug at the same time each day. After 24 hours, 75 percent
>>> of the drug remains in the patient's system.
>>> What is the maximum concentration level of the drug as it stabilizes
>>> in the patient's system?
>>>
>>> The published answer: 1.6 grams
>>>
>>> 2) A bathtub is full of water and is later drained. The
>>> height (in centimeters), H, of water remaining in the bathtub
>>> after time, t, can be presented by the function H (t) = 44 - 5.5t.
>>> What was the height of the water before the drain was opened?
>>>
>>> The published answer: 44 cm
>>>
>>> I would like to invite comments from this group as to whether or not this
>>> test
>>> is to difficult for an 11th grader?
>>>
>>> Thank you, Yvonne Halpaus
Joseph B.Reid
17 Glebe Road West
Toronto M5P 1C8 TEL. 416-486-6071
