Here are a few questions I encountered on an Invitation UIL test. I don't know if these are A Level or not, but here they are:
(62) [ sqrt(5) ]
I don't know what the square brackets mean. Does anybody have an Idea? I don't have the answer for this one.
(24) The product of the prime factors of 84 is _____-
I put 84, because 84 = 2 * 2 * 3 * 7. Do you know if this is the case or do they only want you to count each factor once?
(34) How many proper subsets does a 4-element set have?
Proper subset, I think, means all subsets except the set itself. Is there a formula for number of subsets? because if there is, obviously you could just make it f(n) - 1.
Thanks,
Vinay
P.S. If this thread gets shut down because of new problems, you can e-mail me at vvr1590@hotmail.com to discuss these.
I did alright at the invitational. I got first place in the 9th and 10th grade division, but if they put all the high school grades together, I would've placed second.
At every invitational I've been to, the contestants have been grouped: 9th and 10th, 11th and 12th.
Sorry I have been super busy and have had no time to even look at this site. I think the answer to the first questions is 2. Usually the brackets mean the smallest whole number less than the value in brackets.
Ex[1] [sqrt(5)] = 2 becasue the sqrt (5) is 2.something so the answer is 2.
Ex[3] [-3.14] = -4 because it is the smallest whole number less than -3.
You might want to check to make sure. What was the answer on that problem. Try to always give answers because it makes my job that much easier.
Yes I went to Lufkin High School (actually the old campus - now they have a relatively new school) so I am very familiar with Nacogdoches, which is just over 20 miles away from Lufkin. Good to hear that East Texas has a strong candidate this year so good luck to you.
I moved into Texas in the 10th grade & didn't know anything about Number Sense. My math teacher asked me to take a Number sense test one day & I scored something like a 21 (or was it a -21). I actually should have been scored much lower because I actually left red eraser marks on the test from where I had erased some of my "carry" marks! Ha!
Looking back I'm not surprised either at the score - it seems to me that people who are smart or think they are fast in math really don't develop a number "sense" on their own that lets them compete very well on these types of tests without learning the tricks.
[n] means the greatest integer less than or equal to n. In the case of 62[sqrt 5], the greatest integer less than or equal to the square root of 5 is 2 since the square root of 5 is approximatley 2.2.
When they ask for the product of the prime factors of 84, you need to keep in mind that the prime factors of 84 are 2, 3 and 7, therefore 2(3)(7) is 42.
An n-element set has 2 to the n power number of subsets. The proper subsets are the subsets of the set, excluding the set itself. For example : A 4-element set has 2 to the 4 power subsets or 16 subsets. This set has 15 proper subsets.
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