(01/10/96)
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MathMagic Cycle 22: Level 10-12 Regular
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PRIMO MATHEMATICS
1) Can you find 2 prime numbers whose sum is prime?
2) Can you find 2 prime numbers whose product is prime?
3) What is the smallest positive number divisible by 1, 2, 3, 4, 5,
and 6.
4) What is the smallest non-negative number divisible by
1, 2, 3, 4, 5, and 6.
5) What is the smallest number divisible by 1, 2, 3, 4, 5, and 6.
6) The numbers 24, 25, 26, 27, 28 is a string of 5 consecutive
composite numbers. Can you find another string of five consecutive
composite numbers less than 100.
7) What is the longest string of consecutive composites less than
200.
8) Twin primes are 2 primes that differ by 2. List all twin primes
less than 30.
9)A Mersenne prime is any prime number of the form 2^p - 1, where
p is prime. Find 3 mersenne primes. Is 199 a mersenne prime?
Is 63 a mersenne prime?
10)If a prime is mersenne, then it can be used to produce a perfect
number. A perfect number is any whole number whose sum of proper
divisors is equal to the number itself. If 2^p - 1 is prime then
(2^p - 1)(2^(p-1)) is a perfect number. Find at least 3 perfect
numbers and check.
11) Find the sum of the reciprocals of ALL the divisors of each
perfect number in #10. What do you notice?
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MathMagic Cycle 22: Level 10-12 Advanced
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STATISTICALLY SPEAKING...
1) Find 3 numbers whose mode is 8 and mean is 10. What is the median
of these 3 numbers?
2) Find the mean median and mode
X Value | 2 3 4 5
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Frequency | 4 2 5 1
.
2) Find the mean median and mode
X Value | 2 3 4 5
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Frequency | 40 20 50 10
.
3) Based on your results, what can you determine regarding the mean
median and mode for the distributions above?
4) If the distribution continues proportionally as above, what is
the frequency distribution for n=180 observations?
5) A probability mass function expresses the frequency of each
observation as a probability rather than a frequency. Write the
probability mass function. Assume that only 2, 3, 4, and 5 are
possible.
6) Use your PMF in #5 to find each probability:
A) x<4
B) x>4
C) x=4
D) x is even
E) Which is more likely: x is even or x is odd.
F) The odds of an occurrence = probability it occurs divided by
probability it does not occur.
Find the odds of "x is 3."
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Good luck
MrH