(01/10/96)
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MathMagic Cycle 22: Level 7-9 Regular
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GEOMETRIC PROBABILITY
Geometric probability is the study of probability in which the
possibilities are based on areas of geometric figures. For example.
Draw a square ABCD with AB=4. Connect BD. Shade Triangle BCD. A
dart is thrown and hits the interior of the square. The
probability that it hits the shaded region = Area of SHADED
divided by Area of TOTAL REGION. So, the probability = 8/16 = 1/2 =
0.5
Use this concept to find the following probabilities that a
dart which falls at random on the given geometric figure, will
fall in the shaded region described.
1) Rectangle ABCD. Draw the diagonals and label the intersection E.
Shade triangle DEC.
2) Two concentric circles with radii 2 and 3 respectively. Shade
inside the large circle but outside the small one.
3) A circle of radius 6 with a circle inside it whose diameter is
the radius of the first circle. Shade inside the large but outside
the small.
4) Inscribe a square in a circle of diameter 6. Shade the area inside
the circle but outside the square. (HINT: to find the area of the
square, remember that a square is also a rhombus.)
5) Now draw a scalene triangle. Describe how to divide and shade
it so that the probability of hitting the shaded region is 1/2.
6) If a dart is dropped on a map of the world, what is the probability
it will land on:
A) water
B) the United States
C) Your State or Country
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MathMagic Cycle 22: Level 7-9 Advanced
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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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Good luck
MrH