Nassau County Interscholastic Mathematics League : Team
4:24 PM
Muhammad Yusuf
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1. If x % of x is
2.25, and x > 0, find x.
2. Find the sum of the
three smallest composite numbers that have no prime factor less than 10.
3. The product of n distinct
integers is 18. Find the maximum value of n.
4. Points A and D are
on opposite sides of BC, AB ⊥
BC,
and CD ⊥
BC,
AB = 9, BC = 21, and CD = 11. Find AD.
5. One of the roots of
x2 + Bx + C = 0, where B and C are integers, is √2 + 1. Find|B + C|.
6. In triangle ABC, AB
= 5, BC = 6, and AC = 7. Point O is outside the triangle and in the interior of
angle A. A circle with center O is tangent to side BC at Q, and to sides AB and
AC extended at P and R, respectively. Find BQ.
7. The polynomial P(x)
has degree 3 and leading coefficient 1. If P(1) = 1, P(2) = 2, and P(3) = 3,
find P(4).
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