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Math Test 2012

8:17 AM

Muhammad Yusuf , Posted in Math Competitions , 0 Comments

1. A natural number is a palindrome if its digits read the same from left to right as they do from right to left. For example, 3521253 is a palindrome. How many 3digit numbers are palindromes that are divisible by 11?

(A) none of them are divisible by 11

(B) 4

(C) 8

(D) 22

(E) 90

2. Triangle ABC has area 12. If side AB has length 6 and side BC has length 5, what must be the length of side AC?

(A) 5

(B) √37

(C) √97

(D) √109

(E) More than one answer is possible with the given information.

3. A club with 15 members must choose a delegation of 4 members to serve at a convention. Team members Jacob and Sarah refuse to serve on a delegation together. How many delegations are possible?

(A) 130

(B) 143

(C) 156

(D) 169

(E) None of the above

4. If

then

(A) 64

(B) 27

(C) 8

(D)127/64

(E) 1

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C of C Math Marathon 2012

8:08 AM

Muhammad Yusuf , Posted in Math Competitions , 0 Comments

1. Express 2012 as a difference of two integer squares.

2. Each account on a social networking website has a Personal Identification Number, which is required to be a string of eight decimal digits not containing two consecutive digits that are both odd. So for example 31415926 is not an acceptable PIN but 02252012 is an acceptable PIN. Find the number of acceptable PINs.

3. What is the smallest number of integer squares whose sum is 2012?

4. At a small party there are fifteen door prizes, each of which is randomly given to one of the five guests. What is the probability that each of the five guests receives at least one door prize?

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Nassau County Interscholastic Mathematics League : Team

4:24 PM

Muhammad Yusuf , Posted in Math Competitions , 0 Comments

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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Math Contest : Nassau County Interscholastic Mathematics League (3)

4:16 PM

Muhammad Yusuf , Posted in Math Competitions , 0 Comments

5. Chauncey goes up a flight of 8 stairs. With each step, he goes up either one or two stairs. Find the number of different sequences of steps he can take to the top.

Note that leaping one stair and then two stairs is different from leaping two stairs and then one stair.

6. In convex quadrilateral ABCD, diagonal AC is perpendicular to diagonal BD, AB = 10, BC = 5, and CD = 11. Find AD.

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Math Contest : Nassau County Interscholastic Mathematics League

4:14 PM

Muhammad Yusuf , Posted in Math Competitions , 0 Comments

3. Find the sum of the coefficients in the expansion of (3x – 1)⁴

4. Point A is on a circle whose center is O, AB is tangent to the circle, AB = 6, D is inside the circle, OD = 2, DB intersects the circle at C, and BC = DC = 3. If r is the length of the radius of the circle, find r².

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Nassau County Interscholastic Mathematics League : Contest 1 - 2010/2011

4:11 PM

Muhammad Yusuf , Posted in Math Competitions , 0 Comments

1. Compute 19.27² + 11.73² + (38.54)(11.73).

2. Point A is outside a circle and AB and AC are tangent to the circle at B and C, respectively. Points P and R are on AB and BC, respectively, PR is tangent to the circle at Q, and AB = 20. Find the perimeter of triangle APR.

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ABACUS - JANUARY 2012 : LEVEL 7 - 8

9:11 AM

Muhammad Yusuf , Posted in Math Competitions , 0 Comments

PROBLEM 1. The ages of a father and his two different-aged sons are the powers of the same prime number. Last year everybody's age was a prime number. How old are they now?

PROBLEM 2. Could the sum of seven consecutive integers be a prime number?

PROBLEM 3. A 5-digit number is divisible by 7, 8, and 9. The number created from the first two digits is a prime number, 1 greater than a square number, and the sum of these two digits is a two-digit number. Find this 5-digit number.

PROBLEM 4. Every digit of a 5-digit number is either 1 or a prime number. Not only that, but any number created by any 2, 3, or 4 consecutive digits of this number are prime numbers also. Find this number, and check if it is a prime number or not.

PROBLEM 5. Can you put the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 into two groups so that the sums of the numbers in each group is the same? Can you do this to get the same product in each group?

PROBLEM 6. Are there any five consecutive whole numbers, which can be put into two groups so that the product of the numbers in each group is the same?

PROBLEM 7. In some cases, when 22022 and 20222 are divided by the same 3-digit number, they give the same remainder. Which one of these divisors can be determined by the remainder?

PROBLEM 8. Find a, b, c, and d, such that a^bb = bccbdc

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