DUSO MATHEMATICS LEAGUE
INDIVIDUAL QUESTIONS - MEET #4
JANUARY 5, 2011
1. ALG 1 (MATH A) 3 MINUTES
A laborer can dig a hole 8 feet long by 8 feet wide by 8 feet deep in 8 days. If he works at that same rate, under the same conditions, how many days will it take to dig a hole 4 feet long by 4 feet wide by 4 feet deep?
2. GEOMETRY (MATH A) 6 MINUTES
The plane figure ABC is the union of arc BC, arc AC and arc AB, which are arcs subtended from circles centered at A, B, and C respectively. Each of the circles has a radius of 2. The area of this plane figure can be expresses as .
Find k and express your answer in simplest form.
A Hint: A
BC BC
Hint: If the segments , , and are drawn, an equilateral triangle is formed, and the length of each side of the triangle will be 2.
3. ALG.2/TRIG. (MATH B) 6 MINUTES
Solve for the positive integer values of x and y, where x y
and express your answer as the ordered pair (x, y).
DUSO MATHEMATICS LEAGUE
INDIVIDUAL QUESTIONS - MEET #4
JANUARY 5, 2011
4. GEOMETRY (MATH B) 6 MINUTES
Write the equation of the line through point A and perpendicular to , if the coordinates of points A, B, and C are A(4, 1), B(-3, 1) and C( 5, -3). Give your answer in the form of , where p, q, and r are integers.
5. ALG 1 (MATH A) 5 MINUTES
Find a quadratic equation of the form where a, b, and c are integer coefficients, whose roots are the reciprocals of the roots of the following equation:
6. ALG.2/TRIG. (MATH B) 6 MINUTES
Find all positive values of x that satisfy the following equation and express those values in simplest form.
DUSO MATHEMATICS LEAGUE
GROUP TEAM QUESTION- MEET #4
JANUARY 5, 2011
1. A grid is made out of toothpicks as shown below. The grid is 16 boxes wide and 13 boxes high. The sides of each box are formed by 3 yellow toothpicks placed horizontally and 2 red toothpicks placed vertically. All of the boxes are the same size. Find the total number of toothpicks used.
2. How many integers “n” correctly satisfy the following conditions:
ab = n
a and b are integers
b = a + 2
< n < 300
3. Using the letters “O”, “N” , “E”, “R”, “A”, “J”, how many 3 letter arrangements can be formed so that the 3 letters are in alphabetical order, with no letters repeated?
DUSO MATHEMATICS LEAGUE
SOLUTIONS - MEET #4
JANUARY 5, 2011
Answers for GROUP TEAM QUESTION
1). 2). 3).
(Solutions for the Group question)
Individual Questions selected from the DUSO Question Bank, revised/editted by J.S.
Relay team question written for DUSO by J.A. DUSO Editor J.S.
DUSO MATHEMATICS LEAGUE
SOLUTIONS - MEET #4
JANUARY 5, 2011
Answers for INDIVIDUAL QUESTIONS
1). 1 2). 3). (12, 4) 4). 5). 6).
(or -2x+ y = -7)
Solutions for the Individual questions)