MATH FIELD DAY 2004 RELAYS

Relay A

A1. Find the slope of the line

 

A2. Let k be the number you receive. Find the sum of 12k +11k + … + 2k + k .

 

A3. Let k be the number you receive. Find the largest integer n such that 4n^5 < k .

 

A4. Let k be the number you receive. Find the area of the right triangle with one leg of length
k and the other of length k + 2 .

 

A5. Let k be the number you receive. Find the y-coordinate of the point where the line of slope
k through the point (1, 2) intersects the line x = 3 .

 

Relay B

B1. Find x if

 

B2. Let k be the number you receive. Find the value of

 

B3. Let k be the number you receive. Find the larger of the two consecutive integers whose
sum is k .

 

B4. Let k be the number you receive. Find the radius of a circle whose area is kπ .

 

B5. Let k be the number you receive. Find the x -value of the solution of the system:

 

Relay C

C1. In how many different ways can we arrange three objects in a row?

 

C2. Let k be the number you receive. Suppose there are k people, labeled with the numbers 1,
2, …, k , sitting clockwise around a circle. If we start counting clockwise from person 1,
what is the label of the 45th person counted?

 

C3. Let k be the number you receive. Calculate the following:

 

C4. Let k be the number you receive. In the following figure, AB = k , ∠ABC = 90ยบ , and

Find AC.

 

C5. Let k be the number you receive. In the following figure, AB = k , BD = 4, and DE = 1.
Find CE.

 

 

Relay D

D1. Find the area of an isosceles right triangle whose hypotenuse has length

 

D2. Let k be the number you receive. If a rectangle’s length is 2 more than its width and the
rectangle has as area of 6k , find the rectangle’s width.

 

D3. Let k be the number you receive from the front and m be the number you receive from the
rear. If Fran can paint a room in k days and Ollie can paint a room of equal size in m
days, how many days will it take the two of them working together to paint 5 rooms?

 

D4. Let k be the number you receive. If the quadratic equation x^2 + bx + c = 0 has k and -11
as roots, find b.

 

D5. How many CDs can you buy from an online store if you have $100 to spend, the CDs cost
$9.99 apiece, and there is a fixed shipping cost of $6.95 for any order?