3. Give Each Team Member Small Pieces of Paper to Use As Passing Slips

Relay Rules

1. Divide class into teams of 3. Teams may not communicate with one another verbally during a relay. Seat them in columns so that team members are in front and behind one another. (Note: Since I do this after the AP test, I actually divide my class into teams of 6 and each position works with partners.) 2. Give each front team member question Relay 1-1. Give the middle team member Relay 1-2. Give the last team member Relay 1-3. 3. Give each team member small pieces of paper to use as “passing slips”. 4. Each team member completes the assigned problem. When they get an answer, they pass it behind them to the next team member. Questions 2 and 3 include the notation “TNYWR”. This stands for “The Number You Will Receive”. 5. At the end of 3 or 4 minutes (up to you), call time and collect answers from the last person in each team. At the end of 6 or 8 minutes (up to you) call time again and collect answers from the last person. Correct answers received at the first call of time are worth 6 points. Correct answers received at the end of the last call are worth 3 points. Only the latest collected paper should be graded (i.e. students can guess after 4 minutes, but correct it at 8 minutes. If their guess is correct after 4 minutes, they should not submit a new paper at 8 minutes – because it would only be worth 3 points). 6. Repeat with Relays 2, 3, and 4. The winning team is the team with the most points after 4 relays.

Note: This idea comes from the ARML competition which includes relays. If you are familiar with ARML relays, it’s the same idea. I give more time in calculus than they give in ARML. Relay 1-1 Relay 2-1

Find the limit and pass back the answer. If f(x) = x2 – 9x + 14 x - 9 lim x 9 x - 3 Pass back the larger zero of the function.

Relay 1-2 Relay 2-2

Let n = TNYWR Let n = TNYWR f(x) = nx2 – 4nx The circle has a radius of n.

Pass back the x-coordinate that gives the Pass back the area of the square. minimum value of the function.

Relay 1-3 Relay 2-3

Let n = TNYWR Let n = TNYWR

Find the area between the curves y = x2 and If this is a linear function, turn in the y-intercept y =nx. Turn in the answer as a reduced fraction x y (improper is OK) 2 n 4 96

Relay 3-1 Relay 4-1

Find the limit and pass back the answer. If this function is continuous for all x, pass back (5+h )2 - 5 2 the value of b. lim h 0 h 2x+ b , x 4 f( x ) = x2, x > 4

Relay 3-2 Relay 4-2 Let n = TNYWR Let n = TNYWR If this function is differentiable for all x, pass back Find the slope of the tangent to the curve at the value of m (0, 0). nx- 4, x 4 f(x) = sin(nx) f( x ) = mx2 +12, x > 4 Relay 3-3 Relay 4-3

If the radius of a circle is increasing at a rate of 1 If this function is continuous for all x, turn in the cm per minute, turn in how fast the area of the value of b circle is increasing at the instant the radius is 3x+ b , x 4 equal to n. f( x ) = nx3, x > 4 Answers Relay 1-1 Relay 2-1

Find the limit and pass back the answer. If f(x) = x2 – 9x + 14 x - 9 lim = 6 Pass back the larger zero of the function. x 9 x - 3 7

Relay 1-2 Relay 2-2

Let n = TNYWR Let n = TNYWR f(x) = nx2 – 4nx The circle has a radius of n.

Pass back the x-coordinate that gives the minimum value of Pass back the area of the square. the function. x= 2 98

Relay 1-3 Relay 2-3

Find the area between the curves y = x2 and If this is a linear function, turn in the y-intercept y =nx. Turn in the answer as a reduced fraction (improper x y 4 2 n is OK) 3 4 96 100

Relay 3-1 Relay 4-1

Find the limit and pass back the answer. If this function is continuous for all x, pass back the value of (5+h )2 - 5 2 b. lim =10 h 0 2x+ b , x 4 h f( x ) = b = 8 x2, x > 4

Relay 3-2 Relay 4-2 Let n = TNYWR Let n = TNYWR If this function is differentiable for all x, pass back the value Find the slope of the tangent to the curve at of m (0, 0). nx- 4, x 4 f(x) = sin(nx) 10 f( x ) = m=1 mx2 +12, x > 4 Relay 3-3 Relay 4-3 Let n = TNYWR 20p If the radius of a circle is increasing at a rate of 1 cm per Let n = TNYWR minute, turn in how fast the area of the circle is increasing at the instant the radius is equal to n. If this function is continuous for all x, turn in the value of b 3x+ b , x 4 f( x ) = b=52 nx3, x > 4