Questions+for+the+quiz

Graphical model questions
1. Mbita Christa the troll went to visit Grandma Croos. First, she walked 400m through the forest for 50min. Then she climbed 1000m up Candy Mountain which took her 2h. She stopped to eat gumdrops for 20min then walked along the yellow brick road for 250m for 30min until she got to grandma's house. She stayed with grandma, eating and chilling, for 3h. She then went back the way she came. After she walked through the forest, she continued walking for 45min for 800m until she got to her house under the bridge. Graph her journey. BONUS: How long did she take?

2. Adam Tish is walking on a taut tightrope that stretches from the 12th floor window of the McDonald’s corporation building, to the 7th floor of the Wendy’s corporation building across the street. In both buildings, there is 10m between floors. She starts at the edge of the tightrope in the McDonald’s window. She walks down the tightrope to a point level with the 9th floor. This takes 2 minutes. At this point, the tightrope snaps, but Tish is able to hold on. In 12 seconds, she falls from the 9th to 5th floor, while still holding the rope. She begins to pull herself up towards the top of the tightrope. She reaches the 10th floor after 4 minutes of climbing. However, she cannot hold on anymore and lets go, accelerating towards the ground. She falls to the 4th floor in 5 seconds. At this point, Superman flies in and catches her, holding her at the fourth floor for 1 minute. He then brings her to the ground at a slow constant speed, taking 3 minutes to get to the ground. Draw an elevation versus time graph to model this situation.

3. Tasha Fred was climbing up the stairs at the CN tower. He climbed a total horizontal distance of 500m. He took 20s to climb the first 100m. He then took 50s to climb the next 50m. He climbed the next 150m in 35s, and then he took a break for 15s. The next 100m took him 45s, and then last 100m took him 40s. Graph the height vs time and speed vs time graphs.

4. Megan Elizabeth is on her way to school. She walks 7km/h for 80 to get to the bus stop. The bus picks her up and travels 60km/h for 5km down the twisty road until it reaches the main road where it travels at 80km/h for 10km. When the bus gets to town it slows down to 50km/h for 1km until it reaches the school. At school Elizabeth gets off the bus and walks 150m to her locker at 6km/h. Draw a distance vs. time graph to model this scenario.

Polynomial
1. Yi The height of a diver above the water is modelled by the function h(t)= -2t^­2 + 5t + 11, where t represents the time in seconds and h(t) represents the height in metres. a) What is the instantaneous rate of change in height when the diver reaches maximum height at t = 1.25s b) What is the average rate of change in height between the intervals of 0≤t≤1.2

2.Tris Rejy was doing the CN Tower Edge Walk when a faulty wire broke and she fell 2000 ft. Her speed increased as she fell. Her fall was modled by the function d(t)= -5t^2 + 2000 where t is the time in seconds and d is the distance in feet. a) Calculte the average speed between 2s and 6s b) Calculate the instantaneous speed at 5s

3. George The population of a town is represented by the function P(t)=5t^2+10t+5000 where P(t) represents the total population and t is the time in years since 2010 a) Calculate the average rate of change for the years 2010 - 2020. b) Calculate the instantaneous rate of change for the year 2012, and give the population size for the year 2012.

4.Christa Alice falls down a rabbit hole. The speed(m/s) she is travelling is modeled by f(t) = 0.001t^3 - 0.001t^2 - 2 where t is time in minutes. a) If she fell down the rabbit hole at 12:00pm, what is her average speed between 12:30pm and 1pm? b) What is the speed she was travelling at, at 2:30pm?

Rational
1. Cheryl A visiting semester takes over the wet lab; however, they do not know that there is a gas leak. The concentration of chlorine gas in the wet lab can be modelled by the function c(t) = (30t)/(200+4t), where c is the grams per cubic metre, and t is the time in minutes. a) What is the average rate at which the concentration is changing during the second hour? b) What is the rate at which the concentration is changing after half an hour?

2. Roshni Reginald decides he wants to walk on a tightrope. His speed and distance is represented by the function S(t) = (2t)/(3 + t), S representing speed, and t representing the time in seconds. a) Determine his average rate of change within the first 7 seconds. b) Determine his instantaneous rate of change after 30 seconds.

3. Monette There is high demand for Lights' new album, represented by the equation D(x) = (100x)/(1+x). x is measured in thousands of CDs sold. a) Determine the average rate of change for the first 50 thousand CDs sold. b) Determine the instantaneous rate of change at the sale of 12,000 CDs.

4.  Uzair The population of Gordon's class can be estimated as a function of the number of jokes has told where: f(j)= 30- ((0.6j^2)/(j+100)) After 100 jokes, all of his original class of 30 is gone. a) find the rate of change of students after 50 jokes          b) find the average rate of change of students

Exponential
1. Celton Kate is growing bacteria for a biology lab and the amount of bacteria (in thousands) in a given culture dish is given by the function f(x)=2* 2 ^(x/20) at x minutes. a) What is the average rate of growth in the first 5 minutes? b) What is the instantaneous rate of growth at 5 minutes?

2. Alex The fatigue level of a math student in Gordon’s math class is dependent on the time spent sitting in his math class. This relationship is modelled by the equation F(t) = 10^t – 1, where “F(t)” is the fatigue level in “fatigue-points” and “t” is the time in seconds. a) What is the average rate of change in the fatigue level of a student from 5 to 13 seconds in Gordon’s math class? b) If the instantaneous rate of change in the fatigue level of a student reaches or exceeds 15 fatigue-points/second, then the student will go into a coma and he/she will require immediate medical treatment to avoid death. Will the student have achieved this state after 1 second in Gordon’s class? What is the instantaneous rate of change in the fatigue level after 1 second?

3. Matthew f(x) = 8 + 5 ^ (t) can be used to represent repair costs in thousands of dollars at a monster truck rally, where t is time in minutes. a) Determine average costs after 12 minutes b) What is the instantaneous damage costs at 3 minutes?

Trigonometric
1.Katie The function f(x)=3sin(2pix)+10 models the distance in centimeters of a point on the wheel of a car from the road as it drives along the road. a) What is the average rate of change for 3<=x<=8 minutes b)what is the instantaneous rate of change at x=5 minutes

2.Rejy Tris is on a ferris wheel. Her height as a function of time can be modelled by the function h(t)=1/2 (4sin(t+3)) -2, where t is in seconds and h is in meters. a) What is her average rate of change during the first minute? b)What is her instantaneous rate of change at 22 seconds?

3. Mark The distance of red pin on the wheel of fortune from the floor in inches is modeled by the function f(x) = 20cos[2(x - pi/2)] - 20. a) What is the instantaneous rate of change for pi/4 seconds b) What is the average rate of change for the interval or pi to 2pi seconds

4. Brittany The algae tide tank in the Science Arcade at the OSC rises and falls to simulate high and low tides. The function h(t)= sin (pi/8t) models the vertical movement of the ship, h, in meters, at t seconds. a) Determine the average rate of change at 10 seconds b) What is the instantaneous rate of change at 8 seconds?