Grade 11 Math Performance Task Worksheet

Grade 11 Math Performance Task

Read each performance task carefully and answer all questions. Show your work for full credit. Use appropriate mathematical models and justify your reasoning.

1. A gardener wants to enclose a rectangular garden using 120 feet of fencing. One side of the garden is against an existing wall, so no fencing is needed along that side. What are the dimensions of the garden that would maximize its area? What is the maximum area?

2. A projectile is launched upward from a platform 10 meters high with an initial velocity of 40 meters per second. The height of the projectile (h) in meters after t seconds is given by the equation: h(t) = -4.9t^2 + 40t + 10.

a. What is the maximum height reached by the projectile and when does it reach this height?

b. When will the projectile hit the ground?

c. Create a sketch of the projectile's height over time on a coordinate plane. Label the axes and key points (initial height, maximum height, time to hit ground).

3. A company's monthly sales (in thousands of dollars) for the past six months were: 150, 165, 155, 170, 180, 160. Calculate the following measures of central tendency and dispersion.

a. Mean:  

b. Median:  

c. Mode:  

d. Range:  

e. Standard Deviation (round to two decimal places):  

4. A cylindrical water tank has a radius of 3 meters and a height of 10 meters.