The task is to make up an exam style question of your choice worth 7 marks on algebra in context and quadratics. Create your own mark scheme on it.
You can also highlight potential mistakes people answering the question may make therefore add tips and hints and it must be for top/high level stundents.
You take an 8in x 10in sheet of paper and remove an 2"x2" square from each corner. You fold up the resulting flaps to form an open-top box.
a) (2 pt) What is volume of the box?
b) (2 pt) What is the area of the box's walls (excluding the base)?
c) (2 pt) If instead of 2-inch squares, you removed x-inch squares, write an expression to represent the area of the box's walls.
d) (1 pt) Find the value of x that maximizes the wall area. Hint: graph your answer to (c).
a) 4*6*2 = 48 in^3. A common mistake would be for students to subtract only 2 from each dimension, giving 6*8*2 = 96 in^3. One point for correct units.
b) Two walls are 4x2, and two walls are 6x2. 40in^2. One point for correct units.
c) Depending on what you want to test, you might consider providing this answer in the problem, in preparation for part d: x(10-x + 10-x + 8-x + 8-x) = x(36-4x)
d) Graphing the function, students should see that the vertex of the parabola occurs at x = 4.5.
Consider asking follow-up or challenge questions: What is the volume of the box for this value of x? Is this the maximum volume that the box could have? etc.