Prior to entering the realm of imaginary numbers, it is important that the students have an elementary understanding of radicals. This quiz was created with the intention of checking for that understanding. As an overview the skills I am assessing in this quiz are:
1) Solving simple radical equations.
2) Check for and identify extraneous solutions*
3) Simplify radical expressions.
*Anticipated Remediation: The students often neglect to check for extraneous solutions.
I allow students time to work on the quiz. When this is competed, I encourage them to continue working through their final project activities that are all due at the end of the semester.
In my experience, the students will have the most difficulty in #1-10 with the problems that require them to multiply by the conjugate to simplify. Algebra II students regularly make the mistake of flipping the signs of BOTH terms in the denominator when attempting to multiply by the conjugate. As remediation for this skill, I have my students use the distributive property for a wide variety of special binomial products that are conjugates of each other. For example, problems like (2+3i)(2-3i) and (5+12i)(5-12i). This reminds them of the important feature of the conjugate - the middle terms (the i's) cancel off.
In #11-14 students will fail to check their answers for extraneous solutions if this is not constantly reinforced before the quiz. Even in our work with the accident reconstructionist, the students were exposed to answers that simply "did not make sense" - - this application, more than anything else, drives home the importance of plugging in and checking the obtained solutions.