Error Sleuths
About This Worksheet
This worksheet helps twelfth-grade Pre-Calculus students practice finding and correcting mistakes in nonlinear inequality solutions. Students review six worked statements where someone has made an error involving critical values, interval signs, endpoint choices, or domain restrictions. Their job is to identify what went wrong and write the correct solution.
The examples include both polynomial and rational inequalities. Some mistakes come from using the wrong critical values, while others come from including a forbidden denominator value or choosing the wrong sign interval.
What Students Practice
Students practice reading solution reasoning carefully and checking it step by step. They decide whether the critical values are correct, whether all required intervals were considered, and whether the final endpoints are handled properly.
The worksheet also strengthens mathematical explanation. Students must say what the error is, not just replace the answer.
Why This Skill Matters
Nonlinear inequalities involve several stages, so mistakes can happen in more than one place. A student may factor correctly but test the intervals incorrectly, or they may find the right intervals but write the endpoints wrong.
Learning to diagnose those mistakes helps students improve their own problem solving. It also reinforces the full process from start to finish.
Common Challenges
Students may only look at the final interval and miss an earlier error in the setup. Encourage them to start with the critical values and move forward one step at a time.
Another common mistake is giving a vague correction such as “wrong interval.” Students should identify the specific issue, such as missing a denominator restriction or including an excluded endpoint.
How To Use It
Teachers can use this worksheet for partner discussion, small-group review, homework, or exam preparation. It works especially well near the end of a nonlinear inequalities unit.
Parents and homeschool teachers can ask, “What was the first step that went wrong?” Fixing the earliest mistake usually makes the rest of the correction much easier.
Grade Alignment
This Grade 12 Pre-Calculus worksheet reinforces complete nonlinear inequality solving, including critical values, interval testing, and domain restrictions.
Students should already know the standard sign-analysis process. After this practice, they can evaluate full proposed solutions with greater confidence.