Common Mistakes
Pre-calculus · Honors Math · Introduction to calculus
Real mistakes students make on limit properties and continuity—and how to catch and fix them.
Focus for this topic: Apply limit laws; determine continuity at a point.
Frequent mistakes
### 1. Domain errors
What it looks/sounds like: Logging a nonpositive quantity or dividing by zero mid-solution.
Why it happens: Algebraic steps ignore restrictions until the end (or forever).
How to fix: State domain restrictions before solving; check candidates against them.
### 2. Extraneous roots after irreversible steps
What it looks/sounds like: Keeping solutions introduced by squaring or clearing logs incorrectly.
Why it happens: Students treat every algebraic step as reversible.
How to fix: Substitute every candidate into the original equation and discard failures.
### 3. Off-by-one in sequence indexing
What it looks/sounds like: Using n = 1 when the formula expects n = 0 (or the reverse).
Why it happens: “First term” language is ambiguous across textbooks.
How to fix: Write the first few terms with indices before plugging into a formula.
### 4. Mixing inverse operations (exp vs log)
What it looks/sounds like: Exponentiating when logging was needed, or applying log base incorrectly.
Why it happens: Inverse pairs are memorized but applied to the wrong side.
How to fix: Name the inverse you need, apply it to both sides, then simplify carefully.
### 5. Feature misread on a graph/formula
What it looks/sounds like: Wrong asymptotes, vertices, or end behavior for the parent relation.
Why it happens: Students compute parameters without tying them to the picture.
How to fix: Sketch key features from the equation before answering detail questions.
How to avoid them
1. Restate what 7.3 asks in one sentence before computing. 2. Name the method or representation you will use. 3. Define variables with units before writing symbols. 4. Check one easy special case, diagram estimate, or unit/domain check after a long solution. 5. Ask: does this answer match the required form and the prompt?
Quick self-check
- [ ] I can name two mistakes for 7.3
- [ ] I can explain why one of those mistakes happens
- [ ] I can fix one wrong solution by naming the broken step
- [ ] I can check that my final form matches what the prompt asked
Related materials
- Parent Guide, Exam Strategy, and Study Guide for 7.3 (same folder)
- Review and practice-test tiers under this topic when present