Exam Strategy
Pre-calculus · AP · Polynomial and Rational Functions
Prepare for AP Precalculus multiple-choice and free-response items on Change in Tandem: matching representations and justifying increasing/decreasing behavior on a named interval.
What "ready" looks like
- Matches one relationship across equation, table, graph, and verbal forms
- States increasing/decreasing with a named interval
- Justifies with the definition: for all \(a < b\) in the interval, compare \(f(a)\) and \(f(b)\)
- Spots when a description is not a function (two outputs for one input)
- Avoids claiming “always increasing” when the graph only rises on part of the domain
Before the quiz or test
1. Rehearse the increasing and decreasing definitions out loud with symbols. 2. Do two short items: one representation match, one increase/decrease justification. 3. Skim Common Mistakes for 1.1 (interval language, input/output mix-ups). 4. On graph items, plan to mark two points before writing inequalities.
Multiple-choice tips
- Eliminate choices that never name an interval when the stem asks where the function increases.
- On “which table matches,” check that each input appears once.
- If two graphs look similar, test a specific pair \(a < b\) against the claimed behavior.
- Watch for verbal stems that describe a relation that is not a function.
- Calculator graphs still need an interval statement in your reasoning.
Free-response / written tips
- Write the definition once, then plug in your chosen \(a\) and \(b\).
- Label axes or table headers (input vs output) before arguing.
- If the graph changes direction, split into intervals; do not force one global claim.
- Use precise language: “increasing on \([2,5]\)” not only “increasing.”
- When translating verbal → analytic, define what \(x\) and \(f(x)\) represent.
Common traps
- Using end behavior or asymptotes (later topics) instead of tandem/increasing language
- Claiming increasing because the rightmost point is highest, ignoring a dip
- Swapping input and output in a story problem
- Comparing \(f(a)\) and \(f(b)\) without establishing \(a < b\)
Quick checklist
- [ ] Interval is named whenever I say increasing or decreasing
- [ ] Justification uses \(a < b\) and compares outputs correctly
- [ ] Representations describe the same rule
- [ ] Function test (one output per input) checked when relevant
- [ ] No hole/asymptote/end-behavior detour unless the stem asks for it
Related materials
- Family Overview — coaching language for home
- Study Guide — practice pacing and classroom checks
- Common Mistakes — deeper diagnosis of tandem errors
- Practice sets, Review, and Practice Test under topic 1.1