Maximize your score by writing like an AP grader.
1️⃣ “Show All Work” – The Non-Negotiable Rule
✏️ Every symbolic step earns credit. Calculator answers alone never do.
| Task Type | What to Show | Zero-Credit Triggers |
|---|---|---|
| Derivatives / Integrals | Show differentiation/integration before substituting. Simplify algebraically. | Only writing final numeric value. |
| Substitution / FTC | Write full setup (e.g. ∫v(t)dt = s(b) – s(a)). | Skipping integral limits or variable. |
| Modeling / Units | Include units and interpret meaning. | Missing or inconsistent units (e.g. ft/sec² → ft/sec). |
| Table / Graph Data | Cite directly: “From the table, f′(2) = –1.” | Using unstated approximations. |
| Piecewise / Discontinuity | Evaluate both sides, clearly label LHS/RHS. | Claiming “not continuous” without limit evidence. |
2️⃣ Justification Phrases That Earn Rubric Points
Use grader-approved sentence structures.
| Concept | AP-Scoring Phrases |
|---|---|
| First Derivative Test | “Since f′(x) changes from + to – at x = c, f has a local maximum.” |
| Second Derivative Test | “f′(c) = 0 and f″(c) > 0 ⇒ local minimum.” |
| Concavity / Inflection | “f″(x) changes sign at x = a ⇒ point of inflection.” |
| Increasing / Decreasing | “f′(x) > 0 on (a,b) ⇒ f is increasing.” |
| Continuity | “Left and right limits equal f(c) ⇒ continuous at x = c.” |
| Accumulation / FTC | “∫ₐᵇ f′(x)dx = f(b) – f(a), representing total change.” |
| Differential Equation | “The slope field shows positive slopes ⇒ solution is increasing.” |
| Velocity / Position | “v(t) changes sign ⇒ particle changes direction.” |
3️⃣ Rubric Triggers Checklist
| ✅ Do This | ⚠️ Avoid This |
|---|---|
| Write algebraic setup before calculator answer. | Giving only numeric results. |
| State intervals with correct notation. | Writing “x = 2–4” instead of “2 ≤ x ≤ 4.” |
| Label all extrema: local vs absolute. | Writing just “maximum” without type. |
| Justify with derivative or limit — not visual guess. | “It looks increasing” → no credit. |
| Include units in final interpretation. | Leaving units blank. |
| Use ≈ for rounded values. | Writing calculator outputs as exact. |
4️⃣ Common Penalty Traps
| ❌ Error | 💡 Corrected Version |
|---|---|
| “f increases where f′ > 0 and decreases where f′ < 0.” (without interval) | “f is increasing on (1,3) because f′(x) > 0 there.” |
| “f has a min at x=2” (no justification) | “f′(2)=0 and f′ changes from – to + ⇒ local minimum.” |
| “∫v(t)dt = distance” (wrong interpretation) | “∫v(t)dt = net displacement; use |
| “The function is continuous because it’s a polynomial.” (irrelevant) | “Polynomials are continuous for all real x ⇒ f continuous everywhere.” |
5️⃣ Mini FRQ Example – Full-Credit Justification
Prompt:
A particle moves with velocity v(t)=t²–4t+3.
Find when it changes direction.
Full-Credit Solution:
v(t)=0 ⇒ t=1,3.
Check sign:
– For t<1, v(t)>0
– For 1<t<3, v(t)<0
– For t>3, v(t)>0
✅ Justify: “Since v(t) changes sign from + to – at t=1 and from – to + at t=3, the particle changes direction at t=1 and t=3.”
6️⃣ Calculator vs Non-Calculator Strategy
| Section | Expectation |
|---|---|
| Calculator-Allowed FRQs | Show symbolic setup, then numeric value (≈). Don’t derive by hand. |
| No-Calculator FRQs | Show every algebraic manipulation and simplification. |
7️⃣ Exam-Day “Top 3 Habits”
🕐 Spend ≤15 min per FRQ
✍️ Start each answer with a clear sentence restating what you’re finding
📏 Write units last and double-check sign/concavity consistency
🎯 Formula for a 5:
“Claim → Reason → Evidence” in every part.
That’s how graders see mastery.