AP Calculus Calculator & Desmos Skills Sheet

Step-by-step strategies for TI-84 and Desmos — built for digital exam success.


1️⃣ Calculator Use Policy – The Golden Rules

Graders reward setup + reasoning, not button pressing.

RuleExplanation
Always show your symbolic setup before using a calculator.Example: Write ∫₀² v(t) dt = s(2) − s(0) before entering it.
Use for rounded values.Do not report calculator output as exact.
Identify the command used.e.g. “Using nDeriv on TI-84” or “Using derivative(f(x)) in Desmos.”
Interpret the result in context.Add a one-sentence explanation (e.g. “The particle’s position decreases by 2 units.”)

2️⃣ TI-84 Essential Commands

SkillCommand / PathExam Usage
Derivative at a PointMATH → 8: nDeriv(f(x), x, a)Instantaneous rate or slope at x=a.
Numerical IntegralMATH → 9: fnInt(f(x), x, a, b)Accumulation / area between curves.
Root or Zero2nd → TRACE → 2: zeroSolving f(x)=0 for sign changes.
Min / Max Finder2nd → TRACE → 3: min or 4: maxFor absolute extrema or optimization.
SolverMATH → 0: SolverEquation solving, e.g. implicit cases.
Table2nd → GRAPHCompare f(x) and f′(x) quickly.
Function RecallY1(X)Reuse stored functions in other operations.

3️⃣ Desmos (Bluebook Digital Exam) Essentials

FeatureHow to UseExam Tip
Derivative GraphType derivative(f(x)) or f'(x)Visualize slope sign and turning points.
Definite Integral∫_a^b f(x) dxGreat for area visualization—still write setup!
Intersection PointsClick/tap intersectionState x-value explicitly in your justification.
Tables+ → TableEvaluate f(x), f′(x), f″(x) efficiently.
Parameter SlidersUse a, b, c in definitionsUseful for modeling & curve shifting.
RegressionTable → write y_1 ~ a x_1^2 + b x_1 + cBuild models in applied problems.
Function Definitione.g. v(t)=t^2−4t+3Enables symbolic use in derivatives/integrals.

4️⃣ Common Errors & Traps

Mistake💡 Correction / Reminder
Using nDeriv to find full derivative function.nDeriv gives numeric value only, not symbolic form.
Using fnInt over discontinuities or corners.Check graph visually — piecewise functions can mislead results.
Missing parentheses in complex integrands.Always use parentheses: fnInt((x^2+1)/(x+3), x, 0, 2).
Reporting calculator-only results.Always include formula setup + ≈ result.

5️⃣ “When to Use” Strategy Table (Expanded)

TaskBest ToolWhy / Strategy
Instantaneous rate / slopeTI-84 nDeriv or Desmos derivativeFast verification of derivative sign/value.
Definite integral / accumulationfnInt or ∫_a^b f(x)dx in DesmosConfirm total change or area efficiently.
Finding zeros or intersectionsEitherDetermine sign changes or meeting points.
Absolute min/max on intervalTI-84 min / max or Desmos graphEvaluate both endpoints & critical points.
Curve length or surface areaTI-84 fnInt / Desmos integralFor ∫√(1+(dy/dx)²)dx or ∫2πr ds calculations.
Average rate of changeCalculator for numeric speedStill write (f(b)−f(a))/(b−a) explicitly.
Regression / curve fittingDesmosFor modeling from data tables.

6️⃣ Advanced Desmos Pro Tips

ScenarioPro Technique
Data ModelingUse regression syntax y_1 ~ a x_1 + b or quadratic form for best fit.
Parametric VisualizationDefine x(t)=..., y(t)=...; plot both and adjust t-range.
Polar GraphsUse r = f(θ) mode; visually verify symmetry.
Multiple FunctionsAssign colors and label intersections for comparative FRQs.

7️⃣ Exam-Day Calculator Discipline

PrincipleActionable Habit
Time ManagementSpend ≤3–4 minutes per calculator subpart. If stuck, write setup, compute ≈ value, move on.
Rounding PrecisionUse three significant digits unless stated otherwise. Always mark ≈ before rounded values.
ConsistencyDouble-check signs, intervals, and limits after calculator use.
InterpretationEvery numeric result must include a one-line statement explaining meaning in context.
Backup StrategyIf calculator malfunctions, write setup + indicate “cannot compute.” Partial credit is still earned.

⚙️ Summary Mantra:
“Calculator for confirmation, not discovery.
Reason first. Verify second.”