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.
| Rule | Explanation |
|---|
| 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
| Skill | Command / Path | Exam Usage |
|---|
| Derivative at a Point | MATH → 8: nDeriv(f(x), x, a) | Instantaneous rate or slope at x=a. |
| Numerical Integral | MATH → 9: fnInt(f(x), x, a, b) | Accumulation / area between curves. |
| Root or Zero | 2nd → TRACE → 2: zero | Solving f(x)=0 for sign changes. |
| Min / Max Finder | 2nd → TRACE → 3: min or 4: max | For absolute extrema or optimization. |
| Solver | MATH → 0: Solver | Equation solving, e.g. implicit cases. |
| Table | 2nd → GRAPH | Compare f(x) and f′(x) quickly. |
| Function Recall | Y1(X) | Reuse stored functions in other operations. |
3️⃣ Desmos (Bluebook Digital Exam) Essentials
| Feature | How to Use | Exam Tip |
|---|
| Derivative Graph | Type derivative(f(x)) or f'(x) | Visualize slope sign and turning points. |
| Definite Integral | ∫_a^b f(x) dx | Great for area visualization—still write setup! |
| Intersection Points | Click/tap intersection | State x-value explicitly in your justification. |
| Tables | + → Table | Evaluate f(x), f′(x), f″(x) efficiently. |
| Parameter Sliders | Use a, b, c in definitions | Useful for modeling & curve shifting. |
| Regression | Table → write y_1 ~ a x_1^2 + b x_1 + c | Build models in applied problems. |
| Function Definition | e.g. v(t)=t^2−4t+3 | Enables 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)
| Task | Best Tool | Why / Strategy |
|---|
| Instantaneous rate / slope | TI-84 nDeriv or Desmos derivative | Fast verification of derivative sign/value. |
| Definite integral / accumulation | fnInt or ∫_a^b f(x)dx in Desmos | Confirm total change or area efficiently. |
| Finding zeros or intersections | Either | Determine sign changes or meeting points. |
| Absolute min/max on interval | TI-84 min / max or Desmos graph | Evaluate both endpoints & critical points. |
| Curve length or surface area | TI-84 fnInt / Desmos integral | For ∫√(1+(dy/dx)²)dx or ∫2πr ds calculations. |
| Average rate of change | Calculator for numeric speed | Still write (f(b)−f(a))/(b−a) explicitly. |
| Regression / curve fitting | Desmos | For modeling from data tables. |
6️⃣ Advanced Desmos Pro Tips
| Scenario | Pro Technique |
|---|
| Data Modeling | Use regression syntax y_1 ~ a x_1 + b or quadratic form for best fit. |
| Parametric Visualization | Define x(t)=..., y(t)=...; plot both and adjust t-range. |
| Polar Graphs | Use r = f(θ) mode; visually verify symmetry. |
| Multiple Functions | Assign colors and label intersections for comparative FRQs. |
7️⃣ Exam-Day Calculator Discipline
| Principle | Actionable Habit |
|---|
| Time Management | Spend ≤3–4 minutes per calculator subpart. If stuck, write setup, compute ≈ value, move on. |
| Rounding Precision | Use three significant digits unless stated otherwise. Always mark ≈ before rounded values. |
| Consistency | Double-check signs, intervals, and limits after calculator use. |
| Interpretation | Every numeric result must include a one-line statement explaining meaning in context. |
| Backup Strategy | If calculator malfunctions, write setup + indicate “cannot compute.” Partial credit is still earned. |
⚙️ Summary Mantra:
“Calculator for confirmation, not discovery.
Reason first. Verify second.”