AP Calculus AB · Intensive Program
Get AP Calculus ab 5 in 30 Days
A day-by-day roadmap from zero to a perfect score — no cramming, no gaps.
~75 min/day
Daily commitment
4 Phases
Structured learning
30 Days
Full AB coverage
Score: 5
The target
Each day builds on the last. Don not skip ahead — the sequence is intentional.
- Click any topic to open the full lesson with worked examples and hints.
- Complete all tasks before moving to the next day.
- Keep an error log — mistakes you repeat are points you are leaving on the table.
Phase 0 · Days -5 to 0🌉
Pre-Calculus Power Bridge
Solidify algebra and function foundations to remove all 'tool-based' obstacles before Calculus.
-5
Function Bootcamp
60 min- Number systems and logic symbols
- Function modeling and applications
- Domain and range restrictions
- Injective and surjective mappings
- Composition and recursive patterns
- Symmetry and inverse functions
-4
Algebra Survival Skills
45 min- Factoring for limit cancellation
- Complex fraction simplification
- Rationalization with conjugates
- Power and root exponent laws
- Completing the square mastery
- Simplification via substitution
-3
Trigonometry Essentials
75 min- Unit Circle & ASTC quadrant mastery
- Special values (30-60-90 & 45-45-90)
- Pythagorean & Double-Angle identities
- Inverse Trig domain/range restrictions
- Notation: sin⁻¹(x) vs (sin x)⁻¹
-2
Exponential & Log Mastery
60 min- Exponent laws & fractional power conversion
- Inverse relationship between 'e' and 'ln'
- Log properties: Product, Quotient, & Power
- Solving growth/decay (Aeʳᵗ) equations
- Growth Hierarchy: Exponential > Polynomial > Log
-1
Graphical Intuition & Rate of Change
45 min- AROC calculation (Secant line slope)
- Visualizing the limit: Secant to Tangent
- IROC concept: Slope at a single point
- Geometric formulas (Sphere/Cone/Triangles)
- Absolute value splitting & transformations
0
AP Calculus AB — Course Introduction
10 min- Understand the exam structure: MCQ + FRQ breakdown
- Learn how the 1–5 scoring scale works
- Set up your error log and study routine
Phase 1 · Days 1–5∞
Limits & Continuity
Build rock-solid intuition for limits—the language everything else is written in.
1
Intro to Limits & Algebraic Laws
90 min- Graphical & numerical approach, limit notation
- Sum/product/quotient rules, direct substitution
- 6 practice problems
2
Limits at Infinity
60 min- Horizontal asymptotes
- Dominant term analysis
- 4 practice problems
3
Squeeze Theorem
60 min- Classic sin(x)/x proof
- Trigonometric limits
- 3 practice problems
4
Continuity
75 min- 3 conditions for continuity
- Types of discontinuity
- IVT
5
Phase 1 Review & Quiz
75 min- Formula cheat sheet review
- 25-question timed quiz
- Self-grade
Phase 2 · Days 6–15d/dx
Derivatives
Master every differentiation rule and apply them fluently under exam conditions.
6
The Derivative — Definition & Basic Rules
120 min- Limit definition, tangent/normal lines, differentiability vs continuity
- Power, constant, sum/difference rules
- Product rule & quotient rule
7
Chain Rule, Trig & Inverse Derivatives
120 min- Composite function pattern, all 6 trig derivatives
- Inverse function derivative theorem
- All 6 inverse trig derivatives
8
Implicit, Exponential/Log & Higher-Order Derivatives
110 min- Implicit differentiation
- e^x, general bases, logarithmic differentiation
- Higher-order derivatives (incl. implicit d²y/dx²)
9
Rates of Change & Particle Motion
75 min- Velocity, speed, acceleration
- Position/velocity/acceleration graphs
- Particle motion problems
10
Related Rates & Exponential Growth/Decay
120 min- 5-step related rates strategy, classic setups
- Law of exponential change, half-life
- Linearization & differentials
11
Phase 2 Review & Quiz
75 min- Formula cheat sheet review (Day 6–10)
- 25-question timed quiz
- Self-grade
12
Extreme Values, Rolle's & the Mean Value Theorem
100 min- Critical points & the Closed Interval Method for absolute extrema
- Rolle's Theorem
- Mean Value Theorem + proof-style problems
13
Analyzing Functions with Derivatives
120 min- Monotonicity & First Derivative Test, concavity & Second Derivative Test
- Inflection points
- Connecting the graphs of f, f′, and f″
14
L'Hôpital's Rule & Optimization
110 min- Indeterminate forms: 0/0, ∞/∞, ∞·0, ∞−∞, exponential forms
- 4-step optimization strategy
- Fence / box / can / minimum-distance setups
15
Phase 2 Final Review & Quiz
75 min- Formula cheat sheet review (Day 12–14)
- 25-question timed quiz
- Self-grade
Phase 3 · Days 16–22∫
Integrals
Build antidifferentiation fluency, connect derivatives and integrals through the FTC, and drill the highest-weighted unit on the exam.
16
Antiderivatives & Basic Integration
100 min- Power, e^x, trig, 1/x = ln|x| antiderivative rules
- Arctangent & arcsine forms, completing the square
- Indefinite integrals & initial-value problems
17
Riemann Sums & Numerical Approximation
90 min- Definite integral as a limit of Riemann sums
- Left, right, midpoint, trapezoidal + over/under estimates
- Approximating an integral from a table
18
The Definite Integral & the Fundamental Theorem
90 min- Properties of the definite integral
- FTC Part 1: evaluate with antiderivatives
- FTC Part 2: d/dx ∫ form + chain rule
19
U-Substitution & Accumulation Functions
100 min- u-substitution, indefinite & definite (change the limits)
- Accumulation functions g(x) = ∫ f
- Extrema, concavity & inflections of g from the graph of f
20
Differential Equations, Slope Fields & Exponential Models
90 min- Separable equations + initial value problems
- Reading / sketching slope fields
- dy/dt = ky, half-life & doubling time
21
Average Value & Particle Motion
90 min- Average value formula + MVT for Integrals
- Displacement vs. total distance (split at v = 0)
- Position from velocity + initial condition
22
Phase 3 Review & Quiz
75 min- Formula cheat sheet review (Day 16–21)
- 25-question timed quiz
- Self-grade
Phase 4 · Days 23–305
Geometric Applications & Final Sprint
Master area and volume integrals, then simulate real exam conditions and eliminate remaining weak spots.
23
Area & Volume with Integrals
100 min- Area between curves (dx and dy, crossing)
- Disk & washer method, rotation about a line
- Volume by known cross sections
24
Theorems Review
60 min- IVT, EVT, MVT, MVT for Integrals, FTC
- When each applies
- Justification wording
25
FRQ Strategy Deep-Dive
75 min- How the 6 questions are scored
- Justification phrase bank
- Calculator rules
26
Practice Exam — Multiple Choice
120 min- Two full timed MCQ papers (Exam A & B)
- All 8 units
- Self-score & error log
27
FRQ Practice Exam 1
90 min- Full 6-question paper: Part A (2, calculator) + Part B (4, no calculator)
- ~15 min per question
- Point-by-point self-grade
28
FRQ Practice Exam 2
90 min- Full 6-question paper: Part A (2, calculator) + Part B (4, no calculator)
- ~15 min per question
- Point-by-point self-grade
29
Final Cheat Sheet
45 min- Whole-course formula & theorem sheet
- Read start to finish
- Flag anything unfamiliar
30
Exam Day Preparation 🎯
30 min- Taper, don't cram
- Pack the night before
- Time budget & justification reminders
- Sleep 8+ hours, arrive early
Pro Tip: Track Your Progress
Check off each day as you complete it. The simple act of marking progress releases dopamine and keeps you consistent. A streak of 7 days is a habit. A streak of 30 days is mastery.