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
31 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.
Prep Week
-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.
Week 1
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 6–17d/dx
Derivatives
Master every differentiation rule and apply them fluently under exam conditions.
Week 2
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, nested chain rule, all 6 trig function derivatives
- Inverse function derivative theorem, second derivatives of inverse functions
- All 6 inverse trig derivatives
8
Implicit Differentiation & Exponential/Logarithmic Derivatives
105 min- Circle/ellipse/curve examples, higher-order implicit derivatives
- e^x and general base exponentials
- Natural & general logarithms, logarithmic differentiation
9
Rates of Change & Particle Motion
75 min- Velocity, speed, acceleration, jerk
- Position/velocity/acceleration graphs
- Particle motion problems
10
Related Rates & Exponential Growth/Decay
120 min- 5-step related rates strategy, classic setups (ladder, cone, shadow)
- Law of exponential change, half-life & continuous compounding
- Linearization & differentials
11
Phase 2 Review & Quiz
75 min- Formula cheat sheet review
- 25-question timed quiz
- Self-grade
Week 3 (Part)
12
Extreme Value Theorem & Critical Points
75 min- Local vs absolute extrema
- Critical points (Fermat's theorem)
- Closed interval method for absolute extrema
13
Mean Value Theorem & Rolle's Theorem
75 min- Rolle's Theorem
- Mean Value Theorem
- Classic MVT/Rolle's proof-style problems
14
Increasing/Decreasing, First & Second Derivative Tests, Concavity
120 min- Monotonicity from the sign of f', First Derivative Test, sign charts
- Concave up/down from the sign of f''
- Inflection points, Second Derivative Test for local extrema
15
L'Hôpital's Rule
90 min- 0/0 and ∞/∞ forms
- ∞·0 and ∞-∞ forms
- Exponential indeterminate forms (0^0, ∞^0, 1^∞)
Phase 3 · Days 18–25∫
Integrals
Connect differentiation and integration through the Fundamental Theorem and build calculation speed.
Week 4 (Part)
18
Riemann Sums
Coming Soon- Left, right, midpoint, trapezoidal
- Overestimate vs underestimate
- 3 problems
19
Definite Integral Definition
Coming Soon- Notation and properties
- Area under curve interpretation
- 5 problems
20
Fundamental Theorem Part 1
Coming Soon- d/dx ∫ form
- 5 accumulation function problems
- AP FRQ pattern
21
Fundamental Theorem Part 2
Coming Soon- Evaluation theorem
- Antiderivatives from rules
- 8 problems
22
u-Substitution
Coming Soon- Pattern recognition
- Indefinite and definite forms
- 10 problems
Week 5 (Part)
23
Area Between Curves
Coming Soon- Setup strategy
- Intersection points
- 4 FRQ-style problems
24
Average Value & Accumulation
Coming Soon- Average value theorem
- Particle motion problems
- 5 problems
25
Integration Review
Coming Soon- 20-question mixed set
- Timed 30 minutes
- Error log
Phase 4 · Days 26–315
Exam Simulation
Simulate real exam conditions, sharpen FRQ writing, and eliminate remaining weak spots.
Final Week
26
FRQ Strategy Deep-Dive
Coming Soon- Scoring rubric analysis
- Justify your answer techniques
- 2 full FRQs
27
Full MCQ Section Practice
Coming Soon- 45 questions, 105 minutes
- Calculator + no-calculator parts
- Self-score
28
Full FRQ Section Practice
Coming Soon- 6 FRQ questions, 90 minutes
- Rubric self-grade
- Targeted review
29
Weak Spot Elimination
Coming Soon- Review error log from all phases
- Re-do 10 hardest problems
- Formula sheet review
30
Light Review + Rest
Coming Soon- Flip through notes
- 5 confidence-building problems
- Sleep 8+ hours 😴
31
Exam Day 🎯
Coming Soon- Arrive early
- Trust your prep
- Get your 5
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.