Complete Mastery Problem Sets Collection

Interleaved Practice Materials for All PASUM Courses

Overview

This collection contains 61 interleaved problems across 5 courses, designed for intensive exam preparation. Each problem combines 2-4 topics to build pattern recognition and exam readiness.

Course Problems Days Topics Combined
Mathematics II 15 5 Geometry, Series, Taylor-Maclaurin, Trig Integration
Chemistry II 12 4 Equilibrium, Kinetics, Electrochemistry, Organic
Physics II 12 4 Electrostatics, AC Circuits, Magnetism, Modern Physics
Advanced Math II 10 3 Complex Numbers, Inverse Trig, Hyperbolic Functions
Mathematics III 12 4 Probability, Distributions, Hypothesis Testing, Matrices
TOTAL 61 20 All Core Topics

Course Collection Overview

graph TD
    A[Complete Mastery Collection<br/>61 Problems] --> B[Mathematics II<br/>15 probs / 5 days]
    A --> C[Chemistry II<br/>12 probs / 4 days]
    A --> D[Physics II<br/>12 probs / 4 days]
    A --> E[Advanced Math II<br/>10 probs / 3 days]
    A --> F[Mathematics III<br/>12 probs / 4 days]
    B --> G[Shared Skills]
    C --> G
    D --> G
    E --> G
    F --> G
    G --> G1[Pattern Recognition]
    G --> G2[Cross-Topic Thinking]
    G --> G3[Exam Readiness]

Quick Access by Course

FAD1014 — Mathematics II

15 Problems | 5-Day Plan

  • Geometry (Circle, Parabola, Ellipse, Hyperbola)
  • Series Expansion (Binomial, Power Series)
  • Taylor & Maclaurin Series
  • Trigonometric Integration

Sample Problem: The Oscillating Circle — combines circle geometry with Maclaurin series and trigonometric area integrals.

FAD1018 — Chemistry II

12 Problems | 4-Day Plan

  • Chemical Equilibrium & Ionic Equilibria
  • Solubility Product
  • Kinetic Chemistry
  • Electrochemistry
  • Thermochemistry
  • Organic Chemistry (Stereochemistry, Reactions)

Sample Problem: Blood Buffer System — combines equilibrium, ionic equilibria, and thermochemistry in a biological context.

FAD1022 — Physics II

12 Problems | 4-Day Plan

  • Electrostatics
  • Capacitors & Dielectrics
  • AC Circuits & Analysis
  • Magnetism & Inductance
  • Semiconductors
  • Modern Physics & Photoelectric Effect

Sample Problem: Smartphone Touchscreen — combines electrostatics, capacitors, and energy calculations in a modern device.

FAC1004 — Advanced Mathematics II

10 Problems | 3-Day Plan

  • Complex Numbers & De Moivre's Theorem
  • Complex Logarithms & Loci
  • Inverse Trigonometric Functions
  • Hyperbolic Functions

Sample Problem: Digital Filter Design — combines complex numbers, Euler's formula, and inverse trig in signal processing context.

FAD1015 — Mathematics III

12 Problems | 4-Day Plan

  • Probability Theory & Counting
  • Probability Distributions (Binomial, Poisson, Normal, Exponential)
  • Sampling & Estimation
  • Hypothesis Testing
  • Matrices & Linear Algebra

Sample Problem: Network Security Analysis — combines conditional probability, Bayes' theorem, and counting rules in cybersecurity context.

Study Schedule Recommendations

Intensive Exam Prep (3-4 weeks)

Week 1: Mathematics II (Days 1-5) + Chemistry II (Days 1-2)
Week 2: Chemistry II (Days 3-4) + Physics II (Days 1-4)
Week 3: Mathematics III (Days 1-4) + Advanced Math II (Days 1-3)
Week 4: Review weak areas + Past year papers

Balanced Study (6-8 weeks)

Week 1-2: One course mastery set (3-4 problems/week)
Week 3-4: Second course mastery set
Week 5-6: Third course mastery set
Week 7-8: Remaining courses + Review

Pre-Exam Crash (1 week)

Day 1: Mathematics II Problems 1-3
Day 2: Mathematics II Problems 4-6 + Chemistry II Problems 1-2
Day 3: Chemistry II Problems 3-6
Day 4: Physics II Problems 1-6
Day 5: Mathematics III Problems 1-6
Day 6: All remaining problems
Day 7: Review mistakes + Formula sheets

Pedagogical Approach

These mastery sets use interleaved practice — mixing topics within and across problems — which research shows:

  • ✅ Improves long-term retention by 43%
  • ✅ Enhances problem-type recognition
  • ✅ Builds transferable problem-solving skills
  • ✅ Reduces "illusion of competence" from blocked practice

Contrast with Tutorials:

  • Tutorials: 10 similar problems in a row (builds fluency)
  • Mastery Sets: Each problem requires technique identification (builds exam readiness)

See: Analysis — Tutorial vs Interleaved Mastery Comparison

Formula Reference Quick Links

Each mastery set includes:

  • Topic-specific formulas
  • Constant values
  • Key equations
  • R code snippets (where applicable)

Navigate to individual sets for detailed references.

Tips for Success

  1. Don't skip the verification steps — comparing approximate vs exact answers builds metacognition
  2. Time yourself — aim for 30-45 minutes per problem
  3. Use formula sheets — these test application, not memorization
  4. Review mistakes immediately — identify which topic caused the error
  5. Mix courses — after completing one set, review another to maintain interleaving

Related Resources

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