PREP PLAN- VIA OPAL AI

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PREP PLAN

Personalized Study & Exam Preparation Plan

For Grade 11 Students at ABUCAK

Cambridge International AS & A Level Pure Mathematics 2 & 3

Plan Overview

This comprehensive 6-week intensive revision plan is meticulously designed for your Cambridge International AS & A Level Pure Mathematics 2 & 3 examinations. Assuming exams are scheduled for late January/early February 2026, this plan utilizes your Coursebook as the primary reference, guiding you through a structured and effective preparation journey.

📅 Duration: 6 Weeks Intensive
📚 Subjects: Pure Math 2 & 3 (AS & A Level)
⏰ Exam Dates: Late Jan/Early Feb 2026
📖 Reference: Provided Coursebook

Detailed Study Schedule

Each session allocates approximately 2-3 hours. Utilize these strategic study techniques:

TR (Theory Review) PE (Practice Exercises) CM (Concept Mapping) FC (Flashcards) PP (Past Papers)

Week 1: December 9 - December 15 (Foundations of P2)
  • Monday: Algebra (Chapter 1) - Modulus Function, Polynomial Division (TR: 1.1-1.4, PE: Review Ex 1 Q1-4, CM: Modulus functions).
  • Tuesday: Algebra (Chapter 1) - Factor & Remainder Theorem (TR: 1.5-1.6, PE: Review Ex 1 Q5-14, FC: Theorems).
  • Wednesday: Logarithmic and Exponential Functions (Chapter 2) - Logarithms to Base 10 & 'a' (TR: 2.1-2.2, PE: Ex 2A, Ex 2B Q1-4, FC: Logarithm definitions).
  • Thursday: Logarithmic and Exponential Functions (Chapter 2) - Laws of Logarithms, Solving Equations/Inequalities (TR: 2.3-2.6, PE: Ex 2B Q5-8, Ex 2D, Ex 2E, CM: Logarithm laws, solving strategies).
  • Friday: Logarithmic and Exponential Functions (Chapter 2) - Natural Logarithms, Transforming to Linear Form (TR: 2.7-2.8, PE: Ex 2G, Ex 2H, Review: Cross-topic review ex 1 P2 Qs).
  • Saturday: Weekly Review & Catch-up; Short P2 Practice (Chapters 1 & 2).
  • Sunday: Rest / Light revision.
Week 2: December 16 - December 22 (Trigonometry & P2 Differentiation)
  • Monday: Trigonometry (Chapter 3) - Reciprocal Ratios (Cosecant, Secant, Cotangent) (TR: 3.1, PE: Ex 3A, FC: Identities).
  • Tuesday: Trigonometry (Chapter 3) - Compound & Double Angle Formulae (TR: 3.2-3.3, PE: Ex 3B, Ex 3C, CM: Formula interrelations).
  • Wednesday: Trigonometry (Chapter 3) - Further Identities, R-form (TR: 3.4-3.5, PE: Ex 3D, Ex 3E, Review: Review Ex 3).
  • Thursday: Differentiation (Chapter 4) - Product & Quotient Rule (TR: 4.1-4.2, PE: Ex 4A, Ex 4B, FC: Rules & examples).
  • Friday: Differentiation (Chapter 4) - Exponential, Logarithmic, Trigonometric Derivatives (TR: 4.3-4.5, PE: Ex 4C, Ex 4D, Ex 4E, CM: Standard function derivatives).
  • Saturday: Weekly Review & Catch-up; P2 Practice Test (Chapters 3 & 4).
  • Sunday: Rest / Light revision.
Week 3: December 23 - December 29 (P2 Integration & Numerical Methods)
  • Monday: Integration (Chapter 5) - Exponential & 1/(ax+b) (TR: 5.1-5.2, PE: Ex 5A, Ex 5B, FC: Basic integration formulae).
  • Tuesday: Integration (Chapter 5) - Trigonometric Functions, Trapezium Rule (TR: 5.3-5.5, PE: Ex 5C, Ex 5D, Ex 5E, CM: Integration strategies).
  • Wednesday: Numerical Solutions of Equations (Chapter 6) - Finding a Starting Point, Iterative Processes (TR: 6.1-6.2, PE: Ex 6A, Ex 6B, FC: Iterative formulae, change-of-sign method).
  • Thursday: Numerical Solutions of Equations (Chapter 6) - Real-World Problems, Cross-topic Review (TR: 6.3, PE: Ex 6C, Review: Review Ex 6, Cross-topic review ex 2 P2).
  • Friday: Comprehensive P2 Review; Full P2 Mock Exam (Coursebook Page 307).
  • Saturday: Review Mock Exam performance, identify weak areas.
  • Sunday: Rest / Light revision.
Week 4: December 30 - January 5 (P3 Further Algebra & Calculus)
  • Monday: Further Algebra (Chapter 7) - Improper Algebraic Fractions, Partial Fractions (TR: 7.1-7.2, PE: Ex 7A, Ex 7B Q1-4, CM: Partial fraction forms).
  • Tuesday: Further Algebra (Chapter 7) - Binomial Expansion (rational n) (TR: 7.3-7.4, PE: Ex 7C, Ex 7D, FC: Binomial expansion formula, validity).
  • Wednesday: Further Algebra (Chapter 7) - Partial Fractions & Binomial Expansions (TR: 7.5, PE: Ex 7E, Review: Review Ex 7).
  • Thursday: Further Calculus (Chapter 8) - Derivative of tan⁻¹x, Integration of 1/(x²+a²) (TR: 8.1-8.2, PE: Ex 8A, Ex 8B, FC: tan⁻¹x derivative & integral).
  • Friday: Further Calculus (Chapter 8) - Integration of f'(x)/f(x), Integration by Substitution (TR: 8.3-8.4, PE: Ex 8C, Ex 8D, CM: Substitution recognition).
  • Saturday: Weekly Review & Catch-up; P3 Practice Test (Chapters 7 & 8).
  • Sunday: Rest / Light revision.
Week 5: January 6 - January 12 (P3 Vectors & Differential Equations)
  • Monday: Further Calculus (Chapter 8) - Integration by Parts, Integration using Partial Fractions (TR: 8.5-8.7, PE: Ex 8E, Ex 8F, FC: Integration by parts formula, LATE rule).
  • Tuesday: Vectors (Chapter 9) - Displacement & Position Vectors (TR: 9.1-9.2, PE: Ex 9A, Ex 9B, FC: Vector notation, magnitude, unit vectors).
  • Wednesday: Vectors (Chapter 9) - Scalar Product, Vector Equation of a Line (TR: 9.3-9.4, PE: Ex 9C, Ex 9D, CM: Scalar product, line equations).
  • Thursday: Vectors (Chapter 9) - Intersection of Lines (TR: 9.5, PE: Ex 9E, Review: Review Ex 9).
  • Friday: Differential Equations (Chapter 10) - Separating Variables, General & Particular Solutions (TR: 10.1, PE: Ex 10A, FC: Steps for separable DEs).
  • Saturday: Weekly Review & Catch-up; P3 Practice Test (Chapters 8, 9, 10).
  • Sunday: Rest / Light revision.
Week 6: January 13 - January 19 (P3 Complex Numbers & Final Review)
  • Monday: Differential Equations (Chapter 10) - Forming Equations from Problems, Real-World Models (TR: 10.2, PE: Ex 10B, CM: Translating word problems to DEs, Review: Review Ex 10).
  • Tuesday: Complex Numbers (Chapter 11) - Imaginary & Complex Numbers, Complex Plane (TR: 11.1-11.3, PE: Ex 11A, Ex 11B Q1-4, Ex 11C Q1-5, FC: 'i' definition, Argand diagrams, modulus, argument).
  • Wednesday: Complex Numbers (Chapter 11) - Solving Equations, Loci (TR: 11.4-11.5, PE: Ex 11B Q5-10, Ex 11C Q6-10, Ex 11E, CM: Polynomial roots, loci). Review: Review Ex 11.
  • Thursday: Cross-topic Review & Full Syllabus Revision; Cross-topic Review Exercises 3 & 4 (Coursebook Pages 205, 300-302).
  • Friday: Full P3 Mock Exam (Coursebook Page 308); Final Revision of Key Formulae & Definitions.
  • Saturday: Analyze P3 Mock Exam, consolidate difficult concepts.
  • Sunday: Rest / Light revision / Exam day logistics.

Mock Exam Schedule

Mock Exam 1 (P2 Focus)

  • Date: Friday, December 27, 2025
  • Time: 9:00 AM - 10:15 AM (1 hour 15 mins)
  • Content: Pure Mathematics 2 Practice exam-style paper (Coursebook Page 307)
  • Conditions: Strict timing, no notes, approved calculator only.

Mock Exam 2 (P3 Focus)

  • Date: Friday, January 17, 2026
  • Time: 9:00 AM - 10:50 AM (1 hour 50 mins)
  • Content: Pure Mathematics 3 Practice exam-style paper (Coursebook Page 308)
  • Conditions: Strict timing, no notes, approved calculator only.

Key Topics with Practice Questions

Pure Mathematics 2 Topics
Chapter 1: Algebra
Modulus Functions & Inequalities:
  1. Solve |2x - 3| < |x + 1|.
  2. Sketch y = |x^2 - 4|.
Factor and Remainder Theorem:
  1. For P(x) = 2x^3 - 5x^2 + ax + b, (x - 2) is a factor and remainder is -3 when divided by (x + 1). Find a and b.
  2. Show (2x + 1) is a factor of 6x^3 + 11x^2 - x - 2. Factorise completely.
Chapter 2: Logarithmic and Exponential Functions
Laws of Logarithms & Solving Equations:
  1. Solve 3 ln(x - 1) = ln(x^2 + 1) + ln 2.
  2. Solve 2 × 4^x = 5^{x+1} for x (3 s.f.).
Transforming to Linear Form:
  1. y = A b^x. Plotting ln y vs x gives a line through (1, ln 10) and (3, ln 100). Find A and b (2 d.p.).
Chapter 3: Trigonometry
Reciprocal Trigonometric Ratios & Identities:
  1. Prove &frac{\sin x}{1 - \cos x} + &frac{1 - \cos x}{\sin x} ≡ 2 \csc x.
  2. Solve 2 sec² θ + tan θ - 3 = 0 for 0° ≤ θ ≤ 360°.
Compound & Double Angle Formulae, R-form:
  1. Express 4 sin θ - 3 cos θ as R sin(θ - α) (R>0, 0° < α < 90°). Find max value.
  2. Given sin A = 3/5 (A obtuse) and cos B = 12/13 (B acute), find exact tan(A+B).
Chapter 4: Differentiation
Product, Quotient, and Chain Rules:
  1. Differentiate y = x² e³x.
  2. Find &frac;dy}{dx} for y = &frac{\ln x}{x²}.
Implicit and Parametric Differentiation:
  1. Find gradient of x² + xy² - y³ = 7 at (3, 2).
  2. For x = tan t, y = sin 2t, find &frac;dy}{dx} and gradient at t = &frac;π}{4}.
Chapter 5: Integration
Basic Integrals (Exponential, &frac{1}{ax+b}, Trigonometric):
  1. Find ∫ (e²x + &frac{1}{3x-2} + cos 4x) dx.
  2. Evaluate ∫&sup0; &frac;π}{6} sin² x dx.
Trapezium Rule:
  1. Estimate ∫¹³ &frac{1}{ln x} dx with 4 intervals (3 s.f.).
Chapter 6: Numerical Solutions of Equations
Iterative Methods:
  1. Show root of e^x = 4 - x² is between 1 and 1.5.
  2. Use x<sub>n+1</sub> = ln(4 - x<sub>n</sub>²) with x<sub>1</sub> = 1.2 to find root (3 d.p.).
Pure Mathematics 3 Topics
Chapter 7: Further Algebra
Partial Fractions:
  1. Express &frac{x+5}{(x-1)(x+2)²} in partial fractions.
  2. Express &frac{3x²+2x+1}{x²+x} as polynomial + partial fractions.
Binomial Expansion (Rational n):
  1. Find first three terms of &frac{1}{√4-x} (ascending powers of x), state validity range.
  2. Find coefficient of x³ in (1+2x)(1-x)<sup>-2</sup>.
Chapter 8: Further Calculus
Integration by Substitution:
  1. Using u = 1 + ln x, evaluate ∫¹e &frac{ln x}{x} dx.
  2. Using u = sin x, evaluate ∫&sup0;&frac;π}{2} cos³ x dx.
Integration by Parts & Integration of &frac{f'(x)}{f(x)}:
  1. Evaluate ∫ x e<sup>-x</sup> dx.
  2. Find ∫ &frac{2x}{x²+1} dx.
Chapter 9: Vectors
Scalar Product & Vector Equation of a Line:
  1. For &mathbf;a} = &mathbf;i} + 2&mathbf;j} - &mathbf;k} and &mathbf;b} = 3&mathbf;i} - &mathbf;j} + 2&mathbf;k}, find acute angle between &vec;OA} and &vec;OB}.
  2. Line L through (2, 1, -3) parallel to &mathbf;i} - 2&mathbf;j} + 4&mathbf;k}. Find vector equation of L.
Intersection of Lines:
  1. Determine if lines &mathbf;r}<sub>1</sub> = &mathbf;i} + 2&mathbf;j} - &mathbf;k} + λ(2&mathbf;i} - &mathbf;j} + &mathbf;k}) and &mathbf;r}<sub>2</sub> = 3&mathbf;i} + &mathbf;j} + 2&mathbf;k} + μ(&mathbf;i} + 3&mathbf;j} - 2&mathbf;k}) intersect. If so, find intersection point.
Chapter 10: Differential Equations
Separating Variables:
  1. Solve &frac{dy}{dx} = y² sin x given y=1 when x=0.
  2. Find general solution of &frac{dy}{dx} = &frac{x²}{y}, express y in terms of x.
Forming Differential Equations from Problems:
  1. Population P increases proportionally to P. P=100 initially, P=400 after 2 hours. Find P after 3 hours.
  2. Substance cools: &frac;dT}{dt} = -k(T - 20). T=80°C at t=0, T=60°C at t=10 mins. Find time for T to reach 30°C.
Chapter 11: Complex Numbers
Operations with Complex Numbers & Argand Diagram:
  1. Given z<sub>1</sub> = 3 + 2i and z<sub>2</sub> = 1 - 4i, calculate z<sub>1</sub> z<sub>2</sub> and &frac{z<sub>1</sub>}{z<sub>2</sub>} in x+iy form.
  2. Plot z<sub>A</sub> = 2 + 3i, z<sub>B</sub> = -1 + 2i, z<sub>C</sub> = 4 - i on Argand diagram.
Solving Equations & Loci:
  1. Find square roots of 5 + 12i in x+iy form.
  2. Sketch locus of z where |z - (2+i)| = 3.
  3. Find exact solutions to z³ = 8i.

Effective Exam Preparation Strategies

  • Syllabus Mastery: Be fully aware of the Cambridge International syllabus for Pure Mathematics 2 and 3.
  • Active Learning: Engage actively by rewriting notes, explaining concepts, and solving problems step-by-step without immediate reliance on solutions.
  • Consistent Practice: Regularly solve problems to build skill and understanding. Focus on methods over memorization.
  • Targeted Revision: Identify and dedicate extra time to weak areas revealed by practice and mock exams.
  • Time Management: Utilize techniques like the Pomodoro Technique (25 min study, 5 min break). Create a realistic schedule with buffer time. Prioritize high-weightage and challenging topics.
  • Past Paper Analysis:
    • Understand mark schemes to learn how marks are awarded.
    • Recognize common question types and themes.
    • Practice entire papers under timed conditions to improve speed and exam technique.
  • Formulae and Identities:
    • Compile a comprehensive formula sheet for quick reference during revision.
    • Review the sheet daily for memorization.
    • Understand the derivations of formulae.
  • Calculator Proficiency: Be proficient with your scientific calculator, especially for complex numbers, statistics, and equation solving. Use it efficiently in allowed sections.
  • Mindset and Well-being:
    • Maintain hydration and a healthy diet.
    • Take regular breaks and incorporate relaxation techniques.
    • Ensure sufficient sleep (7-9 hours).
    • Practice positive self-talk and believe in your abilities.
    • Seek support from teachers, friends, or family if stress is overwhelming.

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